We included **HMH Into Math Grade 5 Answer Key PDF** **Module 10 Lesson 1 Interpret a Fraction as Division **to make students experts in learning maths.

## HMH Into Math Grade 5 Module 10 Lesson 1 Answer Key Interpret a Fraction as Division

I Can interpret fractions as representing division of whole numbers.

**Spark Your Learning**

An elementary school receives 5 boxes of minerals for its earth science classes. The 6 science teachers at the school share the boxes equally for their classes. What fraction of a box will each teacher receive?

Answer:

Each teacher will receive \(\frac{6}{5}\),

Explanation:

Given an elementary school receives 5 boxes of minerals for its earth science classes. The 6 science teachers at the school share the boxes equally for their classes. The fraction of a box will each teacher receive is as total it is 6 and there are 5 boxes so each will receive

number of teachers 6 by 5 boxes is \(\frac{6}{5}\).

**Turn and Talk** What would happen if the school had received 8 boxes or 4 boxes? Describe how to determine the fraction of a box each teacher would get for different numbers of boxes.

Answer:

For 8 boxes – \(\frac{6}{8}\),

for 4 boxes – \(\frac{6}{4}\),

Explanation:

If the school had received 8 boxes then 6 teachers will receive as \(\frac{6}{8}\) or if it is 4 boxes then it will be

\(\frac{6}{4}\), therefore the fraction of a box each teacher would get for different numbers of boxes depneds upon number of teachers divided by number of boxes received.

**Build Understanding**

Question 1.

Five students in the science club prepare 4 circuit boards for a small satellite called a CubeSat. If they share the work equally, how many circuit boards does each student prepare?

A. Draw to represent the situation.

Answer:

Explanation:

Given five students in the science club prepare 4 circuit boards for a small satellite called a CubeSat.

If they share the work equally, to represent the situation

A. Drawn to represent the situation as shown above.

B. How does your drawing represent the situation?

Answer:

Four circuits by 5 students,

Explanation:

The drawing reprsents 4 circuits are done by 5 students.

C. What does the expression 4 ÷ 5 model?

Answer:

4 among 5,

Explanation:

The expression models 4 among 5.

Connect to Vocabulary

In an earlier lesson, you divided whole-number dividends by 2-digit divisors to find quotients.

D. Write a division equation to model the situation.

Answer:

4 ÷ 5,

Explanation:

The division equation to model the situation is

4 ÷ 5.

E. What does your quotient represent?

Answer:

0.8,

Explanation:

The quotient represents each student had done

0.8 part of the circuit.

**Turn and Talk** In Part D, you wrote a division equation to model the situation. How does the equation show the relationship between division and a fraction?

Answer:

Fraction: Numerator by denominator,

Explanation:

The relationship between division and fraction is the fraction shows the numerator divided by the denominator.

The number above the fraction bar is the numerator and the one below the fraction bar is the denominator.

A numerator represents the number of parts out of the whole.

Question 2.

Two scientists develop a new substance in a laboratory. They make a total of 5 milliliters. If the substance is shared equally, how many milliliters does each scientist get?

A. Draw to represent the situation.

Answer:

Explanation:

Drawn to represent the situation as shown above

\(\frac{5}{2}\).

B. How does your visual model represent the dividend, the divisor, and the quotient of a division equation that models this situation?

Answer:

Dividend is 5, divisor is 2 and quotient is 2.5,

Explanation:

The visual model represents the dividend as 5 full the divisor 2 has divided 5 into two parts as quotient 2.5 each in green and cream colors.

C. What is the size of each group and what does it mean for this situation?

Answer:

Each group is 2.5, it is half of 5,

Explanation:

As quotient is 2.5 the size of each group is 2.5, it means 5 is divided into 2 parts so the each group is of 2.5.

D. What division expression models the situation?

Answer:

\(\frac{5}{2}\),

Explanation:

Given two scientists develop a new substance in a laboratory. They make a total of 5 milliliters.

If the substance is shared equally, the division expression model for the situation is \(\frac{5}{2}\),

E. Divide the expression you wrote in Part D and compare it to your answer in Part C.

Answer:

Both are same,

Explanation:

Milliliters does each scientist get and the division expression model for the situation we have is \(\frac{5}{2}\),

on dividing we get each will get 2.5 milliliters which is same as we got in part C each group has 2.5,

So both are same.

