Mental Math Strategies for Multiplication

Mental Math Strategies for Multiplication

pp.113

Page 116

Word Problems

Multiple Choice

11.Each elephant at a zoo eats 100 pounds of hay and 5 pounds of fruits and vegetables everyday. How many pounds of food does the zoo need to feed one elephant for one week?

Use mental math to solve.

• 105 x 7 = (100 x 5) + (100 x 7) = 500 + 700= 1,200

• 105 x 7 = (100x7) + (5x7)= 735 pounds

Answer:

100 + 5 = 105 pounds x 7 days

105 x 7 = (100x7) + (5x7)= 700+35 =735 pounds

Multiple Choice

12.Ashley and 3 friends are planning a trip. The cost of the trip is $599 per person. How much will the trip cost Ashley and her friends? Explain how to use mental math to find the answer.

• 4x599= 4 x (600-1) = (4x 600) - (4x1)= 2,400-4=$2,396

• 3x599= 3 x (600-1) = (3x 600) - (3x1)= 1,800-3=$1,797

Ans.

4x599= 4 x (600-1) = (4x 600) - (4x1)= 2,400-4=$2,396

Multiple Choice

13.Kyle has a rock collection. On Monday, he found 16 new rocks. On Tuesday, he gave 9 rocks to his friends. After giving away the rocks. Kyle had 122 rocks left in his collection. How many rocks did Kyle have to start with.

• 16-9 = 7 ; 122-7= 115 rocks

• 122+16= 138 ; 138-9=129 rocks

Ans.

16-9 = 7 ; 122-7= 115 rocks

Multiple Choice

14.Quinn used compensation to find the product of 4 x 307. First , she found 4 x 300=1,200. Then she adjusted the product by subtracting 4 groups of 7 to get her final answer of 1,172. Explain Quinn's mistake and the correct answer.

Her solution looks like this: 4 x307 = (4x 300) - (4x7)

• She should have multiplied the expressions instead of subtracting

• She should have added the expressions instead of subtracting.

Ans.

4x 307 = (4x300) + (4x7) = 1,200 + 28

She should have adjusted 1,200 by adding 4x7, instead of subtracting.

Multiple Choice

15.Do you think it be better to use breaking apart or compensation to find the product of 5x 328? Explain why and show how to find the product.

• Breaking Apart : 5x (300 + 20 + 8) = 1,500 + 100 + 40 += 1,640

• Compensation : (5x300) + (5x28) =1,500 + 140 = 1,640

Ans.

Breaking apart; It gives numbers that are easy to multiply mentally.

5x (300 + 20 + 8) = 1,500 + 100 + 40 = 1,640

Multiple Select

16.Which of the following expressions shows how to use mental math to find the product of 4x27?

Select all that apply.

• (4 x 20) + (4 x 7)

• 4 x (20 x 7)

• (4 x 30) - (4 x 3)

• (4 x 25) + (4 x 2)

• 4 x 2 x 7

Multiple Select

Which of the following expressions shows how to use mental math to find the product of 4 x 2,025? Select all that apply.

• 4 x (2,000 + 20 + 5)

• (4 x 2,000) + 25

• (4 x 2,000) + (4 x 25)

• 4 x (2,000 + 25)

• (4 x 2,000 x 25)

Multiple Choice

19. The longest blue whale on record was about 18 scuba divers in length. Use breaking apart to estimate the length of the blue whale.

• 6x18= 18 x6 = 108 feet

• (6x10)+ (6x8)= 60 +48= 108 feet

Ans.

(6x10)+ (6x8)= 60 +48= 108 feet

About 108 feet

Multiple Choice

20.Explain how to estimate the length of the whale using compensation.

• 6x 20 =120 ; 6x2=12 ;

  120-12=108 feet

• 6x 18 = 18 x6 = 108 feet

Ans.

6x 20 =120 ; 6x2=12 ;

120-12=108 feet

About 108 feet

Open Ended

21. In an election, 589,067 people voted. Write 589,067 in expanded form and using number names.

Ans.

Expanded form : 500,000 + 80,000 + 9,000 + 60 + 7

Number names : five hundred eighty-nine thousand, sixty-seven

Open Ended

22.Davidson's Bakery bakes 108 cookies and 96 muffins every hour. How many baked goods are baked in 4 hours? Use mental math to solve.

Ans.

108 + 96 = 204;

4 x 204 = 4 x (200 +4) = (4x 200) + (4 x 4) = 800 + 16 = 816

816 baked goods

Multiple Select

23.Which of the following expressions shows how to use mental math to find the product of 8 x 490? Select all the apply.

• 8 + (400 x90)

• (8x400) + (8x90)

• (8x400) + (8x9)

• (8x500) - (8x10)

• 8 x (500x10)

Multiple Select

24. Which of the following expressions shows how to use mental math to find the product of 4 x 2,025? Select all that apply.

• 4 x ( 2,000 + 20 + 5)

• ( 4x 2,000) + 25

• ( 4x 2,000) + ( 4 x 25)

• 4 x (2,000 + 25)

• (4 x 2,000 x 25)