Refer to our Texas Go Math Grade 3 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 3 Lesson 7.4 Answer Key Distributive Property.

## Texas Go Math Grade 3 Lesson 7.4 Answer Key Distributive Property

**Essential Question**

How can you use the Distributive Property to find products?

**Unlock the Problem**

Mark bought 6 new fish for his aquarium. He paid $7 for each fish. How much did he spend in all?

Find 6 × $7

- Describe the groups in this problem.
- Circle the numbers you will use to solve the problem.

**You can use the Distributive Property to solve the problem.**

The Distributive Property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products.

**Remember**

sum—the answer to an addition problem

addends—the numbers being added

**Activity**

Materials, square tiles

Make an array with tiles to show 6 rows of 7.

So, Mark spent $___ for his new fish.

Break apart the array to make two smaller arrays for facts you know.

**Math talk**

**Mathematical Processes**

What other ways could you break apart the 6 × 7 array?

Answer:

Other ways could you break apart the 6 × 7 array:

6 × 7 = (6 × 4) + (6 × 3)

6 × 7 = (6 × 5) + (6 × 2)

6 × 7 = (6 × 1) + (6 × 6)

Explanation:

Other ways could you break apart the 6 × 7 array

6 × 7 = (6 × 4) + (6 × 3)

= 24 + 16

= 42.

6 × 7 = (6 × 5) + (6 × 2)

= 30 + 12

= 42.

6 × 7 = (6 × 1) + (6 × 6)

= 6 + 36

= 42.

**Share and Show
**Question 1.

Draw a line to show how you could break apart this 6 × 8 array into two smaller arrays for facts you know.

- What numbers do you multiply? ___ and ___

___ and ___ - What numbers do you add? ___ + ___

6 × 8 = 6 × (___ + ___)

6 × 8 = (___ × ___) + (___ × ____)

6 × 8 = ___ + ____

6 × 8 = ___

Answer:

6 × 8 = 48.

Explanation:

6 × 8 = 6 × ( 5+ 3 )

6 × 8 = ( 6 × 5 ) + ( 6 × 3 )

6 × 8 = 30 + 18

6 × 8 = 48.

**Math Talk**

**Mathematical Processes**

Why do you have to add to find the total product when you use the Distributive Property?

Write one way to break apart the array.

Then find the product.

Answer:

6 × 8 = 48.

Explanation:

6 × 8 = 6 × (4 + 4)

= (6 × 4) + (6 × 4)

= 24 + 24

= 48.

Question 2.

Answer:

Explanation:

5 × 8 = 5 × (6 + 2)

= (5 × 6) + (5 × 2)

= 30 + 10

= 40.

Question 3.

Answer:

Explanation:

4 × 7 = 4 × (3 + 4)

= (4 × 3) + (4 × 4)

= 12 + 16

= 28.

**Problem Solving
**Question 4.

Shade tiles to make an array that shows a fact with 7, 8, or 9 as a factor. Write the fact. Explain how you found the product.

Answer:

Explanation:

Number of rows = 8.

Number of columns = 9.

Product = Number of rows × Number of columns

= 8 × 9 = 72.

**Problem Solving
**Question 5.

**H.O.T. Sense or Nonsense?**Robin says, “I can find 8 × 7 by multiplying 3 × 7 and doubling it.” Does her statement make sense? Justify your answer.

Answer:

Her statement makes sense because 8 × 7 = (3 × 7) + (3 × 7) + (2 × 7) = 56.

Explanation:

8 × 7 = (3 + 3 + 2) × 7

= (3 × 7) + (3 × 7) + (2 × 7)

= 21 + 21 + 14

= 42 + 14

= 56.

Question 6.

**H.O.T. Multi-Step** Brandon needs 8 boxes of spinners for his fishing club. The cost of each box is $9. How much will Brandon pay?

8 × $9 = ___

Answer:

Amount of money Brandon needs to pay = $72.

Explanation:

Number of boxes of spinners for his fishing club Brandon needs = 8.

Cost of each box = $9.

Amount of money Brandon needs to pay = Number of boxes of spinners for his fishing club Brandon needs × Cost of each box

= 8 × $9

= $72.

**Look at how Brandon solved the problem.**

**Find and describe his error.**

8 × 9 = (4 × 9) + (5 × 9)

8 × 9 = 36 + 45

8 × 9 = 81

**Use the array to help solve the problem and correct Brandon’s error.**

8 × 9 = (4 + 4) × 9

8 × 9 =(___ × ___) + (__ × ___)

8 × 9 = ___ × ___

8 × 9 = ____

So, Brandon will pay $___ for the spinners.

