We included HMH Into Math Grade 6 Answer Key PDF Module 3 Review to make students experts in learning maths.

Vocabulary

reciprocal
multiplicative inverse

Complete the following to review your vocabulary for this module.

Question 1.
Describe in your own words what it means for two numbers to be reciprocals, or multiplicative inverses.
______________
Answer: Multiplicative Inverse or Reciprocal. The reciprocal of a number is this fraction flipped upside down. When the product of two numbers is one, they are called reciprocals or multiplicative inverses of each other.

Question 2.
Give an example of two numbers that are reciprocals, or multiplicative inverses.
_________________
Answer: The reciprocal of 5 is one-fifth (1/5 or 0.2), and the reciprocal of 0.25 is 1/4.

Concepts and Skills

Question 3.
Which number sentences are true? Select all that apply.
A. $$\frac{1}{2}$$ ÷ 3 = 2 × $$\frac{1}{3}$$
B. $$\frac{2}{3}$$ ÷ $$\frac{4}{5}$$ = $$\frac{3}{2}$$ ÷ $$\frac{4}{5}$$
C. $$\frac{7}{10}$$ ÷ $$\frac{1}{42}$$ = $$\frac{7}{10}$$ × 42
D. $$\frac{5}{9}$$ ÷ $$\frac{5}{6}$$ = $$\frac{5}{9}$$ × $$\frac{6}{5}$$
E. $$\frac{5}{10}$$ ÷ $$\frac{2}{10}$$ = $$\frac{5}{10}$$ × $$\frac{2}{10}$$
A. $$\frac{1}{2}$$ ÷ 3 = 2 × $$\frac{1}{3}$$
$$\frac{1}{2}$$ ÷ 3 = (1×1)/(2×3) = $$\frac{1}{6}$$
B. $$\frac{2}{3}$$ ÷ $$\frac{4}{5}$$ = $$\frac{3}{2}$$ ÷ $$\frac{4}{5}$$
$$\frac{2}{3}$$ ÷ $$\frac{4}{5}$$ = $$\frac{5}{6}$$
$$\frac{3}{2}$$ ÷ $$\frac{4}{5}$$ = 1$$\frac{7}{8}$$
C. $$\frac{7}{10}$$ ÷ $$\frac{1}{42}$$ = $$\frac{7}{10}$$ × 42 is true
D. $$\frac{5}{9}$$ ÷ $$\frac{5}{6}$$ = $$\frac{5}{9}$$ × $$\frac{6}{5}$$ is true
E. $$\frac{5}{10}$$ ÷ $$\frac{2}{10}$$ = $$\frac{5}{10}$$ × $$\frac{2}{10}$$
$$\frac{5}{10}$$ ÷ $$\frac{2}{10}$$ = $$\frac{5}{10}$$ × $$\frac{10}{2}$$
So, Option C, D are correct answers.

Question 4.
What is the value of the expression 1$$\frac{2}{3}$$ × 2$$\frac{4}{5}$$?
___________________________
1$$\frac{2}{3}$$ × 2$$\frac{4}{5}$$
Convert from mixed fraction to the improper fraction.
$$\frac{5}{3}$$ × $$\frac{14}{5}$$ = $$\frac{5×14}{3×5}$$ = $$\frac{70}{15}$$ = 4$$\frac{2}{3}$$

Question 5.
Use Tools A piece of wood was 12 feet long. Kendra cut the wood into pieces $$\frac{2}{3}$$ foot long. How many pieces did Kendra make? State what strategy and tool you will use to answer the question, explain your choice, and then find the answer.
Given that,
A piece of wood was 12 feet long. Kendra cut the wood into pieces $$\frac{2}{3}$$ foot long.
12 ÷ $$\frac{2}{3}$$ = $$\frac{12}{1}$$ ÷ $$\frac{2}{3}$$
= $$\frac{12×3}{1×2}$$
= $$\frac{36}{2}$$
= 18
Thus Kendra can make 18 pieces.

Question 6.
Which expression is equivalent to $$\frac{2}{3}$$ ÷ $$\frac{3}{5}$$ ?
A. $$\frac{2}{3}$$ × $$\frac{3}{5}$$
B. $$\frac{2}{3}$$ × $$\frac{5}{3}$$
C. $$\frac{3}{2}$$ × $$\frac{3}{5}$$
D. $$\frac{3}{2}$$ × $$\frac{5}{3}$$
Answer: B. $$\frac{2}{3}$$ × $$\frac{5}{3}$$
Explanation:
$$\frac{2}{3}$$ ÷ $$\frac{3}{5}$$
This can be written in the multiplication inverse as,
$$\frac{2}{3}$$ ÷ $$\frac{3}{5}$$ = $$\frac{2}{3}$$ × $$\frac{5}{3}$$
Option B is the correct answer.

Question 7.
Mitchell spent 1$$\frac{3}{4}$$ hours at the doctor’s office and a total of 1$$\frac{1}{2}$$ hours driving to and from the appointment. Which expression shows the total number of hours Mitchell spent away from home for his visit to the doctor?
A. 1$$\frac{3}{4}$$ – 1$$\frac{1}{2}$$
B. 1$$\frac{3}{4}$$ × 1$$\frac{1}{2}$$
C. 1$$\frac{3}{4}$$ ÷ 1$$\frac{1}{2}$$
D. 1$$\frac{3}{4}$$ + 1$$\frac{1}{2}$$
Answer: D. 1$$\frac{3}{4}$$ + 1$$\frac{1}{2}$$
Explanation:
Given,
Mitchell spent 1$$\frac{3}{4}$$ hours at the doctor’s office and a total of 1$$\frac{1}{2}$$ hours driving to and from the appointment.
To find the total number of hours Mitchell spent away from home for his visit to the doctor we have to add the number of hours he spent.
So, the expression will be 1$$\frac{3}{4}$$ + 1$$\frac{1}{2}$$
Option D is the correct answer.

