We included **HMH Into Math Grade 5 Answer Key PDF** **Module 11 Lesson 6 Solve Division Problems Using Visual Models and Equations **to make students experts in learning maths.

## HMH Into Math Grade 5 Module 11 Lesson 6 Answer Key Solve Division Problems Using Visual Models and

Equations

I Can solve problems involving the division of fractions and whole numbers.

**Step It Out**

Question 1.

Rohan and Sim are building a terrarium. The first layer is made of sand. They can use a scoop to add sand to make the first layer. Rohan has a \(\frac{1}{3}\)-cup scoop and Sim has a \(\frac{1}{4}\)-cup scoop.

A. Write and solve an equation to model the number of scoops needed to fill the first layer if only Rohan’s scoop is used. How many scoops are needed?

Answer:

Equation:

3 ÷ \(\frac{1}{3}\),

9 cups scoop,

Explanation:

Given Rohan has a \(\frac{1}{3}\)-cup scoop,

The number of scoops needed to fill the first layer 3 cups of sand if only Rohan’s scoop is used equation is

3 ÷ \(\frac{1}{3}\) solving 3 X 3 = 9 – cups scoop.

B. Write and solve an equation to model the number of scoops needed to fill the first layer if only Sim’s scoop is used. How many scoops are needed?

Answer:

3 ÷ \(\frac{1}{4}\),

12 cups scoop,

Explanation:

Given Sim has a \(\frac{1}{4}\)-cup scoop,

The number of scoops needed to fill the first layer 3 cups of sand if only Sim’s scoop is used equation is

3 ÷ \(\frac{1}{4}\) solving 3 X 4 = 12 – cups scoop.

C. If Rohan’s scoop and Sim’s scoop are used to add sand in whole-number cup amounts, what are possible numbers of scoops that each would add?

Answer:

6 cup scoops from Rohan’s cup and

4 cup scoops from Sim’s cup

Explanation:

Rohan must add 6 cup scoops from his cup i.e \(\frac{1}{3}\) scoops X 6 = 2 cups,

Sim must add 4 cup scoops from his cup i.e. \(\frac{1}{4}\) scoops X 4 = 1 cup,

Total = \(\frac{1}{3}\) X 6 + \(\frac{1}{4}\) X 4 =

2 + 1 cups which is 3 cups i.e. the total number of cups required 6 cup scoops from Rohan’s cup and 4 cup scoops from Sim’s cup.

D. Use equations, visual models, or words to justify your answers in Part C.

Answer:

3 = \(\frac{1}{3}\) X 6 + \(\frac{1}{4}\) X 4,

Explanation:

If we use 6 scoops of Rohan’s \(\frac{1}{3}\)– cup scoop and if we use 4 scoops of Sim’s \(\frac{1}{4}\)– cup scoop we get equation as 3 = \(\frac{1}{3}\) X 6 + \(\frac{1}{4}\) X 4 of 3 cups os sand.

**Turn and Talk** How would your answers change if Sim had a \(\frac{1}{2}\)-cup scoop?

Answer:

3 ÷ \(\frac{1}{2}\),

6 cups scoop,

Explanation:

Given if Sim had a \(\frac{1}{2}\)-cup scoop,

The number of scoops needed to fill the first layer 3 cups of sand if only Sim’s scoop is used equation is

3 ÷ \(\frac{1}{2}\) solving 3 X 2 = 6 – cups scoop.

Question 2.

The next layer in the terrarium is made using all of the pebbles in Rohan’s bag. If he uses 5 scoops, about how many kilograms of pebbles does the scoop hold?

A. Write a division equation to model this situation.

Answer:

Division equation:

\(\frac{1}{4}\) ÷ 5,

Explanation:

Given the next layer in the terrarium is made using all of the pebbles in Rohan’s bag. If he uses 5 scoops number of kilograms of pebbles does the scoop hold are the division equation is \(\frac{1}{4}\) ÷ 5.

B. Use a visual model to solve the problem.

Answer:

Explanation:

Using visual model to solve \(\frac{1}{4}\) ÷ 5 divided the 1 rectangle into 4 columns and again into

5 rows, \(\frac{1}{4}\) X \(\frac{1}{5}\) =

\(\frac{1}{4 X 5}\) = \(\frac{1}{20}\).

C. What does the quotient mean in the context of the story?

Answer:

Number of kilograms of pebbles does the scoop hold,

Explanation:

The quotient in the context of the story if the next layer in the terrarium is made using all of the pebbles in Rohan’s bag.

