Section D Practice Problems

Problem 1

There are 85 chairs in the gym. They are arranged in 5 rows with the same number of chairs in each row. How many chairs are in each row? Show your thinking using diagrams, symbols, or other representations.

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Solution

There are 17 chairs in each row. Sample response:

10 \times 5 = 50

7 \times 5 = 35

17 \times 5 = 85

Problem 2

Find the value of $96 \div 6$ . Use base-ten blocks if they are helpful.
Find the value of $52 \div 4$ . Use base-ten blocks if they are helpful.

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Solution

16. Sample response: I first put 1 ten in each of 6 equal groups and there 3 tens and 6 ones, or 36 ones, left so I put 6 ones in each of the groups.
13. Sample response: There are 4 groups, and there are 13 in each group.

Problem 3

Find the value of $78 \div 6$ . Draw a diagram if it is helpful.
Find the value of $42 \div 3$ . Draw a diagram if it is helpful.

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Solution

13. Sample response: I knew I could fit ten 6s in because that’s 60. Then 3 more 6s gave me 78. So, there are thirteen 6s in 78, and $78 \div 6 = 13$ .
14. Sample response: I know that 3 groups of 10 is 30 and 3 groups of 4 is 12, so 3 groups of 10 and 4 more make 42.

Problem 4

Find the value of each quotient. Explain or show your reasoning.

$96 \div 6$
$87 \div 3$

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Solution

16. Sample response:

$6 \times 10 = 60$
$6 \times 6 = 36$
$60 + 36 = 96$
$10 + 6 = 16$
29. Sample response:

$20 \times 3 = 60$
$9 \times 3 = 27$
$60 + 27 = 87$
$20 + 9 = 29$

Problem 5

There are 240 people at the park for the soccer games. There are 150 fans. The rest of the people are on 6 soccer teams. Each team has an equal number of players. How many players are on each soccer team?

Write an equation to represent this situation. Use a letter for the unknown quantity.
Solve the problem. Explain or show your reasoning.

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Solution

Sample response: $(240 - 150) \div 6 = p$ or $6 \times p + 150 = 240$
There are 15 people on each soccer team. Sample response:

$240 - 150 = 90$
$90 \div 6 = 15$

Problem 6

To find the value of $96 \div 3$ , Diego divides $9$ by 3 and $6$ by 3 and says the answer is 32.

Explain why Diego's method works. Use equations or drawings to support your reasoning.
Does Diego's method work to find the value of $78 \div 3$ ? Explain your reasoning.

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Solution

Sample response:

The 9 in 90 is 9 tens and those can be divided into 3 groups of 3 tens. The 6 ones can be divided into 3 groups of 2 ones. So, that is 3 equal groups with 3 tens and 2 ones, or 32, in each group. $96=90+6$ , $90 \div 3=30$ , $6 \div 3=2$ , so $96 \div 3 = 30 + 2 = 32$ .
No, I cannot divide 7 tens into 3 equal groups. I can take 6 of the tens and divide them into 3 equal groups of 2. Then there is 1 ten and 8 ones left, which is 18 ones that can be divided into 3 equal groups of 6 ones. So the value of $78 \div 3$ is 2 tens and 6 ones, or 26.

Problem 7

What are all the different ways you can divide 48 objects into equal groups?

Make a list.
Write a multiplication or division equation for each different way.

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Solution

1 group of 48, 2 groups of 24, 3 groups of 16, 4 groups of 12, 6 groups of 8, 8 groups of 6, 12 groups of 4, 16 groups of 3, 24 groups of 2, 48 groups of 1
Sample response: $1 \times 48 = 48$ , $48 \div 2 = 24$ , $3 \times 16 = 48$ , $48 \div 12= 4$ , $6 \times 8 = 48$ , $48 \div 6 = 8$ , $12 \times 4 = 48$ , $48 \div 16 = 3$ , $24 \times 2 = 48$ , $48 \div 48 = 1$ ,