Section B Practice Problems

Problem 1

Han cuts a 15-foot piece of rope into 4 equal parts. Decide whether each expression represents the length of each part of the rope in feet. Explain or show your reasoning.

  1. 15÷415 \div 4

  2. 4× 154 \times 15

  3. 3343 \frac{3}{4}
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Solution
  1. Yes. Sample response: This is 1 of four equal groups making 15.
  2. No. Sample response: This is 4 times as long as the piece of rope.
  3. Yes. Sample response: 12 feet of the rope gives 4 equal groups of 3. There are 3 feet left and dividing that into 4 equal parts is 34\frac{3}{4} more feet.

Problem 2

Find the value of each expression.

  1. 12×6\frac{1}{2} \times 6
  2. 17×6\frac{1}{7} \times 6
  3. 18×11\frac{1}{8} \times 11
  4. 13×34\frac{1}{3} \times 34
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Solution
  1. 3 or 62\frac{6}{2} (or equivalent)
  2. 67\frac{6}{7} (or equivalent)
  3. 118\frac{11}{8} (or equivalent)
  4. 111311\frac{1}{3} or 343\frac{34}{3} (or equivalent)

Problem 3

Kiran runs 25\frac{2}{5} the length of his road. The road is 9 miles long. How far does Kiran run? Explain or show your reasoning.

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Solution
185\frac{18}{5} mile or 3353\frac{3}{5} mile. Sample response: 2×(9÷5)=1852\times(9\div5)=\frac{18}{5}

Problem 4

  1. A map divides a state park into about 400 equal-size squares. Each square represents 2,178 square feet. Make an estimate for the size of the park in square feet. Explain or show your reasoning.
  2. Each square on the map represents 120\frac{1}{20} acre. How many square feet are in 1 acre? Explain or show your reasoning.
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Solution
  1. Sample response: If I cut up and reassemble the land, it is about 20 squares wide and 20 squares tall. So, that's about 20×2020 \times 20 or 400 squares. That means the land is about 400×2,000400 \times 2,000 or 800,000800,000 square feet. 
  2. 43,560 square feet. Sample response: There are 20×2,17820 \times 2,178 square feet in an acre which is 43,560.

Problem 5

A standard rectangular sheet of paper is 8128 \frac{1}{2} inches wide and 11 inches long. How many square inches does the sheet of paper cover?

If you get stuck, consider using the grid.

Grid. 12 rows of 12 of the same size squares. 

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Solution
931293 \frac{1}{2} square inches. Sample response: If the paper is 8 inches by 11 inches, the area would be 88 square inches. There is an additional 12\frac{1}{2}-by-11-inch piece and the area of that is 112\frac{11}{2} inches or 5125 \frac{1}{2} inches. The total area of the sheet of paper is 931293 \frac{1}{2} square inches.