We included **H****MH Into Math Grade 5 Answer Key**** PDF** **Module 3 Lesson 4 Practice with Division** to make students experts in learning maths.

## HMH Into Math Grade 5 Module 3 Lesson 4 Answer Key Practice with Division

I Can solve a division problem by using a bar model or an equation.

**Step It Out**

1. A comic book store sold 8 times as many copies of the Team Amazing comic book as it sold of the Astonishing Force comic book. The store sold 549 copies of both comic books. How many copies of each comic book were sold?

A. Use a bar model to represent the situation. Label the bars and the total number of copies represented.

B. Write an equation to find the number represented by each box of the bar model. Then find the number.

C. Use the number represented by each box.

- How many copies of Astonishing Force were sold?
- How many copies of Team Amazing were sold? Explain.

Answer:

A.

B. A + T = 549, where T = 8(A),

C. 61 copies of Astonishing Force were sold,

488 copies of Team Amazing were sold,

Explanation:

Given a comic book store sold 8 times as many copies of the Team Amazing comic book as it sold of the Astonishing Force comic book.

The store sold 549 copies of both comic books.

A. Used a bar model to represent the situation. Labeled the bars with Team Amazing comic book, Astonishing Force comic book and the total number of copies 549 represented.

B. Let Team Amazing comic book be T and

Astonishing Force comic book be A so equation is A + T = 549, where T = 8(A),

C. Number of copies of Astonishing Force were sold are A + 8A = 549, 9A = 549, A = 549 ÷ 9 = 61 copies,

The number of copies of Team Amazing was sold are 8 X 61 = 488 copies.**
Turn and Talk** How can you show that your answer is correct by using inverse operations?

Answer:

Inverse:

Team Amazing comic book is 8 times more than Astonishing Force comic book,

Explanation:

By using inverse operation I sold 549 copies of both comic books.

If 61 copies of the Astonishing Force comic book were sold,

How many times Team Amazing comic book is more than

Astonishing Force comic book is 549 – 61 = 488 copies,

488 ÷ 61 = 8.

**Step It Out**

2. The comic book store also sells collectible toys. The Gigantic Kid costs 4 times as much as the Marvelous Marvin. The Hall of Heroes playset costs 7 times as much as the Marvelous Marvin. If the three toys cost $1,044, how much does the Gigantic Kid cost?

A. Represent the situation with a bar model.

B. Write an equation to find the amount represented by each box of the bar model. Then find the number.

C. Write an equation to find the cost of the Gigantic Kid. How much does the Gigantic Kid cost?

Answer:

A.

B. M + G + H = $1,044, as G = 4 M and H = 7 M,

So M + 4M + 7M = $1,044,

M =$87, H =$609,

C. G = $1,044 – H – M,

Cost of Gigantic kid is $348,

Explanation:

Given the comic book store also sells collectible toys.

The Gigantic Kid costs 4 times as much as the Marvelous Marvin.

The Hall of Heroes playset costs 7 times as much as the Marvelous Marvin. If the three toys cost $1,044,

A. Represented the situation with a bar model as shown above,

B. Let M be Marvelous Marvin, G be Gigantic Kid and

H be Hall of Heroes so equation is

M + G + H = $1,044, as G = 4 M and H = 7 M,

So M + 4M + 7M = $1,044,

12 M = $1,044,

M = $1,044 ÷ 12 = $87,

So H = 7 X $87 = $609,

C. Equation for Gigantic Kid is

G = $1,044 – H – M,

G = $1,044 – $609 – $87 = $348,

So cost of Gigantic kid is $348.

**Check Understanding Math Board**

Question 1.

The amount of salt that a truck put on a road after a snowstorm in January was 14 times as much as the amount used in a February storm. The total amount of salt used was 4230 pounds.

- Represent the situation with a bar model.
- How many pounds of salt were used in the January storm?

Answer:

In the January storm 3,948 pounds of salt was used,

Explanation:

The amount of salt that a truck put on a road after a snowstorm in January was 14 times as much as the amount used in a February storm.

The total amount of salt used was 4230 pounds.

Represented the situation with a bar model as shown above,So Let January be J and February be F

J + F = 4230, as J = 14 F, So 14F + F = 4230,

15F = 4230, F = 4230 ÷ 15 = 282 pounds of salt is used in month of february,

In January it is 282 X 14 = 3,948 pounds of salt was used.

**On Your Own**

Question 2.

**Use Structure** Tina’s taco truck sold 3 times as many veggie tacos in August than in September. She sold twice as many in September than in October. She sold 927 veggie tacos during the three months.

- Represent the number of veggie tacos sold with a bar model.
- Write an equation to show the amount represented by each box of the bar model. Then find the amount.
- How many veggie tacos did Tina sell in September? Explain how you know.

Answer:

Equation is A + S + O = 927,

October it is 103 veggie tacos,

September it is 206 veggie tacos,

August it is 618 veggie tacos,

Explanation:

Given Tina’s taco truck sold 3 times as many veggie tacos in August than in September. She sold twice as many in

September than in October.

