Engage NY Eureka Math 5th Grade Module 4 Lesson 21 Answer Key
Eureka Math Grade 5 Module 4 Lesson 21 Sprint Answer Key
A
Multiply Decimals
Answer:
Question 1.
3 × 2 =
Answer:
3 × 2 = 6.
Explanation:
By multiplication 3 by 2, we will get the result as 6
Question 2.
3 × 0.2 =
Answer:
3 × 0.2 = 0.6.
Explanation:
By multiplication 3 by 0.2, we will get the result as 0.6.
Question 3.
3 × 0.02 =
Answer:
3 × 0.02 = 0.06.
Explanation:
By multiplication 3 by 0.02, we will get the result as 0.06.
Question 4.
3 × 3 =
Answer:
3 × 3 = 9.
Explanation:
By multiplication 3 by 3, we will get the result as 9.
Question 5.
3 × 0.3 =
Answer:
3 × 0.3 = 0.9.
Explanation:
By multiplication 3 by 0.3, we will get the result as 0.9.
Question 6.
3 × 0.03 =
Answer:
3 × 0.03 = 0.09.
Explanation:
By multiplication 3 by 0.03, we will get the result as 0.09.
Question 7.
2 × 4 =
Answer:
2 × 4 = 8.
Explanation:
By multiplication 2 by 4, we will get the result as 8.
Question 8.
2 × 0.4 =
Answer:
2 × 0.4 = 0.8.
Explanation:
By multiplication 2 by 0.4, we will get the result as 0.8.
Question 9.
2 × 0.04 =
Answer:
2 × 0.04 = 0.08.
Explanation:
By multiplication 2 by 0.04, we will get the result as 0.08.
Question 10.
5 × 3 =
Answer:
5 × 3 = 15.
Explanation:
By multiplication 5 by 3, we will get the result as 15.
Question 11.
5 × 0.3 =
Answer:
5 × 0.3 = 1.5.
Explanation:
By multiplication 5 by 0.3, we will get the result as 1.5.
Question 12.
5 × 0.03 =
Answer:
5 × 0.03 = 0.15.
Explanation:
By multiplication 5 by 0.03, we will get the result as 0.15.
Question 13.
7 × 2 =
Answer:
7 × 2 = 14.
Explanation:
By multiplication 7 by 2, we will get the result as 14.
Question 14.
7 × 0.2 =
Answer:
7 × 0.2 = 1.4.
Explanation:
By multiplication 7 by 0.2, we will get the result as 1.4.
Question 15.
7 × 0.02 =
Answer:
7 × 0.02 = 0.14.
Explanation:
By multiplication 7 by 0.02, we will get the result as 0.14.
Question 16.
4 × 3 =
Answer:
4 × 3 = 12.
Explanation:
By multiplication 4 by 3, we will get the result as 12.
Question 17.
4 × 0.3 =
Answer:
4 × 0.3 = 1.2.
Explanation:
By multiplication 4 by 0.3, we will get the result as 1.2.
Question 18.
0.4 × 3 =
Answer:
0.4 × 3 = 1.2.
Explanation:
By multiplication 0.4 by 3, we will get the result as 1.2.
Question 19.
0.4 × 0.3 =
Answer:
0.4 × 0.3 = 0.12.
Explanation:
By multiplication 0.4 by 0.3, we will get the result as 0.12.
Question 20.
0.4 × 0.03 =
Answer:
0.4 × 0.03 = 0.012.
Explanation:
By multiplication 5 by 3, we will get the result as 0.012.
Question 21.
0.3 × 0.04 =
Answer:
0.3 × 0.04 = 0.012.
Explanation:
By multiplication 0.3 by 0.04, we will get the result as 0.012.
Question 22.
6 × 2 =
Answer:
6 × 2 = 12.
Explanation:
By multiplication 6 by 2, we will get the result as 12.
Question 23.
0.6 × 2 =
Answer:
0.6 × 2 = 1.2.
Explanation:
By multiplication 0.6 by 2, we will get the result as 1.2.
Question 24.
0.6 × 0.2 =
Answer:
0.6 × 0.2 = 0.12.
Explanation:
By multiplication 0.6 by 0.2, we will get the result as 0.12.
Question 25.
