We included **HMH Into Math Grade 5 Answer Key PDF** **Module 11 Lesson 2 Divide Whole Numbers by Unit Fractions **to make students experts in learning maths.

## HMH Into Math Grade 5 Module 11 Lesson 2 Answer Key Divide Whole Numbers by Unit Fractions

I Can represent division of a whole number by a unit fraction using visual fraction models and equations.

**Step It Out**

Question 1.

Cat and Ann complete a new obstacle course. The course is 2 miles long, and there is an obstacle every \(\frac{1}{4}\) mile. How many obstacles are there?

A. Model the situation with an equation. Let p stand for the number of obstacles.

Answer:

Equation:

p = 2 ÷ \(\frac{1}{4}\),

Explanation:

Given Cat and Ann complete a new obstacle course.

The course is 2 miles long and there is an obstacle every \(\frac{1}{4}\) mile.

Modeling the situation with an equation.

Let p stand for the number of obstacles

Number of obstacles are there

p = 2 ÷ \(\frac{1}{4}\).

B. Represent the division equation on the number line.

How does the number line represent the dividend?

Answer:

2 dividend,

Explanation:

Represented the division equation on the number line.

The number line represent the dividend 2.

Represent the divisor on the number line. Draw tick marks and label the fractions.

Answer:

Divisior on number line is \(\frac{1}{4}\),

Explanation:

Represented the divisor \(\frac{1}{4}\) on the number line. Drawn tick marks and label the fractions as shown above.

Represent the quotient. Count the number of fourths there are in 2 wholes.

Answer:

Quotient – 8

8 fourths,

Explanation:

Represented the quotient as 8,

Counted the number of 8 fourths there are in 2 wholes.

C. How many obstacles does the course have?

Answer:

8 obstacles,

Explanation:

There are 8 obstacles the course have.

**Turn and Talk** When representing fractions on a number line, how is the number of tick marks between each whole number related to the fraction you are representing?

Answer:

The number of tick marks represent the number parts,

Explanation:

Fractions represent parts of a whole.

So, fractions on the number line are represented by making equal parts of a whole i.e. 0 to 1 and the number of those equal parts would be the same as the number written in the denominator of the fraction.

For example, to represent 1/8 on the number line,

we have to divide 0 to 1 into 8 equal parts or 8 tick marks and mark the first part as 1/8.

Question 2.

Cat and Ann practice the rope climb at the obstacle course. The rope is 3 yards long and there is a knot every \(\frac{1}{3}\) yard. How many knots are there?

A. Model the situation with an equation. Let k represent the number of knots.

Answer:

k = 3 ÷ \(\frac{1}{3}\),

Explanation:

Given Cat and Ann practice the rope climb at the obstacle course. The rope is 3 yards long and there is a knot every \(\frac{1}{3}\) yard.

The situation with an equation and let k represent the number of knots is k = 3 ÷ \(\frac{1}{3}\).

B. Use the number line to represent the division equation.

- Represent the dividend by drawing and labeling the tick marks.
- Represent the divisor by drawing and labeling the tick marks.
- Represent the quotient by counting.

Answer:

Explanation:

Used the number line to represent the division equation above,

Represented the dividend 3 by drawing and labeling the tick marks.

Represented the divisor \(\frac{1}{3}\) by drawing and labeling the tick marks.

Represented the quotient by counting 9.

C. How many knots are on the rope?

Answer:

9 knots,

Explanation:

There are 9 knots on the rope.

D. What related multiplication equation can you use to solve the problem? Explain how you know.

Answer:

Multiplication equation:

3 X 3 = 9,

Explanation:

The multiplication equation is

3 X 3 = 9, when 3 ÷ \(\frac{1}{3}\) we

write reciprocal and multiply so 3 X 3 = 9.

