# Into Math Grade 5 Module 11 Lesson 5 Answer Key Interpret and Solve Division of a Unit Fraction by a Whole Number

We included HMH Into Math Grade 5 Answer Key PDF Module 11 Lesson 5 Interpret and Solve Division of a Unit Fraction by a Whole Number to make students experts in learning maths.

## HMH Into Math Grade 5 Module 11 Lesson 5 Answer Key Interpret and Solve Division of a Unit Fraction by a Whole Number

I Can create a story context for a given equation and use a visual fraction model to represent the quotient.

Step It Out

Question 1.
Write a word problem that can be modeled by p = $$\frac{1}{2}$$ ÷ 4. Then use a visual fraction model to solve the problem.
A. Write a word problem that can be modeled by the equation.
Word problem:
” A pizza of $$\frac{1}{2}$$ has been distributed
among 4 friends how much part did each get?”,

Explanation:
Wrote a word problem that can be modeled by the equation.
Word problem:
” A pizza of $$\frac{1}{2}$$ has been distributed
among 4 friends how much part did each get?”.

B. Represent your word problem with a rectangle.

• Divide the rectangle to represent the equation.
• Shade the part to represent the quotient.

Explanation:
Represented my word problem with a rectangle above,
Divided the rectangle to represent the equation
p = $$\frac{1}{2}$$ ÷ 4,
Shaded the part $$\frac{1}{8}$$ to represent
quotient.

C. Explain how you used the rectangle.
First $$\frac{1}{2}$$,
Second $$\frac{1}{2}$$ ÷ 4 parts,

Explanation:
I have divided first whole rectangle into
$$\frac{1}{2}$$ parts then again I divided
$$\frac{1}{2}$$ by 4 parts.

D. What fraction of your rectangle represents the quotient?
$$\frac{1}{8}$$,

Explanation:
The part of $$\frac{1}{8}$$ of my rectangle
represents the quotient.

E. Interpret the quotient in the context of your word problem.
p = $$\frac{1}{8}$$ part of pizza for each friend,

Explanation:
Given word problem:
” A pizza of $$\frac{1}{2}$$ has been distributed
among 4 friends how much part did each get?”,
So let each freind will get part p so p = $$\frac{1}{2}$$ ÷ 4
solving p = $$\frac{1}{2}$$ X $$\frac{1}{4}$$ =
$$\frac{1}{2 X 4}$$ = $$\frac{1}{8}$$,
therefore each friend will get p = $$\frac{1}{8}$$ part of pizza.

Turn and Talk Why should you divide each half of the rectangle into 4 equal groups?
It is $$\frac{1}{2}$$ ÷ 4,

Explanation:
We divide each half of the rectangle into 4 equal groups because it is given to find half and again half is been divided 4 equal groups.

Question 2.
Write a word problem for the equation t = $$\frac{1}{3}$$ ÷ 2. Then use a visual model to solve and represent the quotient.
A. Write a word problem that can be modeled by the equation.
Word problem:
“Billy has $$\frac{1}{3}$$ of a pound of trail mix,
he want to share equally between himself and brother,
how much each will get?”,

Explanation:
Asking to write word problem for the equation
t = $$\frac{1}{3}$$ ÷ 2 so word problem:
“Billy has $$\frac{1}{3}$$ of a pound of trail mix,
he want to share equally between himself and brother,
how much each will get?”.

B. Draw a visual model to represent the quotient.

Explanation:
Drawn a visual model to represent the quotient
$$\frac{1}{6}$$,

C. Interpret the quotient in the context of your problem.
Each will get $$\frac{1}{6}$$ part of trail mix,

Explanation:
Given word problem for the equation
t = $$\frac{1}{3}$$ ÷ 2 as
“Billy has $$\frac{1}{3}$$ of a pound of trail mix,
he want to share equally between himself and brother,
how much each will get?”. Upon solving
t = $$\frac{1}{3}$$ ÷ 2 we get
t = $$\frac{1}{3}$$ X $$\frac{1}{2}$$,
t = $$\frac{1}{3 X 2}$$,
t = $$\frac{1}{6}$$, therefore each will get
$$\frac{1}{6}$$ part of trail mix.

Turn and Talk Does it matter what visual model you use to find the quotient of a unit fraction divided by a whole number? Why might you choose one model over another? Explain.
Yes, it matters,

Explanation:
Yes, it matters we use different visual model to find the quotient of a unit fraction divided by a whole number
Area model: In the area model fractions are represented as parts of an area or region.
Useful manipulatives include rectangular or circular fraction sets, pattern blocks, geoboards and tangrams.
Rectangular or circular sets can be used to develop the understanding that fractions are parts of a whole, to compare fractions, to generate equivalent fractions and to explore operations with fractions.  While the rectangular model is easier to draw precisely, the circular
model emphasizes the part-whole concept of fractions and the meaning of the relative size of a part to the whole.
Linear model: In the linear model lengths are compared instead of areas. Either number lines are
drawn and subdivided or physical materials are compared on the basis of length.
Useful manipulatives include Cuisenaire rods or fraction strips that are easily connected to ideas about
fractions on a number line.
Fraction strips can be used to explore equivalency, comparison of fractions, ordering fractions and number operations with fractions.