0.6 × 0.02 =
Answer:
0.6 × 0.02 = 0.012.
Explanation:
By multiplication 0.6 by 0.02, we will get the result as 0.012.
Question 26.
0.2 × 0.06 =
Answer:
0.2 × 0.06 = 0.012.
Explanation:
By multiplication 0.2 by 0.06, we will get the result as 0.012.
Question 27.
5 × 7 =
Answer:
5 × 7 = 35.
Explanation:
By multiplication 5 by 7, we will get the result as 35.
Question 28.
0.5 × 7 =
Answer:
0.5 × 7 = 3.5.
Explanation:
By multiplication 0.5 by 7, we will get the result as 3.5.
Question 29.
0.5 × 0.7 =
Answer:
0.5 × 0.7 = 0.35.
Explanation:
By multiplication 0.5 by 0.7, we will get the result as 0.35.
Question 30.
0.5 × 0.07 =
Answer:
0.5 × 0.07 = 0.035.
Explanation:
By multiplication 0.5 by 0.07, we will get the result as 0.035.
Question 31.
0.7 × 0.05 =
Answer:
0.7 × 0.05 = 0.035.
Explanation:
By multiplication 0.7 by 0.05, we will get the result as 0.035.
Question 32.
2 × 8 =
Answer:
2 × 8 = 16.
Explanation:
By multiplication 2 by 8, we will get the result as 16.
Question 33.
9 × 0.2 =
Answer:
9 × 0.2 = 1.8.
Explanation:
By multiplication 9 by 0.2, we will get the result as 1.8.
Question 34.
3 × 7 =
Answer:
3 × 7 = 21.
Explanation:
By multiplication 3 by 7, we will get the result as 21.
Question 35.
8 × 0.03 =
Answer:
8 × 0.03 = 0.24.
Explanation:
By multiplication 8 by 0.03, we will get the result as 0.24.
Question 36.
4 × 6 =
Answer:
4 × 6 = 24.
Explanation:
By multiplication 4 by 6, we will get the result as 24.
Question 37.
0.6 × 7 =
Answer:
0.6 × 7 = 4.2.
Explanation:
By multiplication 0.6 by 7, we will get the result as 4.2.
Question 38.
0.7 × 0.7 =
Answer:
0.7 × 0.7 = 0.49.
Explanation:
By multiplication 0.7 by 0.7, we will get the result as 0.49.
Question 39.
0.8 × 0.06 =
Answer:
0.8 × 0.06 = 0.048.
Explanation:
By multiplication 0.8 by 0.06, we will get the result as 0.048.
Question 40.
0.09 × 0.6 =
Answer:
0.09 × 0.6 = 0.054.
Explanation:
By multiplication 0.09 by 0.6, we will get the result as 0.054.
Question 41.
6 × 0.8 =
Answer:
6 × 0.8 = 4.8.
Explanation:
By multiplication 6 by 0.8, we will get the result as 4.8.
Question 42.
0.7 × 0.9 =
Answer:
0.7 × 0.9 = 0.63.
Explanation:
By multiplication 0.7 by 0.9, we will get the result as 0.63.
Question 43.
0.08 × 0.8 =
Answer:
0.08 × 0.8 = 0.064.
Explanation:
By multiplication 0.08 by 0.8, we will get the result as 0.064.
Question 44.
0.9 × 0.08 =
Answer:
0.9 × 0.08 = 0.072.
Explanation:
By multiplication 0.9 by 0.08, we will get the result as 0.072.
B
Multiply Decimals
Question 1.
4 × 2 =
Answer:
4 × 2 = 8.
Explanation:
By multiplication 4 by 2, we will get the result as 8.
Question 2.
4 × 0.2 =
Answer:
4 × 0.2 = 0.8.
Explanation:
By multiplication 4 by 0.2, we will get the result as 0.8.
Question 3.
4 × 0.02 =
Answer:
4 × 0.02 = 0.08.
Explanation:
By multiplication 4 by 2, we will get the result as 0.08.
Question 4.
2 × 3 =
Answer:
2 × 3 = 6.
Explanation:
By multiplication 2 by 3, we will get the result as 6.
Question 5.
2 × 0.3 =
Answer:
2 × 0.3 = 0.6.
Explanation:
By multiplication 2 by 0.3, we will get the result as 0.6.