If he uses 5 scoops number of kilograms of pebbles does the scoop hold i.e \(\frac{1}{20}\) kg.

**Turn and Talk** How could you solve this problem using multiplication?

Answer:

\(\frac{1}{4}\) X \(\frac{1}{5}\),

\(\frac{1}{20}\) kg scoop holds,

Explanation:

Instead of dividing by the whole number 5 scoops we multiply by \(\frac{1}{5}\) as \(\frac{1}{4}\) X \(\frac{1}{5}\) to solve the problem.

**Check Understanding**

Question 1.

Rohan plants seeds in the terrarium. He wants the plants to grow to be 6 inches tall. If the plants grow \(\frac{1}{3}\) inch per week, how many weeks will it take for the plants to grow to be 6 inches tall? Draw a visual model to represent the situation and solve the problem. Then write a division equation to model the problem.

Answer:

18 weeks,

Division equation:

6 ÷ \(\frac{1}{3}\),

Explanation:

Given Rohan plants seeds in the terrarium. He wants the plants to grow to be 6 inches tall. If the plants grow

\(\frac{1}{3}\) inch per week, Number of weeks will it take for the plants to grow to be 6 inches tall is drawn a visual model to represent the situation and the division equation to model the problem is

6 ÷ \(\frac{1}{3}\), solving we get 6 X 3 = 18 weeks.

**On Your Own**

Question 2.

**Model with Mathematics** A truck can carry \(\frac{1}{2}\) ton of oil. The oil is transported equally in 5 drums. How much does one drum of oil weigh? Draw a visual fraction model to represent the situation and solve the problem. Then write a division equation to model the problem.

Answer:

\(\frac{1}{10}\) ton of oil,

Division problem :

\(\frac{1}{2}\) ÷ 5,

Explanation:

Given a truck can carry \(\frac{1}{2}\) ton of oil.

The oil is transported equally in 5 drums.

So one drum of oil weighs is \(\frac{1}{2}\) ÷ 5,

Drawn a visual fraction model to represent the situation and solving the problem as \(\frac{1}{2}\) ÷ 5 =

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

\(\frac{1}{2 X 5}\) = \(\frac{1}{10}\),

therefore one drum of oil weighs \(\frac{1}{10}\) ton of oil,

The division equation to model the problem is

\(\frac{1}{2}\) ÷ 5.

Question 3.

**Model with Mathematics** An ice cream shop has a container with 16 cups of chocolate ice cream. Each scoop of ice cream is \(\frac{1}{2}\) cup. How many scoops of chocolate ice cream can the shop serve? Model this situation with a division equation and write a related multiplication equation to solve.

Answer:

32 scoops of chocolate ice cream,

Division equation:

s = 16 ÷ \(\frac{1}{2}\),

Multiplication equation:

s = 16 X 2,

Explanation:

Given an ice cream shop has a container with 16 cups of chocolate ice cream. Each scoop of ice cream is

\(\frac{1}{2}\) cup. let s be number of many scoops of chocolate ice cream can the shop serve are modeled this situation with a division equation as

s = 16 ÷ \(\frac{1}{2}\) and related multiplication equation is s = 16 X 2 on solving we will get 32 scoops of chocolate ice cream.

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

Question 4.

9 ÷ \(\frac{1}{8}\) = n

Answer:

Multiplication equation:

n = 9 X 8,

n = 72,

Explanation:

Given 9 ÷ \(\frac{1}{8}\) = n,

the multiplication equation is n = 9 X 8,

So n = 72.

Question 5.

n = \(\frac{1}{5}\) ÷ 7

Answer:

Multiplication equation:

n = \(\frac{1}{5}\) X \(\frac{1}{7}\),

n = \(\frac{1}{35}\),

Explanation:

Given n = \(\frac{1}{5}\) ÷ 7

the multiplication equation is

n = \(\frac{1}{5}\) X \(\frac{1}{5}\),

So n = \(\frac{1}{5 X 7}\) = \(\frac{1}{35}\).

Question 6.

\(\frac{1}{8}\) ÷ 6 = n

Answer:

Multiplication equation:

n = \(\frac{1}{8}\) X \(\frac{1}{6}\),

n = \(\frac{1}48}\),

Explanation:

Given n = \(\frac{1}{8}\) ÷ 6

the multiplication equation is

n = \(\frac{1}{8}\) X \(\frac{1}{6}\),

So n = \(\frac{1}{8 X 6}\) = \(\frac{1}{48}\).