Check Understanding

Question 1.
Write and solve a word problem for the equation $$\frac{1}{5}$$ ÷ 2 = c. Represent the quotient using the rectangle.
Word problem:
“How much ice cream will each person get if 2 people
share $$\frac{1}{5}$$ kg of ice cream equally?”,
$$\frac{1}{10}$$ kg of ice cream each will get,

Explanation:
Word problem for the equation $$\frac{1}{5}$$ ÷ 2 = c is
“How much ice cream will each person get if 2 people
share $$\frac{1}{5}$$ kg of ice cream equally?”,
Solving c = $$\frac{1}{5}$$ ÷ 2,
c = $$\frac{1}{5}$$ X $$\frac{1}{2}$$ =
c = $$\frac{1}{5 X 2}$$ = $$\frac{1}{10}$$,
C is the quotient and each person will get $$\frac{1}{10}$$ kg
of icecream, represented the quotient using the rectangle as shown above.

Question 2.
Complete the word problem that is represented by the equation m = $$\frac{1}{6}$$ ÷ 3. Then draw a visual model to represent the quotient.
__________ friends share ________ of a bag of marbles equally. Each friend gets ________ of the whole bag.
3 friends share $$\frac{1}{6}$$ of a bag of marbles
equally. Each friend gets $$\frac{1}{18}$$ of the whole bag,

Explanation:
Completed the word problem that is represented by
the equation m = $$\frac{1}{6}$$ ÷ 3 as
3 friends share $$\frac{1}{6}$$ of a bag of marbles
equally. Each friend gets $$\frac{1}{18}$$ of the whole bag,
So quotient m = $$\frac{1}{6}$$ ÷ 3 =
$$\frac{1}{6}$$ X $$\frac{1}{3}$$ =
$$\frac{1}{6 X 3}$$ = $$\frac{1}{18}$$.
Drawn a visual model to represent the quotient above.

Question 3.
Model with Mathematics Write a word problem for the equation $$\frac{1}{4}$$ ÷ 4 = c. Then write a related multiplication equation to solve.
Word problem:
“I have $$\frac{1}{4}$$ box of erasers,
I share among four friends, What fraction of the box should each friend should get?”,
Multiplication equation:
$$\frac{1}{4}$$ X $$\frac{1}{4}$$,
Each will get $$\frac{1}{16}$$ box of erasers,

Explanation:
Aked to write a word problem for the equation
$$\frac{1}{4}$$ ÷ 4 = c. Word problem
“I have $$\frac{1}{4}$$ box of erasers,
I share among four friends, What fraction of the box
should each friend should get?”,
so let c will be each one will get $$\frac{1}{4}$$ ÷ 4 = c,
Multiplication equation:
$$\frac{1}{4}$$ X $$\frac{1}{4}$$ solving
c= $$\frac{1}{4 X 4}$$,
c = $$\frac{1}{16}$$,
Therefore each will get $$\frac{1}{16}$$ box of erasers.

Question 4.
Use Tools Use the circle to write and solve a word problem involving a clock for m = $$\frac{1}{2}$$ ÷ 6.

Word problem:
“6 people constructed a piece of wall in m = $$\frac{1}{2}$$ hour,
how much time in the clock it will show for one person?”,
$$\frac{1}{12}$$ hour,

Explanation:
Used the circle to write and solve a word problem
involving a clock for m = $$\frac{1}{2}$$ ÷ 6 as
word problem:
“6 people constructed a piece of wall in m = $$\frac{1}{2}$$ hour,
how much time in the clock it will show for one person?”, Solving
m = $$\frac{1}{2}$$ ÷ 6,
m = $$\frac{1}{2}$$ X $$\frac{1}{6}$$,
m = $$\frac{1}{2 X 6}$$,
m = $$\frac{1}{12}$$, therefore it will take
m = $$\frac{1}{12}$$ hour for each person.

Model with Mathematics Complete the word problem to represent the equation. Then draw a visual model to represent and solve the problem.