Question 6.
2 × 0.03 =
Answer:
2 × 0.03 = 0.06.
Explanation:
By multiplication 2 by 0.03, we will get the result as 0.06.
Question 7.
3 × 3 =
Answer:
3 × 3 = 9.
Explanation:
By multiplication 3 by 3, we will get the result as 9.
Question 8.
3 × 0.3 =
Answer:
3 × 0.3 = 0.9.
Explanation:
By multiplication 3 by 0.3, we will get the result as 0.9.
Question 9.
3 × 0.03 =
Answer:
3 × 0.03 = 0.09.
Explanation:
By multiplication 3 by 0.03, we will get the result as 0.09.
Question 10.
4 × 3 =
Answer:
4 × 3 = 12.
Explanation:
By multiplication 4 by 3, we will get the result as 12.
Question 11.
4 × 0.3 =
Answer:
4 × 3 = 12.
Explanation:
By multiplication 4 by 3, we will get the result as 12.
Question 12.
4 × 0.03 =
Answer:
4 × 0.03 = 0.12.
Explanation:
By multiplication 4 by 0.03, we will get the result as 012.
Question 13.
9 × 2 =
Answer:
9 × 2 = 18.
Explanation:
By multiplication 9 by 2, we will get the result as 18.
Question 14.
9 × 0.2 =
Answer:
9 × 0.2 = 1.8.
Explanation:
By multiplication 9 by 0.2, we will get the result as 1.8.
Question 15.
9 × 0.02 =
Answer:
9 × 0.02 = 0.18.
Explanation:
By multiplication 9 by 0.02, we will get the result as 0.18.
Question 16.
5 × 3 =
Answer:
5 × 3 = 15.
Explanation:
By multiplication 5 by 3, we will get the result as 15.
Question 17.
5 × 0.3 =
Answer:
5 × 0.3 = 1.5.
Explanation:
By multiplication 5 by 0.3, we will get the result as 1.5.
Question 18.
0.5 × 3 =
Answer:
0.5 × 3 = 1.5.
Explanation:
By multiplication 0.5 by 3, we will get the result as 1.5.
Question 19.
0.5 × 0.3 =
Answer:
0.5 × 0.3 = 0.15.
Explanation:
By multiplication 0.5 by 0.3, we will get the result as 0.15.
Question 20.
0.5 × 0.03 =
Answer:
0.5 × 0.03 = 0.015.
Explanation:
By multiplication 0.5 by 0.03, we will get the result as 0.015.
Question 21.
0.3 × 0.05 =
Answer:
0.3 × 0.05 = 0.015.
Explanation:
By multiplication 0.3 by 0.05, we will get the result as 0.015.
Question 22.
8 × 2 =
Answer:
8 × 2 = 16.
Explanation:
By multiplication 8 by 2, we will get the result as 16.
Question 23.
0.8 × 2 =
Answer:
0.8 × 2 = 1.6.
Explanation:
By multiplication 0.8 by 2, we will get the result as 1.6.
Question 24.
0.8 × 0.2 =
Answer:
0.8 × 0.2 = 0.16.
Explanation:
By multiplication 0.8 by 0.2, we will get the result as 0.16.
Question 25.
0.8 × 0.02 =
Answer:
0.8 × 0.02 = 0.016.
Explanation:
By multiplication 0.8 by 0.02, we will get the result as 0.016.
Question 26.
0.2 × 0.08 =
Answer:
0.2 × 0.08 = 0.016.
Explanation:
By multiplication 0.2 by 0.08, we will get the result as 0.016.
Question 27.
5 × 9 =
Answer:
5 × 9 = 45.
Explanation:
By multiplication 5 by 9, we will get the result as 45.
Question 28.
0.5 × 9 =
Answer:
0.5 × 9 = 4.5.
Explanation:
By multiplication 0.5 by 9, we will get the result as 4.5.
Question 29.
0.5 × 0.9 =
Answer:
0.5 × 0.9 = 0.45.
Explanation:
By multiplication 0.5 by 0.9, we will get the result as 0.45.
Question 30.
0.5 × 0.09 =
Answer:
0.5 × 0.09 = 0.045.
Explanation:
By multiplication 0.5 by 0.09, we will get the result as 0.045.
