Eureka Math Geometry Module 2 Lesson 26 Answer Key

Engage NY Eureka Math Geometry Module 2 Lesson 26 Answer Key

Eureka Math Geometry Module 2 Lesson 26 Exercise Answer Key

Eureka Math Geometry 2 Module 2 Lesson 26 Exercise Answer Key 1

Exercise 1.
Identify the \(\frac{\text { opp }}{\text { hyp }}\) ratios for ∠A and ∠B.
Answer:
For ∠A: \(\frac{12}{13}\)
For ∠B: \(\frac{5}{13}\)

Exercise 2.
Identify the \(\frac{\text { adj }}{\text { hyp }}\) ratios for ∠A and ∠B.
Answer:
For ∠A: \(\frac{5}{13}\)
For ∠B: \(\frac{12}{13}\)

Exercise 3.
Describe the relationship between the ratios for ∠A and ∠B.
Answer:
The \(\frac{\text { opp }}{\text { hyp }}\) ratio for ∠A is equal to the \(\frac{\text { adj }}{\text { hyp }}\) ratio for ∠B.
The \(\frac{\text { opp }}{\text { hyp }}\) ratio for ∠B is equal to the \(\frac{\text { adj }}{\text { hyp }}\) ratio for ∠A.

Exercise 4.
In ∆ PQR, m∠P = 53.2° and m∠Q = 36.8°. Complete the following table.
Eureka Math Geometry 2 Module 2 Lesson 26 Exercise Answer Key 2
Eureka Math Geometry 2 Module 2 Lesson 26 Exercise Answer Key 3Eureka Math Geometry 2 Module 2 Lesson 26 Exercise Answer Key 3
Answer:
Eureka Math Geometry 2 Module 2 Lesson 26 Exercise Answer Key 4

Exercise 5.
In the triangle below, m∠A = 33.7° and m∠B = 56.3°. Complete the following table.
Eureka Math Geometry 2 Module 2 Lesson 26 Exercise Answer Key 5
Eureka Math Geometry 2 Module 2 Lesson 26 Exercise Answer Key 6
Answer:
Eureka Math Geometry 2 Module 2 Lesson 26 Exercise Answer Key 7

Exercise 6.
In the triangle below, let e be the measure of ∠E and d be the measure of ∠D. Complete the following table.
Eureka Math Geometry 2 Module 2 Lesson 26 Exercise Answer Key 8
Eureka Math Geometry 2 Module 2 Lesson 26 Exercise Answer Key 9
Answer:
Eureka Math Geometry 2 Module 2 Lesson 26 Exercise Answer Key 10

Exercise 7.
In the triangle below, let x be the measure of ∠X and y be the measure of ∠Y. Complete the following table.
Eureka Math Geometry 2 Module 2 Lesson 26 Exercise Answer Key 11
Eureka Math Geometry 2 Module 2 Lesson 26 Exercise Answer Key 12
Answer:
Eureka Math Geometry 2 Module 2 Lesson 26 Exercise Answer Key 13

Exercise 8.
Tamer did not finish completing the table below for a diagram similar to the previous problems that the teacher had on the board where p was the measure of ∠P and q was the measure of ∠Q. Use any patterns you notice from Exercises 1-4 to complete the table for Tamer.
Eureka Math Geometry 2 Module 2 Lesson 26 Exercise Answer Key 14
Answer:
Eureka Math Geometry 2 Module 2 Lesson 26 Exercise Answer Key 15

Exercise 9.
Explain how you were able to determine the sine, cosine, and tangent of ∠Q in Exercise 8.
Answer:
I was able to complete the table for Tamer by observing the patterns of previous problems. For example, I noticed that the sine of one angle was always equal to the ratio that represented the cosine of the other angle. Since I was given sin p, I knew the ratio \(\frac{11}{\sqrt{157}}\) would be the cos q. Similarly, cos p = sin q = \(\frac{6}{\sqrt{157}}\) Finally, I noticed that the tangents of the angles were always reciprocals of each other. Since i was given the tan p = \(\frac{11}{6}\) knew that the tan q must be equal to \(\frac{6}{11}\).

Eureka Math Geometry Module 2 Lesson 26 Problem Set Answer Key

Question 1.
Given the triangle in the diagram, complete the following table.
Eureka Math Geometry 2 Module 2 Lesson 26 Problem Set Answer Key 16
Eureka Math Geometry 2 Module 2 Lesson 26 Problem Set Answer Key 17
Answer:
Eureka Math Geometry 2 Module 2 Lesson 26 Problem Set Answer Key 18

Question 2.
Given the table of values below (not in simplest radical form), label the sides and angles in the right triangle.
Eureka Math Geometry 2 Module 2 Lesson 26 Problem Set Answer Key 19
Eureka Math Geometry 2 Module 2 Lesson 26 Problem Set Answer Key 20
Answer:
Eureka Math Geometry 2 Module 2 Lesson 26 Problem Set Answer Key 21

Question 3.
Given sin α and sin β, complete the missing values in the table. You may draw a diagram to help you.
Eureka Math Geometry 2 Module 2 Lesson 26 Problem Set Answer Key 22
Answer:
Eureka Math Geometry 2 Module 2 Lesson 26 Problem Set Answer Key 23

Question 4.
Given the triangle shown to the right, fill in the missing values in the table.
Eureka Math Geometry 2 Module 2 Lesson 26 Problem Set Answer Key 24
Eureka Math Geometry 2 Module 2 Lesson 26 Problem Set Answer Key 25
Answer:
Using the Pythagorean theorem:
hyp2 = 22 + 62
hyp2 = 4 + 36
hyp2 = 40
hyp = √40
hyp = 2√10
Eureka Math Geometry 2 Module 2 Lesson 26 Problem Set Answer Key 26

Question 5.
Jules thinks that if α and β are two different acute angle measures, then sin α ≠ sin β. Do you agree or disagree? Explain.
Answer:
I agree. If α and β are different acute angle measures, then either α > β or β > α. A right triangle with acute angle a cannot be similar to a right triangle with acute angle f? (unless α + β = 90) because the triangles fail the AA criterion. If the triangles are not similar, then their corresponding sides are not in proportion, meaning their within-figure ratios are not in proportion; therefore, sin α ≠ sin β. In the case where α + β = 90, the given right triangles are similar; however, a and fi must be alternate acute angles, meaning sin α = cos β, and sin β = cos α, but sin α ≠ sin β.

Question 6.
Given the triangle in the diagram, complete the following table.
Eureka Math Geometry 2 Module 2 Lesson 26 Problem Set Answer Key 27
Eureka Math Geometry 2 Module 2 Lesson 26 Problem Set Answer Key 28
Answer:
Eureka Math Geometry 2 Module 2 Lesson 26 Problem Set Answer Key 29

Rewrite the values from the table in simplest terms.
Eureka Math Geometry 2 Module 2 Lesson 26 Problem Set Answer Key 30
Answer:
Eureka Math Geometry 2 Module 2 Lesson 26 Problem Set Answer Key 31

Draw and label the sides and angles of a right triangle using the values of the ratios sin and cos. How is the new triangle related to the original triangle?
Answer:
The triangles are similar by SSS criterion because the new triangle has sides that are \(\frac{1}{3}\) of the length of their corresponding sides in the original triangle.
Eureka Math Geometry 2 Module 2 Lesson 26 Problem Set Answer Key 32

Question 7.
Given tan α and cos β, in simplest terms, find the missing side lengths of the right triangle if one leg of the triangle has a length of 4. Draw and label the sides and angles of the right triangle.
Eureka Math Geometry 2 Module 2 Lesson 26 Problem Set Answer Key 33
Answer:
Eureka Math Geometry 2 Module 2 Lesson 26 Problem Set Answer Key 34
The problem does not specify which leg is 4, so there are two possible solutions to this problem. The values given in the table do not represent the actual lengths of the sides of the triangles; however, they do represent the lengths of the sides of a similar triangle, which is a 30 – 60 – 90 right triangle with side lengths 1, 2, and √3.

Case 1: The short leg of the right triangle is 4:
Eureka Math Geometry 2 Module 2 Lesson 26 Problem Set Answer Key 35

Case 2: The long leg of the right triangle is 4:
Eureka Math Geometry 2 Module 2 Lesson 26 Problem Set Answer Key 36

Question 8.
Eric wants to hang a rope bridge over a small ravine so that it is easier to cross. To hang the bridge, he needs to know how much rope Is needed to span the distance between two trees that are directly across from each other on either side of the ravine. Help Eric devise a plan using sine, cosine, and tangent to determine the approximate distance from tree A to tree B without having to cross the ravine.
Eureka Math Geometry 2 Module 2 Lesson 26 Problem Set Answer Key 37
Answer:
Student solutions will vary. Possible solution:

If Eric walks a path parallel to the ravine to a point P at a convenient distance from A, he could measure the angle formed by his line of sight to both trees. Using the measured angle and distance, he could use the value of the tangent ratio of the angle to determine the length of the opposite leg of the triangle. The length of the opposite leg of the triangle represents the distance between the two trees.