Question 5.
$$\frac{1}{5}$$ ÷ 6 = c
Julie cleans __________ carpets using _________ of a bottle of cleaner. She uses the same amount for each carpet. She uses _________ of a bottle on one carpet.
Word problem:
“Julie cleans 6 carpets using $$\frac{1}{5}$$ of a
bottle of cleaner. She uses the same amount for each carpet.
She uses $$\frac{1}{30}$$ of a bottle on one carpet.

Explanation:
Completed the word problem to represent the equation
$$\frac{1}{5}$$ ÷ 6 = c as
“Julie cleans 6 carpets using $$\frac{1}{5}$$ of a
bottle of cleaner. She uses the same amount for each carpet.
She uses $$\frac{1}{30}$$ of a bottle on one carpet.
Drawn a visual model to represent the equation above
solving $$\frac{1}{5}$$ ÷ 6 = c,
c = $$\frac{1}{5}$$ X $$\frac{1}{6}$$,
c = $$\frac{1}{5 X 6}$$,
c = $$\frac{1}{30}$$.

Question 6.
Attend to Precision For the equation $$\frac{1}{8}$$ ÷ 2 = r:
Write a word problem.
Word problem:
“A plot of $$\frac{1}{8}$$ acres land has been used to grow 2 different crops how much land is used to grow each crop?”,

Draw a visual model to represent the quotient.

Explanation:
Drawn a visual model to represent the quotient as
$$\frac{1}{16}$$

Interpret the quotient in the context of your word problem.
Quotient is $$\frac{1}{16}$$ of land is used to
grow one crop,

Explanation:
Solving r = $$\frac{1}{8}$$ ÷ 2 we get quotient
which is the part of land used to grow one crop,
So $$\frac{1}{8}$$ X $$\frac{1}{2}$$ =
r = $$\frac{1}{8 X 2}$$ = $$\frac{1}{16}$$,
therefore quotient is $$\frac{1}{16}$$ of land is used to
grow one crop.

Question 7.
Use Tools Use the rectangle to represent $$\frac{1}{8}$$ ÷ 3 = p. Then write and solve a word problem that can be modeled by the equation.

Word problem:
“$$\frac{1}{8}$$ portion of orange juice has been divided
among 3 friends each one got how much portion of juice?”,
$$\frac{1}{24}$$ portion each will get,

Explanation:
Used the rectangle to represent $$\frac{1}{8}$$ ÷ 3 = p.
Then wrote a word problem as
“$$\frac{1}{8}$$ portion of orange juice has been divided
among 3 friends each one got how much portion of juice?”,
solving a word problem that can be modeled by the equation is
p = $$\frac{1}{8}$$ ÷ 3,
p = $$\frac{1}{8}$$ X $$\frac{1}{3}$$,
p = $$\frac{1}{8 X 3}$$,
p = $$\frac{1}{24}$$,
therefore each friend will get $$\frac{1}{24}$$
portion of orange juice.

Question 8.
Attend to Precision For the equation b = $$\frac{1}{10}$$ ÷ 4:
Write a word problem.
Word problem:
“$$\frac{1}{10}$$ box of candies have
been divided among 4 friends, each freind got what
portion of candies?”,

Draw a visual model to represent the quotient.

Explanation:
Drawn a visual model to represent the quotient as
$$\frac{1}{40}$$ as shown above.

How are the dividend and divisor represented by your visual model?
Dividend : $$\frac{1}{10}$$,
Divisor : 4,

Explanation:
In visual model the dividend $$\frac{1}{10}$$
is represented as 1 rectangle is been divided into 10 rows and
divisor 4 is represented as 4 columns.

Interpret the quotient in the context of your problem.
Each friend got $$\frac{1}{40}$$ portion of candies,

Explanation:
The quotient in the context of my problem is
upon solving b = $$\frac{1}{10}$$ ÷ 4,
we get portion of candies each got ,
b = $$\frac{1}{10}$$ X $$\frac{1}{4}$$,
b = $$\frac{1}{10 X 4}$$,
b = $$\frac{1}{40}$$,
therefore each friend got $$\frac{1}{40}$$
portion of candies.

Question 9.
Reason For $$\frac{1}{4}$$ ÷ 6 = t, Lena writes the word problem: “A string is 6 feet long. Jen wants to cut the string into $$\frac{1}{4}$$-foot pieces. How many pieces will Jen get?” Why does the word problem not make sense for this equation?
Word problem equation means t = 6 ÷ $$\frac{1}{4}$$
but not the given equation $$\frac{1}{4}$$ ÷ 6 = t,
Given equation is $$\frac{1}{4}$$ ÷ 6 = t, but Lena writes the word problem: “A string is 6 feet long.
Jen wants to cut the string into $$\frac{1}{4}$$-foot pieces.
t = 6 ÷ $$\frac{1}{4}$$ whole divided by unit fraction, not the given equation unit fraction divided by whole so word problem does not make sense.