Question 31.
0.9 × 0.05 =
Answer:
0.9 × 0.05 = 0.045.
Explanation:
By multiplication 0.9 by 0.05, we will get the result as 0.045Question 32.
Question: 32.
2 × 6 =
Answer:
2 × 6 = 12.
Explanation:
By multiplication 2 by 6, we will get the result as 12.
Question 33.
7 × 0.2 =
Answer:
7 × 0.2 = 1.4.
Explanation:
By multiplication 7 by 0.2, we will get the result as 1.4.
Question 34.
3 × 8 =
Answer:
3 × 8 = 24.
Explanation:
By multiplication 3 by 8, we will get the result as 24.
Question 35.
9 × 0.03 =
Answer:
9 × 0.03 = 0.27.
Explanation:
By multiplication 9 by 0.03, we will get the result as 0.27.
Question 36.
4 × 8 =
Answer:
4 × 8 = 32.
Explanation:
By multiplication 4 by 8, we will get the result as 32.
Question 37.
0.7 × 6 =
Answer:
0.7 × 6 = 4.2.
Explanation:
By multiplication 0.7 by 6, we will get the result as 4.2.
Question 38.
0.6 × 0.6 =
Answer:
0.6 × 0.6 = 0.36.
Explanation:
By multiplication 0.6 by 0.6, we will get the result as 0.36.
Question 39.
0.6 × 0.08 =
Answer:
0.6 × 0.08 = 0.048.
Explanation:
By multiplication 0.6 by 0.08, we will get the result as 0.048.
Question 40.
0.06 × 0.9 =
Answer:
0.06 × 0.9 = 0.054.
Explanation:
By multiplication 0.06 by 0.9, we will get the result as 0.054.
Question 41.
8 × 0.6 =
Answer:
8 × 0.6 = 4.8.
Explanation:
By multiplication 8 by 0.6, we will get the result as 4.8.
Question 42.
0.9 × 0.7 =
Answer:
0.9 × 0.7 = 0.63.
Explanation:
By multiplication 0.9 by 0.7, we will get the result as 0.63.
Question 43.
0.07 × 0.7 =
Answer:
0.07 × 0.7 = 0.049.
Explanation:
By multiplication 0.07 by 0.7, we will get the result as 0.049.
Question 44.
0.8 × 0.09 =
Answer:
0.8 × 0.09 = 0.072.
Explanation:
By multiplication 0.8 by 0.09, we will get the result as 0.072.
Eureka Math Grade 5 Module 4 Lesson 21 Problem Set Answer Key
Fill in the blanks. The first one has been done for you.
a. \(\frac{1}{4}\) × 1 = \(\frac{1}{4}\) × \(\frac{3}{3}\) = \(\frac{3}{12}\)
b. \(\frac{3}{4}\) × 1 = \(\frac{3}{4}\) × – = \(\frac{21}{28}\)
Answer:
\(\frac{3}{4}\) × 1 = \(\frac{3}{4}\) × \(\frac{7}{7}\) = \(\frac{21}{28}\)
Explanation:
To justify the answer we will place \(\frac{7}{7}\).
c. \(\frac{7}{4}\) × 1 = \(\frac{7}{4}\) × – = \(\frac{35}{20}\)
Answer:
\(\frac{7}{4}\) × 1 = \(\frac{7}{4}\) × \(\frac{5}{5}\) = \(\frac{35}{20}\)
Explanation:
To justify the answer we will place \(\frac{5}{5}\).
d. Use words to compare the size of the product to the size of the first factor.
Answer:
Each time, the first factor is being multiplied by a fraction equal to 1, so the product is equal to the first factor.
Question 2.
Express each fraction as an equivalent decimal.
a. \(\frac{1}{4}\) × \(\frac{25}{25}\) =
Answer:
\(\frac{1}{4}\) × \(\frac{25}{25}\) = 0.025.
Explanation:
Given that \(\frac{1}{4}\) × \(\frac{25}{25}\) which is \(\frac{25}{100}\) and the equivalent decimal of \(\frac{25}{100}\) is 0.25.
b. \(\frac{3}{4}\) × \(\frac{25}{25}\) =
Answer:
\(\frac{3}{4}\) × \(\frac{25}{25}\) = 0.75.
