Section B Practice Problems

Problem 1

480 dancers make groups of 15. How many groups are there? Explain or show your reasoning.
480 dancers make groups of 30. How many groups are there? Explain or show your reasoning.

Show Solution

Solution

32 groups. Sample response: $30\times15=450$ , $2\times15=30$ , and $30+2=32$
16 groups. Sample response: There are twice as many dancers in each group, so there will be half as many groups.

Problem 2

Explain why $256 \div 4$ is equivalent to $(200 \div 4) + (40 \div 4) + (16 \div 4)$ .
What is the value of $256 \div 4$ ? Show your thinking. Organize your work so it can be followed by others.

Show Solution

Solution

Sample response. I can add up $200 + 40 + 16$ and that's 256. They are partial quotients and added together give $256 \div 4$ .
64. Sample response: $200 \div 4 = 50$ , $40 \div 4 = 10$ , $16 \div 4 = 4$ , $50 + 10 + 4 = 64$

Problem 3

Use partial quotients to find the value of $243 \div 9$ .

divide. 9, long division symbol with two hundred forty three inside

Show Solution

Solution

27. Sample response:

Problem 4

Use partial quotients to find the quotient $636 \div 12$ .
Use partial quotients to find $636 \div 12$ in a different way.

Show Solution

Solution

53. Sample response:

Problem 5

Find $4,252 \div 34$ . Use partial quotients. Show your thinking. Organize your work so it can be followed by others.

Show Solution

Solution

125 with a remainder of 2. Sample response:

I knew I could take away 100 groups of 34 and that left 852. Then I took 10 more and that left 512. I took 10 more leaving 172. Last, I took away 5 more groups of 34 which left 2. Altogether that's 125 with two left over.

Problem 6

The area of a rectangular field is 8,320 square yards. The width is 65 yards. How long is the field? Explain or show your reasoning.

Show Solution

Solution

128 yards. Sample response:

I know that the product of the length and the width is the area, so the quotient of the area and the width is the length.

Problem 7

Suppose a noodle company made a noodle that was 3,624 feet long, and suppose the noodle was shared equally and served 150 people.

Jada estimates that each person would be served about 20 feet of noodle. Do you agree with Jada? Explain or show your reasoning.
Is Jada’s estimate greater than or less than the actual length each person would be served? Explain or show your reasoning.

Show Solution

Solution

Yes. Sample response: 3,624 can be rounded down to 3,000, and $3,000\div150=20$ .
Less. Sample response: 3,000 is less than the actual length of noodle, which means each person would get more than 20 feet of noodle.

Problem 8

Andre makes a noodle that is 102 feet long. The noodle breaks into 2 pieces. One piece is 2 times as long as the other. How long are the 2 noodles? Explain or show your reasoning.
Priya makes a noodle that is 456 feet long. The noodle breaks into 2 pieces. One piece is 5 times as long as the other. How long are the 2 noodles? Explain or show your reasoning.

Show Solution

Solution

34 feet and 68 feet. Sample response: If I put the two noodles together, that's 3 times the length of the shorter noodle, so the length of the shorter noodle is $102 \div 3$ , which is 34 feet. The longer noodle is 2 times that length, or 68 feet.
76 feet and 380 feet. Sample response: If I put the two noodles together, that's 6 times the length of the shorter noodle, so the length of the shorter noodle is $456 \div 6$ , which is 76 feet. The longer noodle is 5 times that length, or 380 feet.

Problem 9

Lin finds the value of $6,596 \div 68$ . She calculates $6,800 - 6,596$ and notices that it is $3 \times 68$ . Lin says that $6,596 \div 68 = 97$ .

Explain Lin's reasoning.
Use Lin's method to calculate $7,448 \div 76$ .

Show Solution

Solution

Sample response: Lin has shown that $100 \times 68 - 6,596 = 3 \times 68$ . This means that $6,596 = 100 \times 68 - 3 \times 68$ . That's the same as $97 \times 68$ .
98. Sample response: $100 \times 76 - 7,448 = 152$ and $152 = 2 \times 76$ , which means that $7,448$ is two 76s less than 100, so $7,448 \div 76 = 98$ .