Question 9.
A fisherman is at point F on the open sea and has three favorite fishing locations. The locations are indicated by points A, B, and C. The fisherman plans to sail from F to A, then toB, then to C, and then back to F. If the fisherman is 14 miles from \(\overline{A C}\), find the total distance that he will sail.
Eureka Math Geometry 2 Module 2 Lesson 26 Problem Set Answer Key 38
Answer:
FP = 14 and can be considered the adjacent side to the 35° angle shown in triangle APF.
Using cosine:
cos 35 = \(\frac{14}{A F}\)
AF = \(\frac{14}{\cos 35}\)
AF ≈ 17.09

Using tangent:
tan 35 = \(\frac{A P}{14}\)
AP = 14 tan 35
AP ≈ 9. 8029
\(\overline{P C}\) is the leg opposite angle PFC in triangle PFC and has a degree measure of 42.5.

Using tangent:
tan 42.5 = \(\frac{P C}{14}\)
PC = 14 tan 42.5
PC ≈ 12.8286

Using cosine:
cos 42.5 = \(\frac{14}{F C}\)
FC = \(\frac{14}{\cos 42.5}\)
FC ≈ 18. 9888

The total distance that the fisherman will sail:
distance = AF + AP + PC + FC
distance = \(\frac{14}{\cos 35}\) +14 tan 35 + 14 tan 42.5 + \(\frac{14}{\cos 42.5}\)
distance ≈ 58.7

The total distance that the fisherman will sail is approximately 58.7 miles.

Eureka Math Geometry Module 2 Lesson 26 Exit Ticket Answer Key

Question 1.
Given the diagram of the triangle, complete the following table.
Eureka Math Geometry 2 Module 2 Lesson 26 Problem Set Answer Key 39
Eureka Math Geometry 2 Module 2 Lesson 26 Problem Set Answer Key 40
Answer:
Eureka Math Geometry 2 Module 2 Lesson 26 Problem Set Answer Key 41

a. Which values are equal?
Answer:
sin s = cos t and cos s = sin t

b. How are tan s and tan t related?
Answer:
They are reciprocals: \(\frac{5}{6} \cdot \frac{6}{5}\) = 1.

Question 2.
If u and y are the measures of complementary angles such that sin u = \(\frac{2}{5}\) and tan v = \(\frac{\sqrt{21}}{2}\) label the sides and angles of the right triangle In the diagram below with possible side lengths:
Eureka Math Geometry 2 Module 2 Lesson 26 Problem Set Answer Key 42
Answer:
A possible solution is shown below; however, any similar triangle having a shorter leg with length of 2x, longer leg with length of x√21, and hypotenuse with length of 5x, for some positive number x, is also correct.
Eureka Math Geometry 2 Module 2 Lesson 26 Problem Set Answer Key 43

3rd Grade Math

Common Core 3rd Grade Math Curriculum, Lessons, Worksheets, Word Problems, Practice Tests

Third Grade Math Lessons provided here are arranged in a way that you can learn Math while playing 3rd Grade Math Games. 3rd Grade Math Topics included covers the concepts such as Four-Digit Numbers, Comparison of Numbers, Geometrical Shapes and Figures, Measurement of Length, Mass, Capacity, Time, and Money, Fractional Numbers, Pictographs, Mental Arithmetic, Patterns, etc.

By Practicing from the Grade 3 Math Worksheets available one can score higher grades in the exams. Get to know the applications of Grade 3 Math Concepts. You can get a good hold of the concepts by simply clicking on the quick links available. Use them as a reference and resolve all your queries and enhance your math skills right from a young age.

3rd Grade Math Topics, Practice Test, Worksheet, Question and Answer Key

We follow a step-wise learning process so that you can understand the concepts better and recognize your mistakes. Keep a track of your learning progress taking the help of the interactive Grade 3 Math Worksheets. You will be accustomed to new concepts, ideas at this stage. Lessons present make it easy for you to absorb the concepts such as time, fractions, geometry, and money in a most efficient way and apply them.

Eureka Math Grade 3 Answer Key

Grade 3 HMH Go Math – Answer Keys

Grade 3 HMH Go Math – Extra Practice Questions and Answers

Big Ideas Math Grade 3 Answers

Formation of Four-Digit Numbers

International and Roman Numerals

Comparison of Numbers

Geometrical Shapes and Figures

Measurement of Length

Measurement of Mass

Measurement of Capacity

Introduction of Indian Money (Rupees and Paise)

Fractional Numbers

Order of Fractions

Data Handling

Mental Arithmetic and Patterns

Advantages of Grade 3 Math Curriculum

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Kindergarten Math

Pre School & Kindergarten Math Curriculum, Worksheets, Activities, Problems, Fun Games

The best way to make young kids love math is to make it exciting for them. Preschool Kindergarten Math Topics designed feature images and quirky Characters. You will have the topics from addition to subtraction, sorting and identifying coins, counting, tracing, coloring, etc. Our Kindergarten Math Topics listed here assist young learners with building fundamental math skills.

Some kids will have a strong grasp of numbers and they are ready to dive right into addition and subtraction. Regardless of your child’s early math concepts, our Kindergarten Math Worksheets provided by subject experts are the perfect supplement to your classroom instruction. In fact, our Kindergarten Math Activities are designed in a way that your kids will love practicing math as a fun activity rather than feeling it difficult.

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There are numerous opportunities to engage your kid and help them learn the Kindergarten Math Concepts without even their knowledge. Through our Kindergarten Math Pages, one can sharpen their early math skills. Simply tap on the quick links available and practice the concepts at your convenience. Kindergarten Math Worksheets make it easy for you to test knowledge on related areas in no time and you can download them for free of cost.

Free Printable Kindergarten Math Worksheets

Practice tracing the numbers from 21 to 30

Practice tracing the numbers from 31 to 40

Practice tracing the numbers from 41 to 50

Practice tracing the numbers from 51 to 60

Practice tracing the numbers from 61 to 70

Practice tracing the numbers from 71 to 80

Practice tracing the numbers from 81 to 90

Practice tracing the numbers from 91 to 100

Missing Number Worksheets

Kindergarten Math Curriculum Goals & Objectives

The goal of the Kindergarten Math Curriculum is to prepare kids for 1st Grade Math.

  • Count Numbers up to 20 and a little beyond.
  • Concept of Equality
  • Count Backwards from 10 to 0.
  • Recognize Numbers and Able to Write Them.
  • Recognize Basic Shapes.
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  • To be able understand the Addition and Subtraction with Smaller Numbers
  • Exposes kids to Two-Digit Numbers.

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There are several advantages of referring to the Pre School Kindergarten Math Topics and we have outlined some of them here. They are as follows

  • Brain Development in Kids is rapid at a young age, and learning from these Kindergarten Math Topics helps them develop inherent problem-solving skills.
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Final Words

We wish the knowledge shared has helped your kids learn math right from an early age. If you have any suggestions or feel any topic is missing do leave us your suggestions so that we can look into them. For more updates on Gradewise Math Worksheets, Practice Problems, Lessons stay tuned to our site.

Preschool Math Activities

Preschool Math Activities for Kids – Lesson Plans, Fun Games, Worksheets, Practice Tests

If you are looking for Preschool Math Activities all in one place then you have come to the right place. We have compiled hands-on math activities that can enhance your math skills. All the Preschool Worksheets are designed in a way that kids can recognize numbers and counting. Find Playful and Engaging Ways to teach math right at your home. We believe the Hands-on Pre-School Math Activities provided will help the kids to inculcate thinking in them at an early age.

Preschool Math Activities, Worksheets, Textbook Questions and Answer Key

Access the Preschool Math Problems on various concepts such as Counting the Numbers from 1 to 20, Identification of Numbers, etc. Simply tap on the quick links available and learn the concepts underlying easily. Our goal is to offer young minds complete lesson plans, develop their ability and skills through various fun learning activities. All the Preschool Activities, Worksheets are designed keeping in mind the student’s pace of understanding.