Explanation:
Given that \(\frac{3}{4}\) × \(\frac{25}{25}\) which is \(\frac{75}{100}\) and the equivalent decimal of \(\frac{75}{100}\) is 0.75.
c. \(\frac{1}{5}\) × – =
Answer:
\(\frac{1}{5}\) × \(\frac{20}{20}\) = 0.20.
Explanation:
Given \(\frac{1}{5}\) and we need to place \(\frac{20}{20}\) which is \(\frac{1}{5}\) × \(\frac{20}{20}\) = \(\frac{20}{100}\) and the equivalent decimal of \(\frac{20}{100}\) is 0.20.
d. \(\frac{4}{5}\) × – =
Answer:
\(\frac{4}{5}\) × \(\frac{20}{20}\) = 0.80.
Explanation:
Given \(\frac{4}{5}\) and we need to place \(\frac{20}{20}\) which is \(\frac{4}{5}\) × \(\frac{20}{20}\) = \(\frac{80}{100}\) and the equivalent decimal of \(\frac{80}{100}\) is 0.80.
e. \(\frac{1}{20}\)
Answer:
\(\frac{1}{20}\) × \(\frac{5}{5}\) = 0.05.
Explanation:
Given \(\frac{1}{20}\) and we need to place \(\frac{5}{5}\) which is \(\frac{1}{20}\) × \(\frac{5}{5}\) = \(\frac{5}{100}\) and the equivalent decimal of \(\frac{5}{100}\) is 0.05.
f. \(\frac{27}{20}\)
Answer:
\(\frac{27}{20}\) × \(\frac{5}{5}\) = 1.35.
Explanation:
Given \(\frac{27}{20}\) and we need to place \(\frac{5}{5}\) which is \(\frac{27}{20}\) × \(\frac{5}{5}\) = \(\frac{135}{100}\) and the equivalent decimal of \(\frac{135}{100}\) is 1.35.
g. \(\frac{7}{4}\)
Answer:
\(\frac{7}{4}\) × \(\frac{25}{25}\) = 1.75.
Explanation:
Given \(\frac{7}{4}\) and we need to place \(\frac{25}{25}\) which is \(\frac{7}{4}\) × \(\frac{25}{225}\) = \(\frac{175}{100}\) and the equivalent decimal of \(\frac{175}{100}\) is 1.75.
h. \(\frac{8}{5}\)
Answer:
\(\frac{8}{5}\) × \(\frac{20}{20}\) = 1.60.
Explanation:
Given \(\frac{1}{5}\) and we need to place \(\frac{20}{20}\) which is \(\frac{8}{5}\) × \(\frac{20}{20}\) = \(\frac{160}{100}\) and the equivalent decimal of \(\frac{160}{100}\) is 1.60.
i. \(\frac{24}{25}\)
Answer:
\(\frac{24}{25}\) × \(\frac{4}{4}\) = 0.96.
Explanation:
Given \(\frac{24}{25}\) and we need to place \(\frac{4}{4}\) which is \(\frac{24}{25}\) × \(\frac{4}{4}\) = \(\frac{96}{100}\) and the equivalent decimal of \(\frac{96}{100}\) is 0.96.
j. \(\frac{93}{50}\)
Answer:
\(\frac{93}{50}\) × \(\frac{2}{2}\) = 1.86.
Explanation:
Given \(\frac{93}{50}\) and we need to place \(\frac{2}{2}\) which is \(\frac{93}{50}\) × \(\frac{2}{2}\) = \(\frac{186}{100}\) and the equivalent decimal of \(\frac{186}{100}\) is 1.86.
k. 2\(\frac{6}{25}\)
Answer:
2\(\frac{6}{25}\) × \(\frac{4}{4}\) = 2.24.
Explanation:
Given 2\(\frac{6}{25}\) which is \(\frac{56}{25}\) and we need to place \(\frac{4}{4}\) which is \(\frac{56}{25}\) × \(\frac{4}{4}\) = \(\frac{224}{100}\) and the equivalent decimal of \(\frac{224}{100}\) is 2.24.
l. 3\(\frac{31}{50}\)
Answer:
3\(\frac{31}{50}\) × \(\frac{2}{2}\) = 3.62.
