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

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.
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?

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.
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.
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?
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?
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.
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.

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?
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.
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?

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?

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.

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?

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.
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.

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.
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
n = 20,

Explanation:
Given 4 ÷ $$\frac{1}{5}$$ = n,
So n = 4 X 5 = 20.

Question 5.
n = 8 ÷ $$\frac{1}{3}$$
n = 24,

Explanation:
Given 8 ÷ $$\frac{1}{3}$$ = n,
So n = 8 X 3 = 24.

Question 6.
4 ÷ $$\frac{1}{9}$$ = n
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?
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?
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.
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.
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.
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
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 ÷ $$\frac{1}{16}$$
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.
$$\frac{1}{10}$$ 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.

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