Practice Traceable Numbers Worksheets for Preschool Kids

Practice tracing the numbers from 1 to 5

Practice tracing the numbers from 6 to 10

Practice tracing the numbers from 11 to 15

Practice tracing the numbers from 16 to 20

Traceable Math Worksheets on Number Names for Kids

Learn to Write Numbers

Identification of Numbers Worksheets

Coloring Sheets

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Go through the advantages of accessing the Preschool Math Topics available here. They are in the following fashion

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Summary

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Eureka Math Grade 2 Module 4 Lesson 6 Answer Key

Eureka Math Answer Key for Grade 2 Chapter 6 meets the content and intent of the School Curriculum. By using the Eureka Math Answers Grade 2 Chapter 6, you can understand the topics easily. so, the students who wish to improve their math skills can go through our Eureka Grade 2 Chapter 6 Answer Key pdf.

Engage NY Eureka Math 2nd Grade Module 4 Lesson 6 Answer Key

People of highly subject expertise prepared the solutions in a concise manner for easy grasping. The ace up your preparation using the Eureka Math Book 2nd Grade Answer Key. By using the Eureka Math Answers Grade 2 Lesson 6, you can understand the concepts in depth and score the highest marks in the exam.

Eureka Math Grade 2 Module 4 Lesson 6 Problem Set Answer Key

Question 1.
Solve using mental math, if you can. Use your place value chart and place value disks to solve those you cannot solve mentally.
a. 6 + 8 = __14___              30 + 8 = __38___             36 + 8 = __44____             36 + 48 = __84____

Answer:
6 + 8 = 14.
30 + 8 = 38.
36 + 8 = 44.
36 + 48 = 84.

Explanation:
In the above-given question,
given that,
solve using mental math.
6 + 8 = 14.
30 + 8 = 38.
36 + 8 = 44.
36 + 48 = 84.

b. 5 + 7 = __12___             20 + 7 = __27___             25 + 7 = __32____             25 + 57 = ___82___

Answer:
5 + 7 = 12.
20 + 7 = 27.
25 + 7 = 32.
25 + 57 = 82.

Explanation:
In the above-given question,
given that,
solve using mental math.
5 + 7 = 12.
20 + 7 = 27.
25 + 7 = 32.
25 + 57 = 82.

Question 2.
Solve the following problems using your place value chart and place value disks. Compose a ten, if needed. Think about which ones you can solve mentally, too!
a. 35 + 5 = __40___             35 + 6 = ___41___

Answer:
35 + 5 = 40.
35 + 6 = 41.

Explanation:
In the above-given question,
given that,
solve using mental math.
35 + 5 = 40.
35 + 6 = 41.

b. 26 + 4 = __30___             26 + 5 = _31_____

Answer:
26 + 4 = 30.
26 + 5 = 31.

Explanation:
In the above-given question,
given that,
solve using mental math.
26 + 4 = 30.
26 + 5 = 31.

c. 54 + 15 = _69____             54 + 18 = __72___

Answer:
54 + 15 = 69.
54 + 18 = 72.

Explanation:
In the above-given question,
given that,
solve using mental math.
54 + 15 = 69.
54 + 18 = 72.

d. 67 + 23 = __90___             67 + 25 = ___92__

Answer:
67 + 23 = 90.
67 + 25 = 92.

Explanation:
In the above-given question,
given that,
solve using mental math.
67 + 23 = 90.
67 + 25 = 92.

e. 45 + 26 = ___71__             45 + 23 = __68___

Answer:
45 + 26 = 71.
45 + 23 = 68.

Explanation:
In the above-given question,
given that,
solve using mental math.
45 + 26 = 71.
45 + 23 = 68.

f. 58 + 23 = __81___             58 + 25 = __83___

Answer:
58 + 23 = 81.
58 + 25 = 83.

Explanation:
In the above-given question,
given that,
solve using mental math.
58 + 23 = 81.
58 + 25 = 83.

g. 49 + 37 = __86___             52 + 36 = __78___

Answer:
49 + 37 = 86.
52 + 36 = 78.

Explanation:
In the above-given question,
given that,
solve using mental math.
49 + 37 = 86.
52 + 36 = 78.

Question 3.
There are 47 blue buttons and 25 black buttons in Sean’s drawer. How many buttons are in his drawer?

Answer:
The number of buttons are in his drawer = 72 buttons.

Explanation:
In the above-given question,
given that,
There are 47 blue buttons and 25 black buttons in Sean’s drawer.
47 + 25 = 72.
so the number of buttons are in his drawer = 72.

For early finishers:

Question 4.
Leslie has 24 blue and 24 pink hair ribbons. She buys 17 more blue ribbons and 13 more pink ribbons from the store.
a. How many blue hair ribbons does she have now?

Answer:
The number of blue hair ribbons does she have now = 41.

Explanation:
In the above-given question,
given that,
Leslie has 24 blue and 24 pink hair ribbons.
She buys 17 more blue ribbons and 13 more pink ribbons from the store.
24 + 17 = 41.
so the number of blue hair ribbons does she have now = 41.

b. How many pink hair ribbons does she have now?

Answer:

The number of pink hair ribbons does she has now = 37.

Explanation:
In the above-given question,
given that,
Leslie has 24 blue and 24 pink hair ribbons.
She buys 17 more blue ribbons and 13 more pink ribbons from the store.
24 + 13 = 37.
so the number of pink hair ribbons does she have now = 37.

c. Jada has 29 more pink ribbons than Leslie. How many pink ribbons does Jada have?

Answer:
The number of pink ribbons does Jada have = 66.

Explanation:
In the above-given question,
given that,
Jada has 29 more pink ribbons than Leslie.
37 + 29 = 66.
so the number of pink ribbons does Jada have = 66.

Eureka Math Grade 2 Module 4 Lesson 6 Exit Ticket Answer Key

Solve using your place value chart and place value disks. Compose a ten, if needed. Think about which ones you can solve mentally, too!

Question 1.
53 + 19 = ____72.___

Answer:
53 + 19 = 72.

Explanation:
In the above-given question,
given that,
solve using mental math.
53 + 19 = 72.

Question 2.
44 + 27 = _____71__

Answer:
44 + 27 = 71.

Explanation:
In the above-given question,
given that,
solve using mental math.
44 + 27 = 71.

Question 3.
64 + 28 = __92_____

Answer:
64 + 28 = 92.

Explanation:
In the above-given question,
given that,
solve using mental math.
64 + 28 = 92.

Eureka Math Grade 2 Module 4 Lesson 6 Homework Answer Key

Question 1.
Solve using mental math, if you can. Use your place value chart and place value disks to solve those you cannot do mentally.
a. 4 + 9 = _13____             30 + 9 = __39___             34 + 9 = __43____             34 + 49 = ___83___

Answer:
4 + 9 = 13.
30 + 9 = 39.
34 + 9 = 43.
34 + 49 = 83.

Explanation:
In the above-given question,
given that,
solve using mental math.
4 + 9 = 13.
30 + 9 = 39.
34 + 9 = 43.
34 + 49 = 83.

b. 6 + 8 = __14___             20 + 8 = __28___             26 + 8 = ___34___             26 + 58 = __84____

Answer:
6 + 8 = 14.
20 + 8 = 28.
26 + 8 = 34.
26 + 58 = 84.

Explanation:
In the above-given question,
given that,
solve using mental math.
6 + 8 = 14.
20 + 8 = 28.
26 + 8 = 34.
26 + 58 = 84.

Question 2.
Solve the following problems using your place value chart and place value disks. Compose a ten, if needed. Think about which ones you can solve mentally, tool
a. 21 + 9 = __30___             22 + 9 = __31____

Answer:
21 + 9 = 30.
22 + 9 = 31.

Explanation:
In the above-given question,
given that,
solve using mental math.
21 + 9 = 30.
22 + 9 = 31.

b. 28 + 2 = __30___             28 + 4 = __32____

Answer:
28 + 2 = 30.
28 + 4 = 32.

Explanation:
In the above-given question,
given that,
solve using mental math.
28 + 2 = 30.
28 + 4 = 32.

c. 32 + 16 = __48___             34 + 17 = __51___

Answer:
32 + 16 = 48.
34 + 17 = 51.

Explanation:
In the above-given question,
given that,
solve using mental math.
32 + 16 = 48.
34 + 17 = 51.

d. 47 + 23 = _70____             47 + 25 = __72___

Answer:
47 + 23 = 70.
47 + 25 = 72.

Explanation:
In the above-given question,
given that,
solve using mental math.
47 + 23 = 70.
47 + 25 = 72.

e. 53 + 35 = _88____             58 + 35 = __93___

Answer:
53 + 35 = 88.
58 + 35 = 93.

Explanation:
In the above-given question,
given that,
solve using mental math.
53 + 35 = 88.
58 + 35 = 93.

f. 58 + 42 = __100___             58 + 45 = ___103__

Answer:
58 + 42 = 100.
58 + 45 = 103.