Explanation:
Given 3\(\frac{31}{50}\) which is \(\frac{181}{50}\) and we need to place \(\frac{2}{2}\) which is \(\frac{181}{50}\) × \(\frac{2}{2}\) = \(\frac{362}{100}\) and the equivalent decimal of \(\frac{362}{100}\) is 3.62.
Question 3.
Jack said that if you take a number and multiply it by a fraction, the product will always be smaller than what you started with. Is he correct? Why or why not? Explain your answer, and give at least two examples to support your thinking.
Answer:
No, Jack is not correct.
Explanation:
As Jack said that if you take a number and multiply it by a fraction and the product will always be smaller than what you started with. He is not correct, as a fraction could increase a number if we multiply it. So if the numerator is higher than the denominator it will increase it, and if the numerator is smaller than the denominator it decreases it. For example (10 × 4) ÷ (1 × 3) which is \(\frac{40}{3}\) = 13.33 which is higher than 10. And the other example is (5 × 10) ÷ (1 × 3) which is \(\frac{50}{3}\) = 16.67 which is higher than 5.
Question 4.
There is an infinite number of ways to represent 1 on the number line. In the space below, write at least four expressions multiplying by 1. Represent one differently in each expression.
Question 5.
Maria multiplied by 1 to rename \(\frac{1}{4}\) as hundredths. She made factor pairs equal to 10. Use her method to change one-eighth to an equivalent decimal.
Answer:
\(\frac{125}{100}\) = 1.25.
Explanation:
Given that Maria multiplied by 1 to rename \(\frac{1}{4}\) as hundredths and she made factor pairs equal to 10. So by using her method to change one-eighth to an equivalent decimal is
\(\frac{1}{8}\) = \(\frac{1}{2×2×2}\) × \(\frac{5×5×5}{5×5×5}\)
= \(\frac{5×5×5}{(2×5)×(2×5)×(2×5)}\)
which will be \(\frac{125}{100}\) = 1.25.
Paulo renamed \(\frac{1}{8}\) as a decimal, too. He knows the decimal equal to \(\frac{1}{4}\), and he knows that \(\frac{1}{8}\) is half as much as \(\frac{1}{4}\) . Can you use his ideas to show another way to find the decimal equal to \(\frac{1}{8}\) ?
Eureka Math Grade 5 Module 4 Lesson 21 Exit Ticket Answer Key
Fill in the blanks to make the equation true.
\(\frac{9}{4}\) × 1 = \(\frac{9}{4}\) × – = \(\frac{45}{20}\)
Answer:
\(\frac{9}{4}\) × 1 = \(\frac{9}{4}\) × \(\frac{5}{5}\) = \(\frac{45}{20}\)
Explanation:
Given that \(\frac{9}{4}\) × 1, so to make the equation true we will place \(\frac{9}{4}\) × \(\frac{5}{5}\) which is \(\frac{45}{20}\).
Question 2.
Express the fractions as equivalent decimals.
a. \(\frac{1}{4}\) =
Answer:
\(\frac{1}{4}\) × \(\frac{25}{25}\) = 0.25.
Explanation:
Given \(\frac{1}{4}\) and we need to place \(\frac{25}{25}\) which is \(\frac{1}{4}\) × \(\frac{25}{25}\) = \(\frac{25}{100}\) and the equivalent decimal of \(\frac{25}{100}\) is 0.25.
b. \(\frac{2}{5}\) =
Answer:
\(\frac{2}{5}\) × \(\frac{20}{20}\) = 0.40.
Explanation:
Given \(\frac{2}{5}\) and we need to place \(\frac{20}{20}\) which is \(\frac{2}{5}\) × \(\frac{20}{20}\) = \(\frac{40}{100}\) and the equivalent decimal of \(\frac{40}{100}\) is 0.40.
c. \(\frac{3}{25}\) =
Answer:
\(\frac{3}{25}\) × \(\frac{4}{4}\) = 0.12.
Explanation:
Given \(\frac{3}{25}\) and we need to place \(\frac{20}{20}\) which is \(\frac{3}{25}\) × \(\frac{4}{4}\) = \(\frac{12}{100}\) and the equivalent decimal of \(\frac{12}{100}\) is 0.12.
d. \(\frac{5}{20}\) =
Answer:
\(\frac{5}{20}\) × \(\frac{5}{5}\) = 0.25.
