## Engage NY Eureka Math 4th Grade Module 6 Mid Module Assessment Answer Key

Question 1.
Write the following fractions as equivalent decimals. Then, model each decimal with the given representation.
a. $$\frac{2}{10}$$ = ___0.2___

2/10 = 0.2.

Explanation:
In the above-given question,
given that,
$$\frac{2}{10}$$.
2/10 = 0.2.

b. $$\frac{3}{100}$$ = __0.03____

3/100 = 0.03.

Explanation:
In the above-given question,
given that,
$$\frac{3}{100}$$.
3/100 = 0.03.

c. $$\frac{4}{10}$$ = ___0.4___

4/10 = 0.4.

Explanation:
In the above-given question,
given that,
$$\frac{4}{10}$$.
4/10 = 0.4.

d. $$\frac{46}{100}$$ = ___0.46___

46/100 = 0.46.

Explanation:
In the above-given question,
given that,
$$\frac{46}{100}$$.
46/100 = 0.46.

e. 7$$\frac{6}{10}$$ = __7.6____

7 + 6/10 = 7.6.

Explanation:
In the above-given question,
given that,
7$$\frac{6}{10}$$.
7 + 6/10 = 7.6.

f. 3$$\frac{64}{100}$$ = __3.64___

364/100 = 3.64.

Explanation:
In the above-given question,
given that,
$$\frac{364}{100}$$.
364/100 = 3.64.

g. 4$$\frac{7}{10}$$ = ___4.7___

47/10 = 4.7.

Explanation:
In the above-given question,
given that,
$$\frac{47}{10}$$.
47/10 = 4.7.

h. 5$$\frac{72}{100}$$ = _5.72____

572/100 = 5.72.

Explanation:
In the above-given question,
given that,
$$\frac{572}{100}$$.
572/100 = 5.72.

Question 2.
Decompose tenths into hundredths using the area model. Express the equivalence of tenths and hundredths with fractions and with decimals.
a. 3 tenths

3 tenths = 0.3.

Explanation:
In the above-given question,
given that,
3 tenths = 3/10.
3/10 = 0.3.

b. 1 and 7 tenths

1 and 7 tenths = 1.7.

Explanation:
In the above-given question,
given that,
1 and 7 tenths = 1 + 7/10.
7/10 = 0.7.
1 + 0.7 = 1.7.

Question 3.
Use number bonds to complete parts (a) and (b) below:
a. Decompose 3.24 by units.
b. Compose 0.03, 0.5, and 2 as one decimal number.

a. 3 hundred, 2 tens and 4 ones.

Explanation:
In the above-given question,
given that,
Decompose 3.24 by units.
3.24 = 3 hundreds.
2 tens and 4 ones.

b. 0.03, 0.5, 2 = 2.53.

Explanation:
In the above-given question,
given that,
compose 0.03 + 0.5 + 2 as one decimal number.
0.03 + 0.5 + 2 = 253.

Question 4.
Model the following equivalence on the place value chart using place value disks.
20 hundredths = 2 tenths

20 hundredths = 2 tenths.

Explanation:
In the above-given question,
given that,
20 hundredths = 20/100.
20/100 = 2/10.
2/10 = 0.2.
2 tenths = 2/10 = 0.2.

Question 5.
Complete the following chart.

 Unit Form Fraction Fraction Expanded Form Decimal Expanded Form Decimal a. 1 tenth 6 hundredths 1$$\frac{6}{100}$$ (1 × 10) + (6 × 1) + (1 ×$$\frac{1}{10}$$ ) + (6 × $$\frac{1}{100}$$) (1 10) + (6 1) + (1 0.06) 16.06 b. 2 tenth 7 hundredths 2$$\frac{7}{10}$$ (2 × 10) + (7 × 1) + (2 ×$$\frac{2}{10}$$ ) + (7 × $$\frac{7}{100}$$) (2 10) + (6 1) + (2 0.01) 26.02 c. 6 hundredths 3 tenths 4 ones 6$$\frac{3}{10}$$ (3 × 10) + (4 × 1) + (4 ×$$\frac{3}{10}$$ ) + (4 × $$\frac{6}{100}$$) (3 10) + (4 1) + (4 0.03) 38.03 d. 5 hundredths 6 tenths 1 one 1$$\frac{5}{10}$$ (6 × 10) + (1 × 1) + (6 ×$$\frac{5}{10}$$ ) + (1 × $$\frac{5}{100}$$) (1 10) + (6 1) + (5 0.01) 16.05 e. 8 hundredths 2 tenths 3 ones 3$$\frac{2}{10}$$ (2 × 10) + (3 × 1) + (7 ×$$\frac{1}{10}$$ ) + (8 × $$\frac{1}{100}$$) (2 10) + (3 1) + (8 0.01) 23.08

1 tenth 6 hundredths.

Explanation:
In the above-given question,
given that,
1 tenth and 6 hundredths.
1$$\frac{6}{100}$$.
16.06.

2 tenths 7 hundredths.

Explanation:
In the above-given question,
given that,
2$$\frac{7}{100}$$.
26.02.

Question 6.
Maya puts groceries into bags. The items and their weights in kilograms are given below.

a. Plot the weight in kilograms of each item on the number line below.

0.25, 0.34, 0.56, 0.25, 0.56, 0.34.

Explanation:
In the above-given question,
given that,
bananas = 0.35.
cheese = 0.56.
carrots = 25/100 = 0.25.
grapes = 56/100 = 0.56.
eggs = 34/100 = 0.34.

b. Write a number sentence using decimals to record the weight in kilograms of the bananas in expanded form.

(3 × 10) + (5 × 1) + ( ×$$\frac{3}{10}$$ ) + ( × $$\frac{5}{100}$$)

Explanation:
In the above-given question,
given that,
bananas = 0.35.
35/100 = 0.35.

c. Write a number sentence using fractions to record the weight in kilograms of the grapes in expanded form.

(5 × 10) + (6 × 1) + ( ×$$\frac{5}{10}$$ ) + ( × $$\frac{6}{100}$$)

Explanation:
In the above-given question,
given that,
grapes = 0.56.
56/100 = 0.56.

Maya packs the eggs and cheese into one of the bags. Together, these items weigh $$\frac{90}{100}$$ kilogram.
d. Use the area model to show that $$\frac{90}{100}$$ can be renamed as tenths.

90/100 = 0.9.

Explanation:
In the above-given question,
given that,
90/100 = 9/10.
zero gets canceled on both sides.
9/10 = 0.9.

e. Use division to show how $$\frac{90}{100}$$ can be renamed as tenths.

90/100 = 0.9.

Explanation:
In the above-given question,
given that,
90/100 = 9/10.
zero gets canceled on both sides.
9/10 = 0.9.

Maya places the bread into the bag with the eggs and cheese. Together, all three items weigh 1 and 15 hundredths kilograms.
f. Use a model and words to explain how 1 and 15 hundredths can be written as a decimal and as a fraction.

1 + 15/100 = 115/100.

Explanation:
In the above-given question,
given that,
115/100 = 115/100.
zero gets canceled on both sides.
115/100 = 1.15.

Maya put the rest of the groceries in a second bag. The items in both bags weigh a total of 2$$\frac{30}{100}$$ kilograms.
g. Using a model and words, explain how many tenths are in 2$$\frac{30}{100}$$.

2$$\frac{30}{100}$$.