Explanation:
In the above-given question,
given that,
solve using mental math.
58 + 42 = 100.
58 + 45 = 103.

g. 69 + 32 = __101___             36 + 62 = _98____

Answer:
69 + 32 = 101.
36 + 62 = 98.

Explanation:
In the above-given question,
given that,
solve using mental math.
69 + 32 = 101.
36 + 62 = 98.

h. 77 + 13 = _90____             16 + 77 = ___93__

Answer:
77 + 13 = 90.
16 + 77 = 93.

Explanation:
In the above-given question,
given that,
solve using mental math.
77 + 13 = 90.
16 + 77 = 93.

i. 59 + 34 = ___93___             31 + 58 = _89____

Answer:
59 + 34 = 93.
31 + 58 = 89.

Explanation:
In the above-given question,
given that,
solve using mental math.
59 + 34 = 93.
31 + 58 = 89.

Solve using a place value chart.

Question 3.
Melissa has 36 more crayons than her brother. Her brother has 49 crayons. How many crayons does Melissa have?

Answer:
The number of crayons does Melissa have = 85.

Explanation:
In the above-given question,
given that,
Melissa has 36 more crayons than her brother.
Her brother has 49 crayons.
49 + 36 = 85.
so the number of crayons does Melissa have = 85.

Question 4.
There were 67 candles on Grandma’s birthday cake and 26 left in the box. How many candles were there in all?

Answer:
The number of candles was there in all =

Explanation:
In the above-given question,
given that,
There were 67 candles on Grandma’s birthday cake and 26 left in the box.
67 + 26 = 93.
so the number of candles was there in all = 93.

Question 5.
Frank’s mother gave him $25 to save. If he already had $38 saved, how much money does Frank have saved now?

Answer:
The money does Frank have saved now = $63.

Explanation:
In the above-given question,
given that,
Frank’s mother gave him $25 to save.
If he already had $38 saved.
25 + 38 = 63.
so the money does Frank have saved now = $63.

7th Grade Math

7th Grade Math Practice, Topics, Test, Problems, and Worksheets

In 7th Grade Math Practice, you will find all Kinds of Topics explained in a clear-cut way. Keeping in mind the Child’s Level of Understanding in Grade 7 we have outlined all the concepts in a simple language so that they understand them easily. Improve your knowledge by practicing the 7th Grade Topics regularly and understand the application of concepts.

We have compiled Practice Tests, Worksheets for the 7th Standard Math Concepts so that you can test your preparation levels. Identify the areas you are not comfortable with and allot time to them so that you can attempt them with confidence in the actual exam. After practicing from these 7th Grade Math Problems you will interpret and compute different types of topics and their problems easily.

Go Math Grade 7 Answer Key Free PDF Download

Students who wish to prepare the 7th Grade Math Concepts can check out the Chapterwise Go Math Grade 7 Answer Key available below. You just need to click on the quick links to access the concerned chapter of Go Math 7th Grade Solution Key. Clarify all your concerns easily by practicing the Step by Step Go Math Grade 7 Solutions on a daily basis.

HMH Go Math 7th Grade Answer Key

Big Ideas Math Book 7th Grade Answer Key

Utilize the Big Ideas Math Book Grade 7 Answer Key for all the Chapters whenever you need Homework Help. The BIM Grade 7 Answer Key available ensures you achieve your learning targets and achieve success in your exams. To make your searching experience simple we have outlined all the Big Ideas Math Grade 7 Answer Key organized as per the Big Ideas Math 7th Grade Textbooks. Simply click on the respective chapter you wanted to prepare and learn all the underlying topics in it easily.

Big Ideas Math Book 7th Grade Advanced Answer Key

Big Ideas Math Book 7th Grade Advanced Answer Key available here covers all the concepts as per the latest syllabus guidelines. Develop a Conceptual Understanding of Grade 7 Math and improve your ability to apply mathematics to solve problems. To make it easy for you we have compiled all the Chapterwise 7th Standard Math Answer Key in a simple and understandable language. You just have to click on the concerned chapter you wish to prepare and allot time accordingly.

7th Grade Math Topics

On this page, you will learn all the Topics that a Grade 7 Student should learn. We have covered all the topics that a middle school student should learn as a part of the curriculum. You will find Chapters such as Integers, Fractions, Decimals, etc. Tap on the concerned chapter you wish to learn the concepts in it accordingly. You just need to tap on the direct links available and avail the topics easily.

Set Theory

Relations and Mapping

Relations and Mapping – Worksheets

Integers

Numbers – Worksheets

Fractions

Fractions – Worksheets

Decimals

BODMAS/PEMDAS Rule

Profit, Loss, and Discount

Profit, Loss and Discount – Worksheets

Ratios and Proportions

Ratios and Proportions – Worksheets

Time and Work

Time and Work – Worksheets

Unitary Method

  • Problems Using Unitary Method
  • Situations of Direct Variation
  • Situations of Inverse Variation
  • Direct Variations Using Unitary Method
  • Direct Variations Using Method of Proportion
  • Inverse Variation Using Unitary Method
  • Inverse Variation Using Method of Proportion
  • Problems on Unitary Method using Direct Variation
  • Problems on Unitary Method Using Inverse Variation
  • Mixed Problems Using Unitary Method

Unitary Method – Worksheets

  • Worksheet on Direct Variation using Unitary Method
  • Worksheet on Direct variation using Method of Proportion
  • Worksheet on Word Problems on Unitary Method
  • Worksheet on Inverse Variation Using Unitary Method
  • Worksheet on Inverse Variation Using Method of Proportion

Simple Interest

  • What is Simple Interest?
  • Calculate Simple Interest
  • Practice Test on Simple Interest

Simple Interest – Worksheets

  • Simple Interest Worksheet

Algebraic Expressions

  • Division of Polynomial by Monomial

Algebraic Expressions – Worksheets

  • Worksheet on Dividing Polynomial by Monomial

Formula

  • Formula and Framing the Formula
  • Change the Subject of a Formula
  • Changing the Subject in an Equation or Formula
  • Practice Test on Framing the Formula

Formula – Worksheets

  • Worksheet on Framing the Formula
  • Worksheet on Changing the Subject of a Formula
  • Worksheet on Changing the Subject in an Equation or Formula

Algebraic Identities

  • Square of The Sum of Two Binomials
  • Square of The Difference of Two Binomials
  • Product of Sum and Difference of Two Binomials
  • Product of Two Binomials whose First Terms are Same and Second Terms are Different
  • Square of a Trinomial
  • Cube of The Sum of Two Binomials
  • Cube of The Difference of Two Binomials
  • Cube of a Binomial
  • Square of a Binomial

Equations

Equations – Worksheets

  • Worksheet on Linear Equations
  • Worksheet on Word Problems on Linear Equation

Inequations

Inequations – Worksheets

  • Worksheet on Linear Inequations

    Geometry

Lines and Angles

Congruence

  • Congruent Shapes
  • Congruent Line-segments
  • Congruent Angles
  • Congruent Triangles
  • Conditions for the Congruence of Triangles
  • Side Side Side Congruence
  • Side Angle Side Congruence
  • Angle Side Angle Congruence
  • Angle Angle Side Congruence
  • Right Angle Hypotenuse Side congruence
  • Pythagorean Theorem
  • Proof of Pythagorean Theorem
  • Converse of Pythagorean Theorem
  • Word problems on Pythagorean Theorem

Polygons

  • Polygon and its Classification
  • Terms Related to Polygons
  • Interior and Exterior of the Polygon
  • Convex and Concave Polygons
  • Regular and Irregular Polygon
  • Number of Triangles Contained in a Polygon
  • Angle Sum Property of a Polygon
  • Problems on Angle Sum Property of a Polygon
  • Sum of the Interior Angles of a Polygon
  • Sum of the Exterior Angles of a Polygon

Polygons – Worksheets

  • Worksheet on Polygon and its Classification
  • Worksheet on Interior Angles of a Polygon
  • Worksheet on Exterior Angles of a Polygon

Quadrilateral

Symmetrical Figure

Coordinate System

  • Coordinate Graph
  • Ordered Pair of a Coordinate System
  • Plot Ordered Pairs
  • Coordinates of a Point
  • All Four Quadrants
  • Signs of Coordinates
  • Find the Coordinates of a Point
  • Coordinates of a Point in a Plane
  • Plot Points on Coordinate Graph
  • Graph of Linear Equation
  • Simultaneous Equations Graphically
  • Graphs of Simple Function
  • Graph of Perimeter vs. Length of the Side of a Square
  • Graph of Area vs. Side of a Square
  • Graph of Simple Interest vs. Number of Years
  • Graph of Distance vs. Time

Mensuration

Mensuration – Worksheets

  • Worksheet on Area and Perimeter of Rectangles
  • Worksheet on Area and Perimeter of Squares
  • Worksheet on Area of the Path
  • Worksheet on Circumference and Area of Circle
  • Worksheet on Area and Perimeter of Triangle

Volume and Surface Area of Solids

Statistics

Grade 7 Math Goals and Objectives

Comprehensive 7th Grade Math Curriculum will concentrate on the below areas and ensure students are achieving these learning targets. They are as under

  • Understand Rational Number Operations
  • Representation of Rational Numbers with Decimals
  • Analyze Proportional Relationships to solve mathematical problems in the real world.
  • Construct and describe geometrical figures and the relationships between them.
  • Solve Problems involving Angle Measure, Area, and Volume.
  • Extend the use of 4 basic arithmetic operations on whole numbers, mixed numbers, decimals, and fractions.
  • Analyze and Interpret Data presented in various forms.
  • Solve Mathematical Problems involving numerical and algebraic expressions, equations and inequalities, etc.

