Section B Practice Problems

Problem 1

There are 35 books in the bookcase. There are 7 books on each shelf. How many shelves are there? Explain how the equations

35 \div 7 = {?}

and

{?} \times 7 = 35

both represent the situation.

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Solution

5 shelves. Sample response:
In both equations, 35 represents all of the books, 7 represents the number of books on each shelf, and ? represents the number of shelves. The division equation shows 35 divided into groups of 7, and the multiplication equation shows groups of 7 make 35.

Problem 2

There are 24 eggs in a container. There are 6 eggs in each row. How many rows of eggs are in the container?

Write an equation that represents the situation. Use a symbol for the unknown. Then answer the question.

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Solution

${?} \times 6 = 24$ , $6 \times {?} =24$ , or $24 \div 6 = {?}$ . There are 4 rows of eggs.

Problem 3

Write a related division fact you know from each multiplication equation.

$8 \times 5 = 40$
$2 \times 9 = 18$

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Solution

$40 \div 5 = 8$ or $40 \div 8 = 5$
$18 \div 2 = 9$ or $18 \div 9 = 2$

Problem 4

Lin knows $8 \times 5 = 40$ . Explain how she can use this fact to find $8 \times 4$ .

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Solution

Sample response:

8 \times 4

is 8 less than

8 \times 5

, so it's

40 - 8

or 32.

Problem 5

Mark or shade parts of the diagram to show the expression $(5 \times 7) + (2 \times 7)$ .
Explain how you could use the diagram to find the value of $7 \times 7$ .

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Solution

Sample response:

See diagram.
The diagram shows that $7 \times 7$ is the same as $(5 \times 7) + (2 \times 7)$ , so it's $35 + 14$ , or $49$ .

Problem 6

Mark or shade the rectangle to show a strategy for finding its area. Then explain how to use the diagram to find the area.

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Solution

56 square units. Sample response: I know

8 \times 5 = 40

and

8 \times 2 = 16

, and then I added 40 and 16 to get 56.

Problem 7

Noah finds $9 \times 8$ by calculating $(10 \times 8) - (1 \times 8)$ .

Make a drawing showing why Noah's strategy works.
Use Noah's strategy to find the value of $9 \times 8$ .

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Solution

Sample response:
72. Sample response: There are 80 squares in the 10 by 8 rectangle and then 8 are taken away to get the 9 by 8 rectangle. That leaves $80 - 8$ , or 72 squares.