Explanation:
Given \(\frac{5}{20}\) and we need to place \(\frac{5}{5}\) which is \(\frac{5}{20}\) × \(\frac{5}{5}\) = \(\frac{25}{100}\) and the equivalent decimal of \(\frac{25}{100}\) is 0.25.
Eureka Math Grade 5 Module 4 Lesson 21 Homework Answer Key
Fill in the blanks.
a. \(\frac{1}{3}\) × 1 = \(\frac{1}{3}\) × \(\frac{3}{3}\) =/9
Answer:
\(\frac{1}{3}\) × 1 = \(\frac{1}{3}\) × \(\frac{3}{3}\) = \(\frac{3}{9}\).
Explanation:
Given that \(\frac{1}{3}\) × 1 = \(\frac{1}{3}\) × \(\frac{3}{3}\) which is \(\frac{3}{9}\)
b. \(\frac{2}{3}\) × 1 = \(\frac{2}{3}\) × – = \(\frac{14}{21}\)
Answer:
\(\frac{2}{3}\) × \(\frac{7}{7}\) = \(\frac{14}{21}\).
Explanation:
Given that \(\frac{2}{3}\) × 1, now we will place \(\frac{7}{7}\) to get the equation true. So \(\frac{2}{3}\) × \(\frac{7}{7}\) which is \(\frac{14}{21}\).
c. \(\frac{5}{2}\) × 1 = \(\frac{5}{2}\) × – = \(\frac{25}{}\)
Answer:
\(\frac{5}{2}\) × 1 = \(\frac{5}{2}\) × \(\frac{5}{5}\) = \(\frac{25}{10}\).
Explanation:
Given that \(\frac{5}{2}\) × 1, now we will place \(\frac{5}{5}\) to get the equation. So \(\frac{5}{2}\) × \(\frac{5}{10}\) which is \(\frac{25}{10}\).
d. Compare the first factor to the value of the product.
Question 2.
Express each fraction as an equivalent decimal. The first one is partially done for you.
a. \(\frac{3}{4}\) × \(\frac{25}{25}\) = \(\frac{3 × 25}{4 × 25}\) = \(\frac{}{100}\)=
Answer:
\(\frac{3}{4}\) × \(\frac{25}{25}\) = \(\frac{75}{100}\)= 0.75
Explanation:
Given that \(\frac{3}{4}\) × \(\frac{25}{25}\) which is \(\frac{75}{100}\) and the equivalent decimal of \(\frac{75}{100}\) is 0.75.
b. \(\frac{1}{4}\) × \(\frac{25}{25}\) =
Answer:
\(\frac{1}{4}\) × \(\frac{25}{25}\) = \(\frac{25}{100}\)= 0.25
Explanation:
Given that \(\frac{1}{4}\) × \(\frac{25}{25}\) which is \(\frac{25}{100}\) and the equivalent decimal of \(\frac{25}{100}\) is 0.25.
c. \(\frac{2}{5}\) × – =
Answer:
\(\frac{2}{5}\) × \(\frac{20}{20}\) = \(\frac{40}{100}\)= 0.40.
Explanation:
Given that \(\frac{2}{5}\) × \(\frac{20}{20}\) which is \(\frac{40}{100}\) and the equivalent decimal of \(\frac{40}{100}\) is 0.40.
d. \(\frac{3}{5}\) × – =
Answer:
\(\frac{3}{5}\) × \(\frac{20}{20}\) = \(\frac{60}{100}\)= 0.60
Explanation:
Given that \(\frac{3}{5}\) and we will place \(\frac{20}{20}\) which is \(\frac{3}{5}\) × \(\frac{20}{20}\) and the equivalent decimal of \(\frac{60}{100}\) is 0.60.
e. \(\frac{3}{20}\)
Answer:
\(\frac{3}{20}\) × \(\frac{5}{5}\) = \(\frac{15}{100}\)= 0.15.
Explanation:
Given that \(\frac{3}{20}\) and we will place \(\frac{5}{5}\) which is \(\frac{3}{20}\) × \(\frac{5}{5}\) = \(\frac{15}{100}\) and the equivalent decimal of \(\frac{15}{100}\) is 0.15.
f. \(\frac{25}{20}\)
Answer:
\(\frac{25}{20}\) × \(\frac{5}{5}\) = \(\frac{125}{100}\)= 1.25.