Why Choose our 7th Grade Math Curriculum?

Master the concepts of Grade 7 Math and study advanced mathematics in a fun learning way. They are as follows

  • 7th Grade Math Practice helps you to achieve learning targets and master the concepts easily.
  • Our Preparation Material keeps students engaged irrespective of their learning method.
  • You can access the 7th Grade Math Topics 24/7 from anywhere for free of cost.
  • 7th Grade Math Worksheets and Practice Tests available make it easy for you to learn challenging concepts too even after school.
  • Learning Exercises and Simulated Assessments provide 7th Grade Standardized Test Practice.

We wish the knowledge shed regarding the 7th Grade Math Topics has enlightened you. If you have any suggestions do leave us your feedback so that we can look into them and add if necessary. Keep in touch with our site to avail latest updates on Gradewise Math Topics in no time.

8th Grade Math

8th Grade Math Practice, Topics, Test, Problems, and Worksheets

Do you have a test coming up and scared about what to prepare for in 8th Grade Math? Don’t Fret as we have included the bunch of topics that you might come across in Grade 8 Maths all in one place. We know the Concepts learned in Grade 8 go a long way in higher grades concepts. Grade 8 Children are advised to practice these concepts regularly and get a good hold of them. Higher-Order Concepts such as Rational Numbers, Irrational Numbers, Exponents, etc. are all introduced in the 8th Standard.

8th Grade Math Topics covered here help you to tackle any kind of Math Problem easily. Grasp the Formulas and Techniques needed for learning 8th Standard Math Concepts in no time. Improve your mathematical abilities by practicing from our 8th Grade Math Problems provided.

Go Math Grade 8 Answer Key

Check out Chapterwise Go Math 8th Grade Answer Key available here during your practice sessions. Make the most out of them and score better grades in your exams. You can access whichever chapter you feel like preparing by tapping on the quick links listed below. Once you click on them you will be redirected to the concerned chapter in no time.

Grade 8 HMH Go Math – Answer Keys

Big Ideas Math Answers Grade 8

Access our Big Ideas Math 8th Grade Answers listed below to resolve all your queries on the Chapters involved. Don’t worry about the accuracy of the Big Ideas Math Grade 8 Solutions as they are given after extensive research. Start Practicing the Chapterwise BIM 8th Grade Answers and no longer feel the concepts of Big Ideas Math Grade 8th difficult.

8th Grade Math Topics

Teaching Grade 8 Math Topics effectively will help your kids to advance their math reasoning and logical ability. Confidence and ability to learn will be improved by referring to the 8th Standard Math Topics available. Thus, they will be prepared for high school studies. If you want to learn more about the 8th Grade Math Concepts have an insight into the below topics and get an idea of what is included in the 8th Grade Curriculum.

All you have to do is simply tap on the quick links available to avail the respective topics and get a grip on them. We included both the theoretical part as well as worksheets for your practice. Our 8th Grade Math Worksheets make it easy for you to test your preparation standard on the corresponding topics. Identify the knowledge gap and improvise on the topics you are facing difficulty with.

Ratio and Proportion

Ratio and Proportion – Worksheets

  • Worksheet on Ratio and Proportion

Significant Figures

Significant Figures – Worksheets

  • Worksheet on Significant Figures

Square

Square – Worksheets

  • Worksheet on Squares

Square Root

Square Root- Worksheets

  • Worksheet on Square Root using Prime Factorization Method
  • Worksheet on Square Root using Long Division Method
  • Worksheet on Square Root of Numbers in Decimal and Fraction Form

Algebraic Expression

  • Algebraic Expression
  • Addition of Algebraic Expressions
  • Subtraction of Algebraic Expressions
  • Multiplication of Algebraic Expression
  • Division of Algebraic Expressions

Formula

Formula – Worksheets

  • Worksheet on Framing the Formula
  • Worksheet on Changing the Subject of a Formula
  • Worksheet on Changing the Subject in an Equation or Formula

Factorization

Factorization – Worksheet

  • Worksheet on Factoring Algebraic Expression
  • Worksheet on Factoring Binomials
  • Worksheet on Factoring by Grouping
  • Worksheet on Factorization by Regrouping
  • Worksheet on Factoring out a Common Binomial Factor
  • Worksheet on Factoring Identities
  • Worksheet on Factoring the Differences of Two Squares
  • Worksheet on Factorization using Formula
  • Worksheet on Factoring Trinomials
  • Worksheet on Factoring Simple Quadratics
  • Worksheet on Factoring Quadratic Trinomials
  • Worksheet on Factoring Trinomials by Substitution
  • Worksheet on Factorization

Equations

Equations – Worksheets

  • Worksheet on Linear Equations
  • Worksheet on Word Problems on Linear Equation

Simultaneous Linear Equations

Simultaneous Linear Equations – Worksheets

  • Worksheet on Simultaneous Linear Equations
  • Worksheet on Problems on Simultaneous Linear Equations

Linear Inequations

Linear Inequations – Worksheets

  • Worksheet on Linear Inequations

Quadratic Equations

Quadratic Equations – Worksheets

  • Worksheet on Quadratic Equations

Percentage

  • Fraction into Percentage
  • Percentage into Fraction
  • Percentage into Ratio
  • Ratio into Percentage
  • Percentage into Decimal
  • Decimal into Percentage
  • Percentage of the given Quantity
  • How much Percentage One Quantity is of Another?
  • Percentage of a Number
  • Increase Percentage
  • Decrease Percentage
  • Basic Problems on Percentage
  • Solved Examples on Percentage
  • Problems on Percentage
  • Real-Life Problems on Percentage
  • Word Problems on Percentage
  • Application of Percentage

Percentage – Worksheets

  • Worksheet on Fraction into Percentage
  • Worksheet on Percentage into Fraction
  • Worksheet on Percentage into Ratio
  • Worksheet on Ratio into Percentage
  • Worksheet on Percentage into Decimal
  • Worksheet on Percentage of a Number
  • Worksheet on Finding Percent
  • Worksheet on Finding Value of a Percentage
  • Worksheet on Percentage of a Given Quantity
  • Worksheet on Word Problems on Percentage
  • Worksheet on Increase Percentage
  • Worksheet on Decrease Percentage
  • Worksheet on increase and Decrease Percentage
  • Worksheet on Expressing Percent
  • Worksheet on Percent Problems
  • Worksheet on Finding Percentage

Profit, Loss, and Discount

Profit, Loss, and Discount – Worksheets

  • Worksheet to Find Profit and Loss
  • Worksheets on Profit and Loss Percentage
  • Worksheet on Gain and Loss Percentage
  • Worksheet on Discounts

Time and Work

  • Time and Work
  • Pipes and Cistern
  • Practice Test on Time and Work

Time and Work – Worksheets

  • Worksheet on Time and Work

Time and Distance

Time and Distance – Worksheets

  • Worksheet on Conversion of Units of Speed
  • Worksheet on Calculating Time
  • Worksheet on Calculating Speed
  • Worksheet on Calculating Distance
  • Worksheet on Train Passes through a Pole
  • Worksheet on Train Passes through a Bridge
  • Worksheet on Relative Speed
  • Worksheet on Decimal into Percentage

Simple Interest

  • What is Simple Interest?
  • Calculate Simple Interest
  • Practice Test on Simple Interest

