Section C Practice Problems

Problem 1

Select all correct statements.

Diagram. Rectangle partitioned into 2 equal parts, each labeled one half.

Diagram. Rectangle partitioned into 3 equal parts, each labeled one third.

Diagram. Rectangle partitioned into 4 equal parts, each part labeled one fourth.

Diagram. Rectangle partitioned into 6 equal parts, each labeled one sixth.

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Solution
A,C,D,E

Problem 2

Each diagram represents 1.

Write as many fractions as you can that are represented by the shaded part of each diagram.

a
b
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Solution

Sample responses:

  1. 12\frac{1}{2}, 24\frac{2}{4}, 48\frac{4}{8}
  2. 13\frac{1}{3}, 26\frac{2}{6}

Problem 3

  1. Tyler draws these number lines and says that 34\frac{3}{4} is equivalent to 23\frac{2}{3}. Explain why Tyler is not correct.

    2 number lines. First, 0 to 2 thirds by thirds, unevenly spaced tick marks. Second, 0 to 3 fourths by fourths, unevenly spaced tick marks.

  2. Find a fraction equivalent to 23\frac{2}{3}.
  3. Find a fraction equivalent to 34\frac{3}{4}.
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Solution

Sample responses:

  1. Tyler's number lines are not accurate. His thirds are not equally spaced. His fourths also are not equally spaced.
  2. 23\frac{2}{3} is equivalent to 46\frac{4}{6}.
  3. 34\frac{3}{4} is equivalent to 68\frac{6}{8}.

Problem 4

  1. Write 10 as a fraction in 2 different ways.
  2. Is 888\frac{88}{8} equivalent to a whole number? Explain or show your reasoning.
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Solution
  1. Sample response: 202\frac{20}{2}, 303\frac{30}{3}
  2. Yes. Sample response: It's equivalent to 11.

Problem 5

Decide if each fraction is equivalent to a whole number. Explain or show your reasoning.

  1. 1002\frac{100}{2}
  2. 1003\frac{100}{3}
  3. 1004\frac{100}{4}
  4. 1006\frac{100}{6}
  5. 1008\frac{100}{8}
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Solution
  1. Yes. Sample response: Each 2 halves make a whole, so 100 halves make 50.
  2. No. Sample response: 3 thirds make a whole, so 99 thirds is 33, and then here is 1 third left over.
  3. Yes. Sample response: Each 4 fourths make a whole, so 40 fourths make 10, 80 fourths make 20, and 100 fourths make 25.
  4. No. Sample response: 6 sixths make a whole, so 60 sixths make 10, 36 sixths more make 6 wholes more, and then there are 4 sixths left over.
  5. No. Sample response: 8 eighths make a whole, so 80 eighths make 10, 16 eighths more make 2 wholes more, and there are 4 eighths left over.

Problem 6

If you continue to fold a fraction strip, how many parts can you fold it into? Can you fold the strip into 100 equal parts? Explain your reasoning.

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Solution

Sample response. If I keep folding in half, I get 2 parts, and then 4 parts, and then 8 parts, and then 16 parts, 32 parts, and 64 parts. If I fold into 3 equal pieces I get 3, then 9, then 27, and then 81 pieces. I could also alternate folding into 3 equal pieces and then 2 equal pieces like we did to get sixths. I could get 12 parts or 18 parts if I fold the fraction strip again into 2 or 3 more equal pieces. And then I could get 24, 36, or 54 parts if I fold again. I don't think I can get 100 equal parts unless I do a more complicated fold.