Question 8.
On 5 days of every week, Jackie runs 2$$\frac{1}{2}$$ miles in the morning. How many total miles does Jackie run every week?
___________________________
Given,
On 5 days of every week, Jackie runs 2$$\frac{1}{2}$$ miles in the morning.
5 × 2$$\frac{1}{2}$$
Convert from mixed fraction to the improper fraction.
2$$\frac{1}{2}$$ = $$\frac{5}{2}$$
5 × $$\frac{5}{2}$$ = $$\frac{25}{2}$$ = 12$$\frac{1}{2}$$
Thus Jackie run 12$$\frac{1}{2}$$ miles every week.

Question 9.
Andy rode his bicycle 2$$\frac{4}{5}$$ miles on Monday and 1$$\frac{3}{10}$$ miles on Tuesday.

A. Write each amount using the LCM.
_____________________
Given,
Andy rode his bicycle 2$$\frac{4}{5}$$ miles on Monday and 1$$\frac{3}{10}$$ miles on Tuesday.
2$$\frac{4}{5}$$ + 1$$\frac{3}{10}$$
LCM of 5 and 10 is 10.
Convert from mixed fraction to the improper fraction.
$$\frac{28}{10}$$ + $$\frac{13}{10}$$

B. How many total miles did Andy ride on the two days?
_____________________
$$\frac{14}{5}$$ + $$\frac{13}{10}$$
LCM of 5 and 10 is 10.
$$\frac{28}{10}$$ + $$\frac{13}{10}$$ = $$\frac{41}{10}$$ = 4.1 miles
Therefore Andy rides 4.1 miles on the two days.

Question 10.
Find the quotient of 4$$\frac{4}{5}$$ ÷ $$\frac{4}{5}$$. Explain how you can use the GCF to write your answer in simplest form.
_____________________
_____________________
4$$\frac{4}{5}$$ ÷ $$\frac{4}{5}$$
Convert from mixed fraction to the improper fraction.
$$\frac{24}{5}$$ ÷ $$\frac{4}{5}$$ = (24 × 5)/(5 × 4)
= $$\frac{120}{20}$$
= 6
4$$\frac{4}{5}$$ ÷ $$\frac{4}{5}$$ = 6

Question 11.
Lynda is making curtains. She has 2$$\frac{1}{3}$$ yards of material. She wants to make 3 curtains. She needs $$\frac{8}{9}$$ yard for each curtain. Does she have enough material to make 3 curtains? Explain.
Given,
Lynda is making curtains. She has 2$$\frac{1}{3}$$ yards of material.
She wants to make 3 curtains.
She needs $$\frac{8}{9}$$ yard for each curtain.
To know whether she is having enough material or not we have to divide 2$$\frac{1}{3}$$ by $$\frac{8}{9}$$
2$$\frac{1}{3}$$ ÷ $$\frac{8}{9}$$
Convert from mixed fraction to the improper fraction.
$$\frac{7}{3}$$ ÷ $$\frac{8}{9}$$
$$\frac{7×9}{3×8}$$
$$\frac{63}{24}$$
2$$\frac{5}{8}$$
So, Lynda does not have enough material to make 3 curtains.

Question 12.
Ken wants to install a row of ceramic tiles on a wall that is 21$$\frac{3}{8}$$ inches wide. Each tile is 4$$\frac{1}{2}$$ inches wide.
A. How many whole tiles does he need? ______________
B. What fraction of a tile must he install at the end of the row to totally fill the space? _____________________
A. Given,
Ken wants to install a row of ceramic tiles on a wall that is 21$$\frac{3}{8}$$ inches wide.
Each tile is 4$$\frac{1}{2}$$ inches wide.
21$$\frac{3}{8}$$ ÷ 4$$\frac{1}{2}$$
Convert from mixed fraction to the improper fraction.
$$\frac{171}{8}$$ ÷ $$\frac{9}{2}$$ = 4$$\frac{3}{4}$$
He needs 4$$\frac{3}{4}$$ whole tiles, you could round it to 5 whole tiles. He needed 4$$\frac{3}{4}$$ whole tiles.
B. To completely fill in all the spaces on the wall evenly, it needs to be 5 even, while, tiles.
To fill in the empty space, you must subtract 5 and 4 3/4, which explains why Part A and the answer 4 3/4
So, Subtraction: 5- 4$$\frac{3}{4}$$ = $$\frac{1}{4}$$

Question 13.
How many times as long is a line measuring 9$$\frac{1}{3}$$ yards as a line measuring
3$$\frac{1}{2}$$ yards? ________
Given,
9$$\frac{1}{3}$$ ÷ 3$$\frac{1}{2}$$
This can be written as
9$$\frac{2}{6}$$ ÷ 3$$\frac{3}{6}$$
Convert from mixed fraction to the improper fraction.
$$\frac{56}{6}$$ × $$\frac{6}{21}$$
$$\frac{56}{21}$$ = 2 $$\frac{14}{21}$$ = 2 $$\frac{2}{3}$$

Question 14.
A mural is 12$$\frac{5}{6}$$ feet long and is divided into 7 equal-length panels. How many feet long is each panel? ______________
A mural is 12$$\frac{5}{6}$$ feet long and is divided into 7 equal-length panels
12$$\frac{5}{6}$$ ÷ 7
12$$\frac{5}{6}$$ = $$\frac{77}{6}$$
$$\frac{77}{6}$$ ÷ 7 = $$\frac{77}{42}$$ = 1$$\frac{5}{6}$$