Simple Interest – Worksheets

  • Simple Interest Worksheet

Compound Interest

  • Compound Interest
  • Compound Interest with Growing Principal
  • Compound Interest with Periodic Deductions
  • Compound Interest by Using Formula
  • Compound Interest when Interest is Compounded Yearly
  • Compound Interest when Interest is Compounded Half-Yearly
  • Compound Interest when Interest is Compounded Quarterly
  • Problems on Compound Interest
  • Variable Rate of Compound Interest
  • Difference of Compound Interest and Simple Interest
  • Practice Test on Compound Interest
  • Uniform Rate of Growth
  • Uniform Rate of Depreciation
  • Uniform Rate of Growth and Depreciation

Compound Interest – Worksheet

  • Worksheet on Compound Interest
  • Worksheet on Compound Interest when Interest is Compounded Half-Yearly
  • Worksheet on Compound Interest with Growing Principal
  • Worksheet on Compound Interest with Periodic Deductions
  • Worksheet on Variable Rate of Compound Interest
  • Worksheet on Difference of Compound Interest and Simple Interest
  • Worksheet on Uniform Rate of Growth
  • Worksheet on Uniform Rate of Depreciation
  • Worksheet on Uniform Rate of Growth and Depreciation

Ratio and Proportion (Direct & Inverse Variation)

  • Direct Variation
  • Inverse Variation
  • Practice Test on Direct Variation and Inverse Variation

Ratio and Proportion – Worksheets

  • Worksheet on Direct Variation
  • Worksheet on Inverse Variation

Probability

  • Probability

Probability – Worksheets

  • Worksheet on Probability

Geometry

Lines and Angles

Parallelogram

Parallelogram – Worksheet

  • Worksheet on Parallelogram

Quadrilateral

Quadrilateral – Worksheets

  • Quadrilateral Worksheet
  • Worksheet on Construction on Quadrilateral
  • Worksheet on Different Types of Quadrilaterals

Three-Dimensional Figures

Three-Dimensional Figures – Worksheets

  • Worksheet on Three Dimensional Figures

Mensuration

Mensuration – Worksheets

  • Worksheet on Area and Perimeter of Rectangles
  • Worksheet on Area and Perimeter of Squares
  • Worksheet on Area of the Path
  • Worksheet on Circumference and Area of Circle
  • Worksheet on Area and Perimeter of Triangle

Volume and Surface Area of Solids

Area of a Trapezium

Area of a Trapezium – Worksheet

  • Worksheet on Trapezium
  • Worksheet on Area of a Polygon

Area Proposition

Area Proposition – Worksheets

  • Worksheet on Same Base and Same Parallels

Data Handling

  • Data Handling
  • Frequency Distribution
  • Grouping of Data

Data Handling – Worksheet

  • Worksheet on Data Handling

Constructing and Interpreting Bar Graphs or Column Graphs

  • Bar Graph or Column Graph

Bar Graphs or Column Graphs – Worksheets

  • Worksheet on Bar Graphs or Column Graphs

Pie Charts or Pie Graphs

  • Pie Chart

Pie Charts or Pie Graphs – Worksheets

  • Worksheet on Pie Chart

Coordinate Geometry

  • Coordinate Graph
  • Ordered pair of a Coordinate System
  • Plot Ordered Pairs
  • Coordinates of a Point
  • All Four Quadrants
  • Signs of Coordinates
  • Find the Coordinates of a Point
  • Coordinates of a Point in a Plane
  • Plot Points on Co-ordinate Graph
  • Graph of Linear Equation
  • Simultaneous Equations Graphically
  • Graphs of Simple Function
  • Graph of Perimeter vs. Length of the Side of a Square
  • Graph of Area vs. Side of a Square
  • Graph of Simple Interest vs. Number of Years
  • Graph of Distance vs. Time

Coordinate Geometry – Worksheet

  • Worksheet on Coordinate Graph

Set Theory

  • Sets Theory
  • Representation of a Set
  • Types of Sets
  • Finite Sets and Infinite Sets
  • Power Set
  • Problems on Union of Sets
  • Problems on Intersection of Sets
  • Difference of two Sets
  • Complement of a Set
  • Problems on Complement of a Set
  • Problems on Operation on Sets
  • Word Problems on Sets
  • Venn Diagrams in Different Situations
  • Relationship in Sets using Venn Diagram
  • Union of Sets using Venn Diagram
  • Intersection of Sets using Venn Diagram
  • Disjoint of Sets using Venn Diagram
  • Difference of Sets using Venn Diagram
  • Examples on Venn Diagram

Relations and Mapping

  • Ordered Pair
  • Cartesian Product of Two Sets
  • Relation
  • Domain and Range of a Relation
  • Practice Test on Math Relation
  • Functions or Mapping
  • Domain Co-domain and Range of Function
  • Math Practice Test on Function

Relations and Mapping – Worksheets

Cube and Cube Roots

  • Cube
  • To Find if the Given Number is a Perfect Cube
  • Cube Root
  • Method for Finding the Cube of a Two-Digit Number
  • Table of Cube Roots

Cube and Cube Roots – Worksheets

  • Worksheet on Cube
  • Worksheet on Cube and Cube Root
  • Worksheet on Cube Root

Rational Numbers

  • Introduction of Rational Numbers
  • What are Rational Numbers?
  • Is Every Rational Number a Natural Number?
  • Is Zero a Rational Number?
  • Is Every Rational Number an Integer?
  • Is Every Rational Number a Fraction?
  • Positive Rational Number
  • Negative Rational Number
  • Equivalent Rational Numbers
  • Equivalent form of Rational Numbers
  • Rational Number in Different Forms
  • Properties of Rational Numbers
  • Lowest form of a Rational Number
  • Standard form of a Rational Number
  • Equality of Rational Numbers using Standard Form
  • Equality of Rational Numbers with Common Denominator
  • Equality of Rational Numbers using Cross Multiplication
  • Comparison of Rational Numbers
  • Rational Numbers in Ascending Order
  • Rational Numbers in Descending Order
  • Representation of Rational Numbers on the Number Line
  • Rational Numbers on the Number Line
  • Addition of Rational Number with Same Denominator
  • Addition of Rational Number with Different Denominator
  • Addition of Rational Numbers
  • Properties of Addition of Rational Numbers
  • Subtraction of Rational Number with Same Denominator
  • Subtraction of Rational Number with Different Denominator
  • Subtraction of Rational Numbers
  • Properties of Subtraction of Rational Numbers
  • Rational Expressions Involving Addition and Subtraction
  • Simplify Rational Expressions Involving the Sum or Difference
  • Multiplication of Rational Numbers
  • Product of Rational Numbers
  • Properties of Multiplication of Rational Numbers
  • Rational Expressions Involving Addition, Subtraction, and Multiplication
  • Reciprocal of a Rational  Number
  • Division of Rational Numbers
  • Rational Expressions Involving Division
  • Properties of Division of Rational Numbers
  • Rational Numbers between Two Rational Numbers
  • To Find Rational Numbers

Rational Numbers – Worksheets

  • Worksheet on Rational Numbers
  • Worksheet on Equivalent Rational Numbers
  • Worksheet on Lowest form of a Rational Number
  • Worksheet on Standard form of a Rational Number
  • Worksheet on Equality of Rational Numbers
  • Worksheet on Comparison of Rational Numbers
  • Worksheet on Representation of Rational Number on a Number Line
  • Worksheet on Adding Rational Numbers
  • Worksheet on Properties of Addition of Rational Numbers
  • Worksheet on Subtracting Rational Numbers
  • Worksheet on Addition and Subtraction of Rational Number
  • Worksheet on Rational Expressions Involving Sum and Difference
  • Worksheet on Multiplication of Rational Number
  • Worksheet on Properties of Multiplication of Rational Numbers
  • Worksheet on Division of Rational Numbers
  • Worksheet on Properties of Division of Rational Numbers
  • Worksheet on Finding Rational Numbers between Two Rational Numbers
  • Worksheet on Word Problems on Rational Numbers
  • Worksheet on Operations on Rational Expressions
  • Objective Questions on Rational Numbers

Fun with Numbers

  • Playing with Numbers
  • Test of Divisibility
  • Number Puzzles and Games

Fun with Numbers – Worksheets

  • Worksheet on Number Puzzles and Games

Exponents

  • Exponents
  • Laws of Exponents
  • Rational Exponent
  • Integral Exponents of a Rational Numbers
  • Solved Examples on Exponents
  • Practice Test on Exponents

