## Engage NY Eureka Math 5th Grade Module 6 Lesson 27 Answer Key

### Eureka Math Grade 5 Module 6 Lesson 27 Problem Set Answer Key

Question 1.
Use the RDW process to solve the word problems below.
a. Julia completes her homework in an hour. She spends $$\frac{7}{12}$$ of the time doing her math homework and $$\frac{1}{6}$$ of the time practicing her spelling words. The rest of the time she spends reading. How many minutes does Julia spend reading?
Time taken by Julia to complete her home work = 1 hour .
Time spent in Doing Math Homework = $$\frac{7}{12}$$
Time spent in Practicing her spelling words = $$\frac{1}{6}$$
Time spent in Reading = x .
Time spent in Doing Math Homework + Time spent in Practicing spelling words + Time spent in Reading = 1hour
$$\frac{7}{12}$$ + $$\frac{1}{6}$$  + x = 1
$$\frac{7 + 2 + 12x }{12}$$ = 1
9 +12x = 12
12x = 12 – 9
12x = 3
x = $$\frac{3}{12}$$
x = $$\frac{1}{4}$$  .
Therefore Time spent in Reading = $$\frac{1}{4}$$ hour .

b. Fred has 36 marbles. Elise has $$\frac{8}{9}$$ as many marbles as Fred. Annika has $$\frac{3}{4}$$ as many marbles as Elise. How many marbles does Annika have?
Number of Marbles with Fred = 36
Number of Marbles with Elise =$$\frac{8}{9}$$  as many marbles as Fred =$$\frac{8}{9}$$ (36)= 32
Number of Marbles with Annika = $$\frac{3}{4}$$ as many marbles as Elise = $$\frac{3}{4}$$ (32) = 24 .
Therefore Number of marbles with Annika = 24 .

Question 2.
Write and solve a word problem that might be solved using the expressions in the chart below.

 Expression Word Problem Solution $$\frac{2}{3}$$ × 18 (26 + 34) × $$\frac{5}{6}$$ 7 – ($$\frac{5}{12}$$ + $$\frac{1}{2}$$)

 Expression Word Problem Solution $$\frac{2}{3}$$ × 18 John brought 18 cakes to his class . His classmates ate $$\frac{2}{3}$$ of cakes. How many cakes are eaten ? $$\frac{2}{3}$$ × 18 = 12 cakes. Number of cakes eaten = 12 . (26 + 34) × $$\frac{5}{6}$$ Ruby is having 26 chocolates. Her sister gave 34 more chocolates to her . Ruby parents ate $$\frac{5}{6}$$ of chocolates. How many chocolates did Ruby parents eaten ? (26 + 34) × $$\frac{5}{6}$$ = 60 × $$\frac{5}{6}$$ = 50 Number of chocolates eaten by Ruby parents = 50 chocolates . 7 – ($$\frac{5}{12}$$ + $$\frac{1}{2}$$) Tina brought 7 pizzas cut into 12 slices each . Tina friend ate 5 slices and her Brother ate $$\frac{1}{2}$$ of pizza . What fraction of pizzas left over ? 7 – ($$\frac{5}{12}$$ + $$\frac{1}{2}$$) = 7 – ($$\frac{5 + 6}{12}$$) = 7 – $$\frac{11}{12}$$ = $$\frac{84 – 11}{12}$$ = $$\frac{73}{12}$$ =6$$\frac{1}{12}$$  pizzas .

### Eureka Math Grade 5 Module 6 Lesson 27 Reflection Answer Key

How did teaching other students how to solve a word problem strengthen your skills as a problem solver? What did you learn about your problem-solving skills? What are your strengths and weaknesses as a problem solver?
Skills of a problem solver
Active listening.
Analysis.
Research.
Creativity.
Communication.
Dependability.
Decision making.
Team-building.

Problem-solving model
a. Define the problem. The system.
b. Think about it. “Let it simmer”.
c. Plan a solution. Consider possible strategies.
d. Carry out the plan. Be patient.
e. Look back. Encourage students to reflect.

Problem-Solving Strengths:
Divergent thinking
Challenges assumptions
Step-by-step approach
Seeks practical information
Builds off others’ ideas
Looks for how the solution impacts people
Looks at the big picture
Checks for connections between different problems

Problem – Solving Weakness :
Inaccurate information of question
Different approaches to solve problem
Explanation with diagrams
Clear explanation so that everyone should understand .

### Eureka Math Grade 5 Module 6 Lesson 27 Homework Answer Key

Question 1.
Use the RDW process to solve the word problems below.
a. There are 36 students in Mr. Meyer’s class. Of those students, $$\frac{5}{12}$$ played tag at recess, $$\frac{1}{3}$$ played kickball, and the rest played basketball. How many students in Mr. Meyer’s class played basketball?
Number of Students in Mr. Meyer’s class = 36 students.
Number of students played tag at recess = $$\frac{5}{12}$$ (36 ) = 15 .
Number of students played kickball = $$\frac{1}{3}$$ (36 ) = 12.
Number of students played basket ball = Total students – students who played ( recess + kickball )= 36 – (15 +12 )
= 36 – 27 = 9 students.
Therefore, Number of students played basket ball = 9 students.

b. Julie brought 24 apples to school to share with her classmates. Of those apples, $$\frac{2}{3}$$ are red, and the rest are green. Julie’s classmates ate $$\frac{3}{4}$$ of the red apples and $$\frac{1}{2}$$ of the green apples. How many apples are left?
Number of Apples Julie brought = 24
Number of red apples = $$\frac{2}{3}$$ ( 24) = 16 .
Number of green apples = total – red apples = 24 – 16 = 8.
Number of red apples eaten = $$\frac{3}{4}$$ ( 16 ) = 12 apples.
Number of green apples eaten = $$\frac{1}{2}$$ ( 8 ) = 4 apples .
Number of red apples left = total red apples – number of red apples eaten = 16 – 12 = 4 apples.
Number of green apples left = total green apples – number of green apples eaten = 8 – 4 = 4 apples.
Total number of apples left = Number of left red apples left +Number of left green apples = 4 + 4 = 8 apples.

Question 2.
Write and solve a word problem for each expression in the chart below.

 Expression Word Problem Solution

 Expression Word Problem Solution 144 × $$\frac{7}{12}$$ Kristy is having 144 eggs. she used $$\frac{7}{12}$$ of eggs to bake cakes . How many eggs are used for baking cakes? 144 × $$\frac{7}{12}$$ = 84 eggs. Number of eggs used for baking a cake = 84 eggs. 9 – ($$\frac{4}{9}$$ + $$\frac{1}{23}$$) Gaurish having 9 apples cut into 9 peices. His brother Mourish ate $$\frac{4}{9}$$ and his sister ate $$\frac{1}{23}$$ of apples . How many Apples are left over ? 9 – ($$\frac{4}{9}$$ + $$\frac{1}{23}$$) = 9 – ($$\frac{92 – 9}{207}$$) = 9 – $$\frac{83}{207}$$ = $$\frac{1863 – 83}{207}$$ = $$\frac{1780}{207}$$ $$\frac{3}{4}$$ × (36 + 12) Gourab having 36 color pencils . His Brother gave 12 more colorpencils to him . Gourab used $$\frac{3}{4}$$ color pencils to draw a picture . How many color pencils are used ? $$\frac{3}{4}$$ × (36 + 12) = $$\frac{3}{4}$$ × (48) = 36 color pencils. Number of color pencils used for picture = 36 color pencils .