Answer:

So, Brandon will pay $72 for the spinners.

Explanation:

8 × 9 = (4 × 9) + (5 × 9)

8 × 9 = 36 + 45

8 × 9 = 81.

Brandon mistake:

8 × 9 = (4 + 4) × 9 not (4 + 5) × 9.

Number of boxes of spinners for his fishing club Brandon needs = 8.

Cost of each box = $9.

Amount of money Brandon needs to pay = Number of boxes of spinners for his fishing club Brandon needs × Cost of each box

= 8 × $9

= (4 + 4) × 9

= (4 × $9) + (4 × $9)

= $36 + $36

= $72.

**Daily Assessment Task
**

**Fill in the bubble for the correct answer choice.**

**You may use models or strategies to solve.**

Question 7.

**Use Diagrams**Maurice planted 8 rows of popcorn plants. There are 6 plants in each row. The array shows Maurice’s garden. How many popcorn plants does Maurice have?

(A) 36

(B) 42

(C) 48

(D) 64

Answer:

Number of popcorn plants Maurice have = 48.

(C) 48.

Explanation:

Number of rows of popcorn plants Maurice planted = 8.

Number of plants in each row = 6.

Number of popcorn plants Maurice have = Number of rows of popcorn plants Maurice planted × Number of plants in each row

= 8 × 6

= (4 + 4) × 6

= (4 × 6) + (4 × 6)

= 24 + 24

= 48.

Question 8.

At a grocery store, the cans of nuts are arranged in 9 rows. There are 6 cans in each row. Which shows one way to find the total number of cans of nuts?

(A) (5 + 4) × 6

(B) (3 + 3) × 6

(C) (5 + 5) × 6

(D) (5 + 3) × 6

Answer:

Total number of cans of nuts = 54.

(A) (5 + 4) × 6.

Explanation:

Number of rows of cans of nuts are arranged in = 9.

Number of cans in each row = 6.

Total number of cans of nuts = Number of rows of cans of nuts are arranged in × Number of cans in each row

= 9 × 6

= (5 + 4) × 6

= (5 × 6) + (4 × 6)

= 30 + 24

= 54.

Question 9.

**Multi-Step** Jillian bought 6 books for $7 each. She paid with $50. How much change should Jillian receive?

(A) $37

(B) $18

(C) $43

(D) $8

Answer:

Amount of change Jillian receives = $8.

(D) $8.

Explanation:

Number of books Jillian bought = 6.

Cost of each book = $7.

Amount of money she paid = $50.

Total amount of books Jillian bought = Number of books Jillian bought × Cost of each book

= 6 × $7

= (3 + 3) × $7

= (3 × $7) + (3 × $7)

= $21 + $21

= $42.

Amount of change Jillian receives = Amount of money she paid – Total amount of books Jillian bought

= $50 – $42

= $8.

**Texas Lest Prep
**Question 10.

Representation Which number sentence below is an example of the Distributive Property?

(A) 6 × 8 = 40 + 8

(B) (8 × 2) × 3 = 8 × (2 × 3)

(C) 6 × 8 = 8 × 6

(D) 6 × 8 = (6 × 2) + (6 × 6)

Answer:

(B) (8 × 2) × 3 = 8 × (2 × 3) number sentence is an example of the Distributive Property.

Explanation:

In mathematics, the distributive property of binary operations generalizes the distributive law, which asserts that the equality .

### Texas Go Math Grade 3 Lesson 7.4 Homework and Practice Answer Key

**Write one way to break apart the array. Then find the product.
**Question 1.

Answer:

Explanation:

4 × 8 = 4 × (4 + 4)

= (4 × 4) + (4 × 4)

= 16 + 16

= 32.

Question 2.

Answer:

Explanation:

5 × 6 = 5 × (2 + 4)

=(5 × 2) + (5 × 4)

= 10 + 20

= 30.

Question 3.

Shade tiles to make an array that shows a fact with 5, 6, or 7 as a factor. Explain how you found the product.

Answer:

Explanation:

Number of rows = 5.

Number of columns = 6.

Product = Number of rows × Number of columns

= 5 × 6

= 5 × (5 + 1)

= (5 × 5) + (5 × 1)

= 25 + 5

= 30.