Exponents – Worksheets

  • Worksheet on Exponents

Simplification  of Algebraic Fractions

  • Algebraic Fractions
  • Arithmetic Fraction and Algebraic Fraction
  • Highest Common Factor of Monomials
  • Highest Common Factor of Monomials by Factorization
  • Lowest Common Multiple of Monomials
  • Lowest Common Multiple of Monomials by Factorization
  • Highest Common Factor of Polynomials
  • Lowest Common Multiple of Polynomials
  • H.C.F. of Polynomials by Factorization
  • Highest Common Factor of Polynomials by Factorization
  • L.C.M. of Polynomials by Factorization
  • Lowest common multiple of Polynomials by Factorization
  • H.C.F. of Polynomials by Division Method
  • H.C.F. of Polynomials by Long Division Method
  • Relation Between H.C.F. and L.C.M. of Two Polynomials
  • Reduce Algebraic Fractions to its Lowest Term
  • Simplification of Algebraic Fractions
  • Rule of Separation of Division
  • Sum and Difference of Algebraic Fractions
  • Problems on Algebraic Fractions
  • Solving Algebraic Fractions
  • Multiplication of Algebraic Fractions
  • Division of Algebraic Fractions

Simplification  of Algebraic Fractions – Worksheets

  • Worksheet on H.C.F. of Monomials
  • Worksheet on L.C.M. of Monomials
  • Worksheet on H.C.F. and L.C.M. of Monomials
  • Worksheet on H.C.F. of Polynomials
  • Worksheet on L.C.M. of Polynomials
  • Worksheet on H.C.F. and L.C.M. of Polynomials
  • Worksheet on Reducing Algebraic Fractions
  • Worksheet on Algebraic Expressions to the Lowest Terms
  • Worksheet on Algebraic Fractions
  • Worksheet on Simplifying Algebraic Fractions

Objectives of 8th Grade Math

Below is the general list of math objectives that 8th Grade Students should attain

  • Identify Rational and Irrational Numbers
  • Calculate and Approximate Principal Square Roots
  • Solve Linear Inequalities in Two Variables.
  • Differentiate between Types of Sampling Techniques.
  • Determine Mean, Median, Mode, and Range of a Set of Real World Data.

Why Choose our 8th Grade Math Curriculum?

Choose the interactive program and help your child master the concepts of Grade 8 Math.

  • Activities aimed helps students to meet their math objectives easily and make the entire learning process stressful.
  • You can access the lessons 24/7 so that you can prepare during your peak learning time be it day or night.
  • Aside from the interactive lessons, we have included printable worksheets to provide you with tons of extra practice.
  • Build additional math skills and achieve your math learning targets without struggling.
  • Student paced learning encourages and keeps you be focused and motivated.
  • Free Online Learning Environment deepens your conceptual knowledge.

Hope the information shared regarding the 8th Grade Math has helped you a lot. If you have any suggestions on concepts to be added to the list feel free to reach us and we will get back to you at the earliest. Bookmark our site to avail Gradewise Math Topics to cater to your math learning needs.

6th Grade Math

6th Grade Math Practice Topics, Test, Problems with Answers, Worksheets

In Grade 6 a lot of topics are covered from Grade 5 but with more depth. Applied Math Concepts like percentages, profit and loss, ratio, and proportions are introduced in 6th Grade. You will get acquainted with concepts of linear equations and algebraic expressions. Worry not, we are here to assist you with the concepts and help you to ace the curriculum without any difficulty.

Students encounter problems on the road to math Proficiency. This is especially true in Grade 6 when complicated theories and models are introduced from all directions. Our experts can make a difference in your learning and help your child overcome the fear of Math.

6th Grade Math Solutions and Topics

We have compiled the Grade 6 Math Practice Problems covering the entire curriculum. All you have to do is simply tap on the 6th Grade concepts you would like to prepare and learn them accordingly. Identify the areas of need and improvise on them accordingly. Interpret and Compute different types of problems easily. You can have an easy transition from Grade 5 to Grade 6 and all the Grade 6 Topics, Problems, Worksheets made available help you to learn something new.

Grade 6 Concepts

  • Decimal Fractions with 10 as Denominator
  • Decimal Fractions with 100 as Denominator
  • Decimal Fractions with 1000 as Denominator
  • Integers and the Number Line
  • Ordering Integers
  • Use of Integers
  • Use of Integers as Directed Numbers
  • Adding Integers
  • Properties of Adding Integers
  • Subtracting Integers
  • Properties of Subtracting Integers
  • Multiplying Integers
  • Properties of Multiplying Integers
  • Dividing Integers
  • Properties of Dividing Integers
  • Worksheet on Integers and the Number Line
  • Worksheet on Use of Integers
  • Worksheet on Ordering Integers
  • Worksheet on Absolute Value of an Integer
  • Worksheet on Adding Integers
  • Worksheet on Subtracting Integers
  • Worksheet on Multiplying Integers
  • Worksheet on Dividing Integers
  • Worksheet on use of Integers as Directed Numbers

Numbers

Estimate

  • Estimate to Nearest Tens
  • Rounding off to the Nearest Tens
  • Estimate to Nearest Hundreds
  • Estimate to Nearest Thousands
  • Estimating Sum and Difference
  • Estimating Product and Quotient

Estimate – Worksheets

  • Worksheet on Estimate
  • Worksheet on Estimation

Natural Numbers

  • Properties of Natural Numbers

Whole Numbers

Fraction

  • Representations of Fractions on a Number Line
  • Fraction as Division
  • Types of Fractions
  • Conversion of Mixed Fractions into Improper Fractions
  • Conversion of Improper Fractions into Mixed Fractions
  • Equivalent Fractions
  • Interesting Fact about Equivalent Fractions
  • Fractions in Lowest Terms
  • Like and Unlike Fractions
  • Comparing Like Fractions
  • Comparing Unlike Fractions
  • Addition and Subtraction of Like Fractions
  • Addition and Subtraction of Unlike Fractions
  • Inserting a Fraction between Two Given Fractions

Number Line

  • Compare Two Numbers using a Number Line
  • Natural Numbers, Whole Numbers, and Integers on Number Lines
  • Addition of Numbers using Number Line
  • Subtraction of Numbers using Number Line
  • Addition of Numbers without using Number Line
  • Subtraction of Numbers without using Number Line
  • Representing Fractions on Number Line
  • Representing Decimals on Number Line

Number Line – Worksheets

  • Worksheet on Fractions and Decimals on Number Line
  • Worksheet on Addition and Subtraction using Number Line
  • Worksheet on Addition and Subtraction without using Number Line

Arithmetic

Profit and Loss

  • To find Profit or Loss when Cost Price and Selling Price are Given
  • To find Selling Price when Cost Price and Profit or Loss are Given
  • To find Cost Price when Selling Price and Profit or Loss are Given
  • Examples on Profit and Loss
  • Calculate Profit Percent
  • Calculate Loss Percent
  • Calculate Profit or Loss Percent
  • Calculate Profit and Selling Price
  • Calculate Loss and Selling Price
  • Overhead Charges
  • Discount and Discount Percent

Profit and Loss – Worksheets

  • Worksheet on Calculating Profit or Loss
  • Worksheet on Calculating Cost Price
  • Worksheet on Calculating Selling Price
  • Worksheet on Cost Price and Selling Price
  • Worksheet on Calculating Profit or Loss Percent
  • Worksheet on Profit or Loss Percent
  • Worksheet on Calculating Overhead Charges
  • Worksheet on Calculating Discount
  • Worksheet on Discount Percent
  • Worksheet on Calculating Discount on Marked Price

Ratios and Proportions

  • Concept of Ratio
  • Properties of Ratios
  • Ratio in Simplest Form
  • Problems on Ratios in Simplest Form
  • Comparison of Ratios
  • Equivalent Ratios
  • Convert Fractional Ratio into Whole Number Ratio
  • Dividing a Quantity in Two given Ratios
  • Dividing a Quantity in Three given Ratios
  • Dividing a Quantity in a given Ratio
  • Concept of Proportion
  • Continued Proportion
  • Properties of Proportion
  • Proportion Problems
  • Word Problems using Proportion

Ratios and Proportions – Worksheets

  • Worksheet on Ratio in Simplest Form
  • Worksheet on Concept of Ratio
  • Worksheet on Basic Problems on Ratio
  • Worksheet on Ratio Problems
  • Worksheet on Simple Word Problems on Ratio
  • Worksheet on Word Problems on Ratio
  • Worksheet on Basic Problems on Proportion
  • Worksheet on Concept of Proportion
  • Worksheet on Simple Word Problems on Proportion
  • Worksheet on Proportion Problems
  • Worksheet on Word Problems on Proportion
  • Multiple Choice Questions on Ratio and Proportion
  • Practice Test on Concept of Ratio and Proportion