**Turn and Talk** How are the dividend, the divisor, and the quotient represented on a number line to show division?

Answer:

Explanation:

On the number line the division is shown as

suppose for example 2÷ \(\frac{1}{3}\) we take 2 lines from 0 to 2 on number line as dividend then divide 0 to 1 with

3 lines to represent \(\frac{1}{3}\) as divisor and conmbined 6 lines of \(\frac{1}{3}\) from 0 to 2 represents quotient as shown above.

**Check Understanding**

**Write a division equation to model the situation. Then complete the number line and write a related multiplication equation to solve the problem.**

Question 1.

A walking trail is 4 miles long. There are benches along the trail every \(\frac{1}{2}\) mile. How many benches are there?

Answer:

Division equation:

4÷ \(\frac{1}{2}\),

Multiplication equation:

4 X 2 = 8,

8 benches,

Explanation:

Given a walking trail is 4 miles long. There are benches along the trail every \(\frac{1}{2}\) mile.

Division equation:

4÷ \(\frac{1}{2}\),

number line is shown above,

Multiplication equation:

4 X 2 = 8,

Number of benches are there 4 ÷ \(\frac{1}{2}\) =

4 X 2 = 8 benches.

**On Your Own**

Question 2.

**Model with Mathematics** Duane and his family are playing a game. Duane scores 11 points. Each tile match is \(\frac{1}{3}\) point. Model the situation with an equation. How many tile matches does Duane make?

Answer:

Equation:

11 ÷ \(\frac{1}{3}\),

Duane makes 33 tile matches,

Explanation:

Given Duane and his family are playing a game.

Duane scores 11 points. Each tile match is \(\frac{1}{3}\) point.

The situation with an equation is 11 ÷ \(\frac{1}{3}\),

Number of tile matches does Duane make are

11 X 3 = 33 tile matches.

Question 3.

**Model with Mathematics** Mila swims 3 miles at the pool. She stops to take a break every \(\frac{1}{2}\) mile. How many times does Mila stop to take a break?

Model the situation with an equation.

Answer:

Equation:

3 ÷ \(\frac{1}{2}\),

6 times,

Explanation:

Given Mila swims 3 miles at the pool.

She stops to take a break every \(\frac{1}{2}\) mile. number of times does Mila stop to take a break, the situation with an equation is 3 ÷ \(\frac{1}{2}\),

3 X 2 = 6 times.

Represent the dividend, divisor, and quotient on the number line.

Answer:

Explanation:

Represented the dividend – 3,

divisor – \(\frac{1}{2}\) and quotient 6 on the number line above.

How many times does Mila stop to take a break? Write a related multiplication equation to represent the number of times Mila stops to take a break.

Answer:

Multiplication equation:

3 X 2 = 6 times,

6 times Mila stops to take a break,

Explanation:

Multiplication equation to represent the number of times

Mila stops to take a break is 3 X 2 = 6,

So 6 times Mila stops to take a break.

**Divide. Write a related multiplication equation to solve.**

Question 4.

4 ÷ \(\frac{1}{5}\) = n

Answer:

n = 20,

Explanation:

Given 4 ÷ \(\frac{1}{5}\) = n,

So n = 4 X 5 = 20.

Question 5.

n = 8 ÷ \(\frac{1}{3}\)

Answer:

n = 24,

Explanation:

Given 8 ÷ \(\frac{1}{3}\) = n,

So n = 8 X 3 = 24.

Question 6.

4 ÷ \(\frac{1}{9}\) = n

Answer:

36,

Explanation:

Given 4 ÷ \(\frac{1}{9}\) = n,

So n = 4 X 9 = 36.

Question 7.

An oceanic probe descends \(\frac{1}{2}\) kilometer each minute. How many minutes will it take the probe to descend 10 kilometers into the deepest part of the ocean?

Answer:

20 minutes,

Explanation:

Given an oceanic probe descends \(\frac{1}{2}\) kilometer

each minute. Number of minutes will it take the probe to

descend 10 kilometers into the deepest part of the ocean is

10 ÷ \(\frac{1}{2}\) = 10 X 2 = 20 minutes.