**Turn and Talk** Denisa divides the expression in Part D and gets \(\frac{5}{2}\), while Cal divides and gets 2\(\frac{1}{2}\). Who is correct and why? How do you know whether the answers are reasonable?

Answer:

Both are correct, both results are same so answers are reasonable

Explanation:

Given Denisa divides the expression in Part D and gets \(\frac{5}{2}\), while Cal divides and

gets 2\(\frac{1}{2}\) as 2\(\frac{1}{2}\) =

2\(\frac{2 X 2 + 1}{2}\) = \(\frac{5}{2}\),

both Denisa and Cal are same both results are same, so

answer is also reasonable.

**Check Understanding**

**Represent the situation with an equation or visual model and solve.**

Question 1.

Three runners in a relay race share the 8-mile distance equally. How many miles does each runner travel?

Answer:

\(\frac{8}{3}\) or 2\(\frac{2}{3}\),

Explanation:

Given three runners in a relay race share the 8-mile distance equally. So miles does each runner travel are

\(\frac{8}{3}\) = \(\frac{2 X 3 + 2}{3}\) = 2\(\frac{2}{3}\).

**On Your Own**

**Model with Mathematics** Model the situation with a division equation and find the quotient.

Question 2.

Five friends share 6 small bags of popcorn, If they share the popcorn equally, how many bags of popcorn does each friend receive?

Answer:

\(\frac{6}{5}\) or 1\(\frac{1}{5}\),

quotient is 1.2 bags of popcorn each friend receive,

Explanation:

Given five friends share 6 small bags of popcorn,

If they share the popcorn equally, Number of bags of

popcorn does each friend receive is \(\frac{6}{5}\) =

\(\frac{5 X 1 + 1}{5}\) = 1\(\frac{1}{5}\).

quotient is 1.2, so 1.2 bags of popcorn each friend receive.

Question 3.

Twelve friends shovel snow from 8 identical driveways, If they share the work evenly, what part of a driveway does each friend shovel?

Answer:

\(\frac{2}{3}\),

Explanation:

Given twelve friends shovel snow from 8 identical driveways,

If they share the work evenly, So part of a driveway does

each friend shovel is \(\frac{8}{12}\) as both

numerator and denominator goes in 4 as 4 X 2 = 8 and

4 X 3 = 12 , so \(\frac{4 X 2 }{4 X 3}\) = \(\frac{2}{3}\).

Question 4.

**Open-Ended** Describe a situation that can be modeled by 3 -H 5. Then draw a visual model to represent the situation and use it to find the quotient.

Answer:

Question 5.

An audio engineer divides 9 feet of cable into 2 equal sections to connect a pair of speakers. How long is each section of cable?

Answer:

Each section is 4.5 feet long,

Explanation:

Given an audio engineer divides 9 feet of cable into

2 equal sections to connect a pair of speakers.

Long is each section of cable \(\frac{9}{2}\),

2) 9(4.5

8

1.0

1.0

0

4.5 feet.

Question 6.

**Reason** Two groups of people sit at different tables in a restaurant. The first group of 6 people orders three small pizzas. The second group of 8 people orders four small pizzas. The people at each table share their pizzas equally. How does the amount of pizza per person at each table compare? Explain.

Answer:

Each table per person will get \(\frac{1}{2}\) amount of pizza,

Explanation:

Given two groups of people sit at different tables in a restaurant. The first group of 6 people orders three small pizzas. The second group of 8 people orders four small pizzas. The people at each table share their pizzas equally, table 1 people they get share as

\(\frac{3}{6}\) = \(\frac{3 X 1}{3 X 2}\) = \(\frac{1}{2}\),

table 2 second group people will get \(\frac{4}{8}\) =

\(\frac{4 X 1}{4 X 2}\) = \(\frac{1}{2}\),

As both tables it is \(\frac{1}{2}\) so each table per person will get \(\frac{1}{2}\) amount of pizza.

**I’m in a Learning Mindset!**

What strategies can I use to model a division situation?

Answer:

Six division strategies,

Explanation:

The six division strategies include:

- equal groups.
- partition.
- fact family.
- repeated subtraction.
- long division.
- short division.