Algebra

Literal Numbers

  • Addition of Literals
  • Subtraction of Literals
  • Multiplication of Literals
  • Properties of Multiplication of Literals
  • Division of Literals
  • Powers of Literal Numbers

Literal Numbers Worksheets

  • Worksheet on Addition of Literals
  • Worksheet on Subtraction of Literals
  • Worksheet on Multiplication of Literals
  • Worksheet on Division of Literals
  • Worksheet on Powers of Literal Numbers

Constants and Variables

Terms

  • Like and Unlike Terms
  • Like Terms
  • Addition of Like Terms
  • Subtraction of Like Terms
  • Adding and Subtracting Like Terms
  • Unlike Terms
  • Addition of Unlike Terms
  • Subtraction of Unlike Terms

Terms Worksheets

  • Worksheet on Terms
  • Worksheet on Like and Unlike Terms
  • Worksheet on Addition of Like Terms
  • Worksheet on Subtraction of Like Terms
  • Worksheet on Adding and Subtracting Like Terms
  • Worksheet on Combining Like Terms
  • Worksheet on Addition of Unlike Terms
  • Worksheet on Subtraction of Unlike Terms

Coefficient

  • Worksheet on Coefficients

Terms of an Algebraic Expression

  • Types of Algebraic Expressions
  • Degree of a Polynomial
  • Addition of Polynomials
  • Subtraction of Polynomials
  • Power of Literal Quantities
  • Multiplication of Two Monomials
  • Multiplication of Polynomial by Monomial
  • Multiplication of Two Binomials
  • Division of Monomials

Terms of an Algebraic Expression – Worksheet

  • Worksheet on Types of Algebraic Expressions
  • Worksheet on Degree of a Polynomial
  • Worksheet on Addition of Polynomials
  • Worksheet on Subtraction of Polynomials
  • Worksheet on Addition and Subtraction of Polynomials
  • Worksheet on Adding and Subtracting Polynomials
  • Worksheet on Multiplying Monomials
  • Worksheet on Multiplying Monomial and Binomial
  • Worksheet on Multiplying Monomial and Polynomial
  • Worksheet on Multiplying Binomials
  • Worksheet on Dividing Monomials

Grade 6 Goals and Objectives

  • Grade 6 Math Practice is created to help you get acquainted with all kinds of topics.
  • Keeping in mind the mental level of a child in 6th Grade all efforts are taken to introduce you to new concepts in a simple language so that you don’t find any difficulty.
  • Difficulty Level of Problems are reduced and mathematical concepts are explained in the simplest way possible so that you will not feel any difficulty in learning.
  • All the Topics are given with a large number of examples so that you will learn the applications of concepts.
  • In 6th Grade, we will introduce you to literal numbers, fractions, ratios, percentages, algebraic expressions, linear equations, etc.

Why Choose our 6th Grade Math Curriculum?

Comprehensive 6th Grade Math will concentrate on the areas listed below and you can achieve your learning targets easily. They are as follows

  • There is no end to the ways your kid in Grade 6 can improve their math skills.
  • Engaging activities will help kids learn math in a new learning way.
  • Strong Emphasis is laid on conceptual understanding rather than repetitive mugging up of concepts.
  • Grade 6 will cover a new concept so that you can see a significant improvement in your performance.

Hope the information shared has enlightened you to the possible extent. If you have any queries do contact us via comment box and our experts will guide you at the earliest possible. For more updates or information of Gradewise Math Concepts bookmark our site.

First Grade Math

First Grade Math Games, Problems, Activities, Worksheets, Practice Test, Questions and Answer Key

Place Value

  • Math Place Value
  • Numbers Worksheet
  • Missing Numbers Worksheet
  • Worksheet on Tens and Ones
  • Number Dot to Dot
  • Before and After
  • Number that Comes Between
  • Greater or Less than and Equal to
  • Ascending Order or Descending Order
  • Number Games

Addition

  • Adding 1-Digit Number
  • Vertical Addition
  • Addition Word Problems – 1-Digit Numbers
  • Missing Number in Addition
  • Missing Addend Sums with 1-Digit Number:
  • Adding with Zero
  • Adding Doubles
  • Addition Fact Sums to 10
  • Addition Fact Sums to 11
  • Addition Fact Sums to 12
  • Addition Fact Sums to 13
  • Addition Facts of 14, 15, 16, 17 and 18

Subtraction

  • Subtracting 1-Digit Number
  • Subtracting 2-Digit Numbers
  • Subtraction Word Problems – 1-Digit Numbers
  • Missing Number in Subtraction

Adding 0 to 9

  • Worksheet on Adding 0
  • Worksheet on Adding 1
  • Worksheet on Adding 2
  • Worksheet on Adding 3
  • Worksheet on Adding 4
  • Worksheet on Adding 5
  • Worksheet on Adding 6
  • Worksheet on Adding 7
  • Worksheet on Adding 8
  • Worksheet on Adding 9

Subtracting 0 to 9

  • Worksheet on Subtracting 0
  • Worksheet on Subtracting 1
  • Worksheet on Subtracting 2
  • Worksheet on Subtracting 3
  • Worksheet on Subtracting 4
  • Worksheet on Subtracting 5
  • Worksheet on Subtracting 6
  • Worksheet on Subtracting 7
  • Worksheet on Subtracting 8
  • Worksheet on Subtracting 9

Money Names and Values

 

Kindergarten Math Activities

Kindergarten Math Games, Problems, Activities, Worksheets, Practice Test, Questions and Answer Key

  • Go Math Grade K Answer Key
  • Big Ideas Math Grade K Answers
  • Eureka Math Grade K Answer Key
  • Number Rhymes
  • Matching the Objects
  • Numbers and Counting up to 10
  • Number the Pictures
  • Numbers up to 10
  • Numbers 1 to 10
  • Count and Write Numbers
  • Count the Numbers and Match
  • Numbers and their Names
  • Numbers and Counting up to 20
  • Learn About Counting
  • Counting Eleven to Twenty with Numbers and Words
  • Counting Numbers from Twenty One to Thirty
  • Counting Numbers from Thirty-One to Forty
  • Geometric Shapes
  • Geometric Objects
  • Time
  • Tell The Time
  • Worksheet on Time
  • Addition
  • Addition on a Number Line
  • Worksheet on Addition I
  • Worksheet on Addition II
  • Odd Man Out
  • Sequence
  • Ordinal Numbers
  • Worksheet on Ordinal Numbers
  • Addition Worksheets
  • Subtraction Worksheets
  • Counting Numbers Practice Test
  • Worksheets on Counting Numbers
  • Worksheet on Counting Numbers 6 to 10
  • What is addition?
  • Worksheet on Kindergarten Addition
  • Kindergarten Addition up to 5
  • Worksheets on Kindergarten Addition up to 5
  • Addition Facts
  • What is zero?
  • Order of Numbers.
  • Worksheets on Addition
  • Before and After Counting Worksheet up to 10
  • Worksheets on Counting Before and After
  • Before, After, and Between Numbers Worksheet up to 10
  • Worksheet on Before, After, and Between Numbers
  • Counting Before, After, and Between Numbers up to 10
  • The Story about Seasons
  • Color by Number Worksheets
  • Worksheet on Joining Numbers

Practice tracing the numbers from 21 to 30

  • Worksheet on Number 21
  • Worksheet on Number 22
  • Worksheet on Number 23
  • Worksheet on Number 24
  • Worksheet on Number 25
  • Worksheet on Number 26
  • Worksheet on Number 27
  • Worksheet on Number 28
  • Worksheet on Number 29
  • Worksheet on Number 30

Practice tracing the numbers from 31 to 40

  • Worksheet on Number 31
  • Worksheet on Number 32
  • Worksheet on Number 33
  • Worksheet on Number 34
  • Worksheet on Number 35
  • Worksheet on Number 36
  • Worksheet on Number 37
  • Worksheet on Number 38
  • Worksheet on Number 39
  • Worksheet on Number 40

Practice tracing the numbers from 41 to 50

  • Worksheet on Number 41
  • Worksheet on Number 42
  • Worksheet on Number 43
  • Worksheet on Number 44
  • Worksheet on Number 45
  • Worksheet on Number 46
  • Worksheet on Number 47
  • Worksheet on Number 48
  • Worksheet on Number 49
  • Worksheet on Number 50

Missing Number Worksheets

  • Missing Numbers up to 10
  • Worksheets on Missing Numbers from 1 to 10
  • Worksheets on Missing Numbers from 1 to 20
  • Worksheets on Missing Numbers from 15 to 25
  • Worksheets on Missing Numbers from 1 to 25

Worksheet on Before, After, and Between Numbers up to 20
Worksheet on Before, After, and Between Numbers up to 50