Question 7.

**Use Tools** Olivia has 9 yards of ribbon to make bows. Each bow uses \(\frac{1}{3}\) yard of ribbon. How many bows can Olivia make?

Draw a visual fraction model to represent the situation and solve the problem.

Answer:

27 bows,

Explanation:

Drawn a visual fraction model to represent the situation,

Given Olivia has 9 yards of ribbon to make bows.

Each bow uses \(\frac{1}{3}\) yard of ribbon.

Number of bows can Olivia make are 9 ÷ \(\frac{1}{3}\) =

9 X 3 = 27 bows,

How many bows can Olivia make? Write a division equation to model the problem.

Answer:

27 bows,

Division equation: 9 ÷ \(\frac{1}{3}\),

Explanation:

Given Olivia has 9 yards of ribbon to make bows.

Each bow uses \(\frac{1}{3}\) yard of ribbon.

Number of bows can Olivia make are 9 ÷ \(\frac{1}{3}\) =

9 X 3 = 27 bows and division equation is

9 ÷ \(\frac{1}{3}\).

Question 8.

**Use Tools** To make a homemade “lava lamp,” you can mix vegetable oil, food coloring, and \(\frac{1}{4}\) tablet of baking soda. How many lava lamps can you make if you have 5 tablets of baking soda?

Draw a visual fraction model to represent the situation and solve the problem.

Answer:

20 lava lamps,

Explanation:

Given to make a homemade “lava lamp,” I can mix

vegetable oil, food coloring, and \(\frac{1}{4}\)

tablet of baking soda. Number of lava lamps I can make

if I have 5 tablets of baking soda are drawn a visual fraction

model to represent the situation above and solving

5 ÷ \(\frac{1}{4}\) = 5 X 4 = 20 lava lamps.

How many lava lamps can you make? Write a division equation to model the problem.

Answer:

20 lava lamps,

Division equation : 5 ÷ \(\frac{1}{4}\),

Explanation:

Given to make a homemade “lava lamp,” I can mix

vegetable oil, food coloring, and \(\frac{1}{4}\)

tablet of baking soda. Number of lava lamps I can make

if I have 5 tablets of baking soda are

5 ÷ \(\frac{1}{4}\) = 5 X 4 = 20 lava lamps.

Division equation is 5 ÷ \(\frac{1}{4}\).

Question 9.

**Model with Mathematics** Six friends are sharing a \(\frac{1}{4}\)-pound package of beads equally. What fraction of a pound of beads does each friend get?

Write a division equation to model the situation.

Answer:

Division equation:

\(\frac{1}{4}\) ÷ 6,

Explanation:

Given six friends are sharing a \(\frac{1}{4}\)-pound

package of beads equally. The fraction of a pound of

beads does each friend get division equation to model the situation

is \(\frac{1}{4}\) ÷ 6.

Write a related multiplication equation to solve.

Answer:

Multiplication equation:

\(\frac{1}{4}\) X \(\frac{1}{6}\),

Explanation:

The related multiplication equation to solve is

\(\frac{1}{4}\) X \(\frac{1}{6}\).

What fraction of a pound of beads does each friend get?

Answer:

Each friend get \(\frac{1}{24}\) pound of beads,

Explanation:

The fraction of a pound of beads does each friend get is

solving \(\frac{1}{4}\) ÷ 6 =

\(\frac{1}{4}\) X \(\frac{1}{6}\) =

\(\frac{1}{4 X 6}\) = \(\frac{1}{24}\).

Therefore each friend will get \(\frac{1}{24}\) pound of beads.

Question 10.

**Construct Arguments** How does the quotient of a unit fraction divided by a whole number compare to the quotient of a whole number divided by a unit fraction?

Answer:

The quotient of a unit fraction divided by

a whole number will be always less than than given

dividend unit fraction and the quotient of

a whole number divided by a unit fraction will be more

than the dividend whole number,

Explanation:

When a unit fraction is divided by a whole number, the quotient is a unit fraction less than the dividend.

Dividing 1/4 into 6 equal parts results in a unit fraction of 1/24 because each 1/4 of the whole is divided into 6 equal parts.

When a whole number is divided by a unit fraction the result is each unit being divided into smaller parts.

Dividing each unit of 6 into four equal parts results in 24

equal parts of onefourths, so the qotient will be a whole number greater than the dividend.

When a whole number is divided by a unit fraction, the quotient is a whole number greater than the dividend.