Question 8.

Each bag of crackers in a box represents \(\frac{1}{15}\) of the box. How many bags of crackers are in 3 boxes?

Answer:

45 bags,

Explanation:

Given each bag of crackers in a box represents

\(\frac{1}{15}\) of the box.

Number of bags of crackers are in 3 boxes are

3 ÷ \(\frac{1}{15}\) = 3 X 15 = 45 bags.

Question 9.

**Construct Arguments** For what whole number value(s) of a is 17 ÷ \(\frac{1}{a}\) less than 17? Justify your reasoning.

Answer:

a = 0,

Explanation:

Asking to find what whole number value(s) of a is

17 ÷ \(\frac{1}{a}\) less than 17 is

If we take a values 2 or more than 2 it will be more

than 17,

If a = 1 then17 ÷ \(\frac{1}{a}\) =

17 X 1 = 17 which is not valid statement not less than 17,

If a = 0 then 17 X 0 < 17 statement is true, So we will take

only for values of a = 0.

Question 10.

**Model with Mathematics** Valerie has 6 feet of red ribbon and 25 feet of blue ribbon that she cuts into equal pieces.

How many pieces of the red ribbon does she cut if each is \(\frac{1}{12}\) foot long? Write a division equation and a related multiplication equation to solve.

Answer:

Division equation:

6 ÷ \(\frac{1}{12}\),

Multiplication equation:

6 X 12 = 72,

72 pieces of red ribbon,

Explanation:

Given Valerie has 6 feet of red ribbon that she cuts into equal pieces.

Number pieces of the red ribbon does she cut if each is

\(\frac{1}{12}\) foot long ,

division equation is 6 ÷ \(\frac{1}{12}\),

Multiplication equation: 6 X 12 = 72 upon solving we

get 72 pieces of red ribbon.

How many pieces of the blue ribbon does she cut if each is \(\frac{1}{3}\) foot long? Write a division equation and a related multiplication equation to solve.

Answer:

Division equation:

25 ÷ \(\frac{1}{3}\),

Multiplication equation:

25 X 3 = 75,

75 pieces of blue ribbon,

Explanation:

Given Valerie has 25 feet of blue ribbon that she cuts into equal pieces.

Number pieces of the blue ribbon does she cut if each is

\(\frac{1}{3}\) foot long , division equation is 25 ÷ \(\frac{1}{3}\),

Multiplication equation: 25 X 3 = 75 upon solving we

get 75 pieces of blue ribbon.

**Divide. Write a related multiplication equation to solve.**

Question 11.

14 ÷ \(\frac{1}{3}\) = n

Answer:

Multiplication equation:

14 X 3 = n,

n = 42,

Explanation:

Given 14 ÷ \(\frac{1}{3}\) = n, the multiplication equation is 14 X 3 = n,

so n = 42.

Question 12.

n = 5 ÷ \(\frac{1}{16}\)

Answer:

Multiplication equation:

n = 5 X 16,

n = 80,

Explanation:

Given n = 5 ÷ \(\frac{1}{16}\), the multiplication equation is n = 5 X 16,

so n = 80.

Question 13.

**Open-Ended** Maggie has a goal of jogging 100 miles. The distance she rules each day is the same unit fraction. What are some possible fractions of a mile she can run each day and the number of days it will take her to reach her goal? Explain how you found your answers.

Answer:

\(\frac{1}{10}\) of goal miles each day,

10 days,

Explanation:

Given Maggie has a goal of jogging 100 miles.

The distance she rules each day is the same unit fraction.

Some possible fractions of a mile she can run each day and the number of days it will take her to reach her goal,

let’s take substituting she should run

\(\frac{1}{10}\) of goal miles

she run each day, So for 10 days it is

10 ÷ \(\frac{1}{10}\) therefore

10 X 10 = 100 miles.