**Problem Solving
**Question 4.

Shawn makes a tile design by using 7 rows of 8 tiles. Explain how Shawn can break apart his design to find how many tiles he used.

Answer:

Number of tiles he used = 7 × 8 = (4 + 3) × 8 = 56.

Explanation:

Number of rows of tiles design Shawn makes = 7.

Number of tiles in each row = 8.

Number of tiles he used = Number of rows of tiles design Shawn makes × Number of tiles in each row

= 7 × 8

= (4 + 3) × 8

= (4 × 8) + (3 × 8)

= 32 + 24

= 56.

**Texas Test Prep
**

**Lesson Check**

**Fill in the bubble completely to show your answers.**

Question 5.

There are 8 tables in the art class. Five students sit at each table. How many students are in the art class?

(A) 13

(B) 40

(C) 45

(D) 85

Answer:

Number of students are in the art class = 40.

(B) 40.

Explanation:

Number of tables in the art class = 8.

Number of students sit at each table = 5.

Number of students are in the art class = Number of tables in the art class × Number of students sit at each table

= 8 × 5

= (5 + 3) × 5

= (5 × 5) + (3 × 5)

= 25 + 15

= 40.

Question 6.

Seven large trucks are in a parking lot. Each truck has 6 wheels. How many wheels are there in all?

(A) 67

(B) 40

(C) 42

(D) 13

Answer:

Number of wheels are there in all = 42.

(C) 42.

Explanation:

Number of large trucks are in a parking lot = 7.

Number of wheels each truck has = 6.

Number of wheels are there in all = Number of large trucks are in a parking lot × Number of wheels each truck has

= 7 × 6

= (3 + 4) × 6

= (3 × 6) + (4 × 6)

= 18 + 24

= 42.

Question 7.

Jonas buys 6 packages of corn. Each package has 8 ears of corn. Which way can Jonas use to show how many ears of corn he buys?

(A) (4 + 2) × 8

(B) (3 + 2) × 8

(C) (6 + 6) × 8

(D) (4 + 4) × 6

Answer:

Number of ears of corn he buys = 48.

(A) (4 + 2) × 8

Explanation:

Number of packages of corn Jonas buys = 6.

Number of ears of corns each package has = 8.

Number of ears of corn he buys = Number of packages of corn Jonas buys × Number of ears of corns each package has

= 6 × 8

= (4 + 2) × 8

= (4 × 8) + (2 × 8)

= 32 + 16

= 48.

Question 8.

A store sells bags of 9 apples. Mr. Hyon buys 5 bags of apples to make pies. Which way can Mr. Hyon use to show how many apples he buys?

(A) (4 × 9) + (5 × 9)

(B) (3 × 5) + (6 × 5)

(C) (4 × 5) + (5 × 9)

(D) (3 × 5) + (9 × 5)

Answer:

Number of apples he buys = 45.

(B) (3 × 5) + (6 × 5)

Explanation:

Number of apples a store sells bags has = 9.

Number of bags of apples to make pies Mr. Hyon buys = 5.

Number of apples he buys = Number of apples a store sells bags has × Number of bags of apples to make pies Mr. Hyon buys

= 9 × 5

= (3 + 6) × 5

= (3 × 5) + (6 × 5)

= 15 + 30

= 45.

Question 9.

**Multi-Step** Minka buys 8 CDs for $6 each. She pays with three $20 bills. How much change should Minka receive?

(A) $48

(B) $12

(C) $34

(D) $68

Answer:

Amount of money change Minka receives = $12.

(B) $12.

Explanation:

Number of CDs Minka buys = 8.

Cost of each CDs Minka buys = $6.

Amount of 3 bills she pays = $20 × 3 = $60.

Amount of money change Minka receives = Amount of bills she pays – (Number of CDs Minka buys × Cost of each CDs Minka buys)

= $60 – (8 × $6)

= $60 – $48

= $12.

Question 10.

**Multi-Step** Kent buys 5 bags of potatoes that cost $7 each. He gives the clerk $40. How much change should Kent receive?

(A) $35

(B) $12

(C) $68

(D) $5

Answer:

Amount of change Kent receives = $5.

(D) $5.

Explanation:

Number of bags of potatoes Kent buys = 5.

Cost of each bags of potatoes = $7.

Amount of money he gives the clerk = $40.

Amount of change Kent receives = Amount of money he gives the clerk – (Number of bags of potatoes Kent buys × Cost of each bags of potatoes)

= $40 – (5 × $7)

= $40 – $35

= $5.