She sold 927 veggie tacos during the three months.

Represented the number of veggie tacos sold with a bar model as shown above,

Let August be A, September be S and October be O

So A + S + O = 927, As A = 3S,

3S + S + O = 927, As S = 2O,

3(2O) + 2O + O = 927,

6O + 3O = 927,

9O = 927,

O = 927 ÷ 9 = 103 veggie tacos,

Tina sell is september as S = 2S = 2 X 103 = 206 veggie tacos,

A = 6 X 103 = 618 veggie tacos.

Question 3.

**Model with Mathematics** Brody and his father catch an amberjack that weighs 54 pounds. Brody’s mother catches a blue marlin that weighs 432 pounds. How many times as much does the marlin weigh as the amberjack

- Represent the situation with a bar model.

- Write an equation to model the situation. How many times as much does the marlin weigh as the amberjack?

Answer:

8 times as much does the marlin weigh as the amberjack,

54 B = 432 A,

8 times as much does the marlin weigh as the amberjack,

Explanation:

Given Brody and his father catch an amberjack that weighs 54 pounds. Brody’s mother catches a blue marlin that weighs 432 pounds.

So number of times as much does the marlin weigh as the amberjack is 432 ÷ 54 = 8 times,

Represented the situation with a bar model as shown above,

Let A be amberjack and B be blue marlin so the equation is 54 B = 432 A,

So 8 times as much does the marlin weigh as the amberjack.

**On Your Own**

Question 4.

**Use Repeated Reasoning** Three farmers buy a total of 2,249 acres of land at an auction. Farmer Mel buys land that is 3 times as many acres as Farmer Cassius’s land. Farmer Cassius buys land that is 3 times as many acres as Farmer Anne’s land. How many acres of land does each farmer buy?

Answer:

Mel buys 1,557 acres,

Cassius’s buy 519 acres,

Anne’s buy 173 acres,

Explanation:

Given Three farmers buy a total of 2,249 acres of land at an auction. Let Farmer Mel be M, farmer Cassius’s be C and farmer Anne’s be A,

Farmer Mel buys land that is 3 times as many acres as Farmer Cassius’s land so M = 3 C,

Farmer Cassius buys land that is 3 times as many acres as Farmer Anne’s land so C = 3 A and

M + C + A = 2,249,

M = 3 C, C = 3 A,

M = 3 X 3 A = 9 A,

So 9 A + 3 A + A = 2,249 acres,

13 A = 2,249 acres,

A = 2,249 ÷ 13 = 173,

Therefore Mel buy 9 A = 9 X 173 = 1,557 acres,

Cassius buy 3 X 173 = 519 acres of land.

Question 5.

**Model with Mathematics** A local group raised $3,273 during a recent event. The money raised will be shared equally among 3 different charities. How much money will each charity receive? Write an equation to model the situation. Then solve.

Answer:

Equation : 3S = $3,273,

Each charity will receive $1,091,

Explanation:

Given A local group raised $3,273 during a recent event.

The money raised will be shared equally among 3 different charities.

Let s be the equal share so the equation is 3S = $3,273,

Share = $3,273 ÷ 3 = $1,091, therefore each charity will receive $1,091.

Question 6.

**Model with Mathematics** Mrs. Taylor owns a rectangular piece of land that has an area of 5,040 square feet. If the width of the piece of land is 48 feet, what is the length? Write an equation to model the situation. Then solve.

Answer:

L X 48 feet = 5,040 sq feet,

length of the piece of land is 105 feet,

Explanation:

Given Mrs. Taylor owns a rectangular piece of land that has an area of 5,040 square feet. If the width of the piece of land is 48 feet, then let L be the length of the land

so the equation is L X 48 feet = 5,040 sq feet,

l = 5040 ÷ 48 = 105 feet. Therefore length of the piece of land is 105 feet.

Question 7.

**Model with Mathematics** A comic store sells two rare comic books for $1,824. The price of one comic book is 11 times as much as the price of the other.

- Write an equation to model the price of the less expensive comic book. Then find the price.
- Write an equation to model the price of the more expensive comic book. Then find the price.

Answer:

The equation to model the price of the less expensive comic book,

L + 11 L = $1,824, The price of the less expensive comic book is $152,

The equation to model the price of the more expensive comic book,

E = 11 L, The price of the more expensive comic book is $1,672,

Explanation:

Given a comic store sells two rare comic books for $1,824.

The price of one comic book is 11 times as much as the price of the other.

Let less exensive be L and more expensive comic book be E,

L + E = $1,824,

Equation to model the price of the less expensive comic book is

L + 11 L = $1,824,

12L = $1,824, L = $1,824 ÷ 12 = $152,

The equation to model the price of the more expensive comic book.

E = 11 L, as L = $152 , E = 11 X 152 = $1,672.