Explanation:
Given that \(\frac{25}{20}\) and we will place \(\frac{5}{5}\) which is \(\frac{25}{20}\) × \(\frac{5}{5}\) = \(\frac{125}{100}\) and the equivalent decimal of \(\frac{125}{100}\) is 1.25.
g. \(\frac{23}{25}\)
Answer:
\(\frac{23}{25}\) × \(\frac{4}{4}\) = \(\frac{92}{100}\)= 0.92.
Explanation:
Given that \(\frac{23}{25}\) and we will place \(\frac{4}{4}\) which is \(\frac{23}{25}\) × \(\frac{4}{4}\) = \(\frac{92}{100}\) and the equivalent decimal of \(\frac{92}{100}\) is 0.92..
h. \(\frac{89}{50}\)
Answer:
\(\frac{89}{50}\) × \(\frac{2}{2}\) = \(\frac{178}{100}\)= 1.78.
Explanation:
Given that \(\frac{89}{50}\) and we will place \(\frac{2}{2}\) which is \(\frac{89}{50}\) × \(\frac{2}{2}\) = \(\frac{178}{100}\) and the equivalent decimal of \(\frac{178}{100}\) is 1.78..
i. 3 \(\frac{11}{25}\)
Answer:
3\(\frac{11}{25}\) × \(\frac{4}{4}\) = \(\frac{344}{100}\)= 3.44.
Explanation:
Given that 3\(\frac{11}{25}\) and we will place \(\frac{4}{4}\) which is \(\frac{86}{25}\) × \(\frac{4}{4}\) = \(\frac{344}{100}\) and the equivalent decimal of \(\frac{344}{100}\) is 3.44.
j. 5 \(\frac{41}{50}\)
Answer:
5\(\frac{41}{50}\) × \(\frac{2}{2}\) = \(\frac{582}{100}\)= 5.82.
Explanation:
Given that 5\(\frac{41}{50}\) and we will place \(\frac{2}{2}\) which is \(\frac{291}{50}\) × \(\frac{2}{2}\) = \(\frac{582}{100}\) and the equivalent decimal of \(\frac{582}{100}\) is 5.82.
Question 3.
\(\frac{6}{8}\) is equivalent to \(\frac{3}{4}\) . How can you use this to help you write \(\frac{6}{8}\) as a decimal? Show your thinking to solve.
Answer:
\(\frac{75}{100}\) as decimal is 0.75.
Explanation:
Given that \(\frac{6}{8}\) is equivalent to \(\frac{3}{4}\), we can use this as \(\frac{3}{4}\) × \(\frac{25}{25}\) which is \(\frac{75}{100}\) as decimal is 0.75.
Question 4.
A number multiplied by a fraction is not always smaller than the original number. Explain this and give at least two examples to support your thinking.
Answer:
In a fraction, the above number is the numerator and the below number is the denominator. There are many kinds of fractions, some of are proper fraction and improper fraction. In a proper fraction, the numerator is smaller than the denominator. For example \(\frac{3}{4}\), \(\frac{5}{6}\) and in a improper fraction the numerator is bigger than the denominator. For example \(\frac{4}{3}\), \(\frac{6}{5}\)
Question 5.
Elise has \(\frac{3}{4}\) of a dollar. She buys a stamp that costs 44 cents. Change both numbers into decimals, and tell how much money Elise has after paying for the stamp.
Answer:
The remaining money Elise has after paying for her stamps is $0.31.
Explanation:
Given that Elise has \(\frac{3}{4}\) of a dollar and she buys a stamp that costs 44 cents, so to change both numbers into decimals we will pace \(\frac{25}{25}\) which will be \(\frac{3}{4}\) × \(\frac{25}{25}\) = \(\frac{75}{100}\) and n decimals it will be 0.75 and Elise has 0.75 × $1 = $0.75. Now we will convert 44 cents to dollars which will be 44 × \(\frac{1}{100}\) = \(\frac{44}{100}\) and in decimals it will be $0.44. So the remaining money Elise has after paying for her stamps is $0.75 – $0.44 which is $0.31.