Testinar Grade 6 math

Dividing Fractions by Fractions

Students will build Grade 6 mastery of dividing fractions by fractions using models, equations, and test-style reasoning.

CH02-01 The Number System
Name
Date
Score
____ / 8
Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

  1. What is \(\frac{3}{4}\div\frac{1}{2}\)?

    1. \(\frac{3}{8}\)
    2. \(\frac{2}{3}\)
    3. \(1\frac{1}{2}\)
    4. \(2\)

  2. Evaluate: \(\frac{5}{6}\div\frac{1}{3}\)

    1. \(\frac{5}{18}\)
    2. \(\frac{5}{6}\)
    3. \(\frac{5}{2}\)
    4. \(\frac{15}{30}\)

  3. What is \(\frac{2}{3}\div\frac{4}{5}\)?

    1. \(\frac{8}{15}\)
    2. \(\frac{5}{6}\)
    3. \(\frac{6}{7}\)
    4. \(\frac{10}{15}\)

  4. Compute: \(\frac{7}{8}\div\frac{1}{4}\)

    1. \(\frac{7}{32}\)
    2. \(\frac{7}{16}\)
    3. \(3\frac{1}{2}\)
    4. \(\frac{11}{8}\)

  5. A recipe calls for \(\frac{3}{4}\) cup of sugar. If you want to make exactly half of the recipe (so that every ingredient is halved), how much sugar do you need? Which expression represents this situation?

    1. \(\frac{3}{4}\div\frac{1}{2}\)
    2. \(\frac{3}{4}\times\frac{1}{2}\)
    3. \(\frac{3}{4}+\frac{1}{2}\)
    4. \(\frac{1}{2}\div\frac{3}{4}\)

  6. What is \(\frac{4}{5}\div\frac{2}{3}\)?

    1. \(\frac{8}{15}\)
    2. \(\frac{2}{15}\)
    3. \(\frac{10}{12}\)
    4. \(\frac{6}{5}\)

  7. How many \(\frac{1}{4}\)-cup servings are in \(2\) cups?

    1. \(6\)
    2. \(8\)
    3. \(\frac{1}{2}\)
    4. \(4\)

  8. A trail is \(3\frac{1}{2}\) miles long. How many \(\frac{3}{4}\)-mile lengths fit along the trail?

    1. \(2\frac{5}{8}\)
    2. \(4\)
    3. \(4\frac{2}{3}\)
    4. \(5\)
Teacher and parent reference

Answer key and explanations

  1. C. \(1\frac{1}{2}\)

    Friendly reminder: when you divide by a fraction, you can multiply by its reciprocal (“flip” the divisor and multiply). \(\frac{3}{4}\div\frac{1}{2}=\frac{3}{4}\times\frac{2}{1}=\frac{6}{4}\), which simplifies to \(\frac{3}{2}\), or \(1\frac{1}{2}\).

  2. C. \(\frac{5}{2}\)

    Rewrite the division as multiplication by flipping \(\frac{1}{3}\): \(\frac{5}{6}\times\frac{3}{1}=\frac{15}{6}\). Simplify \(\frac{15}{6}\) to \(\frac{5}{2}\) (or mixed form \(2\frac{1}{2}\)).

  3. B. \(\frac{5}{6}\)

    Invert \(\frac{4}{5}\) to \(\frac{5}{4}\), then multiply: \(\frac{2}{3}\times\frac{5}{4}=\frac{10}{12}\). That reduces nicely to \(\frac{5}{6}\).

  4. C. \(3\frac{1}{2}\)

    \(\frac{7}{8}\times\frac{4}{1}=\frac{28}{8}=\frac{7}{2}=3\frac{1}{2}\).

  5. B. \(\frac{3}{4}\times\frac{1}{2}\)

    "Half the recipe" means multiply each ingredient by \(\frac{1}{2}\), not divide by \(\frac{1}{2}\). So you want \(\frac{3}{4}\times\frac{1}{2}=\frac{3}{8}\) cup of sugar.

  6. D. \(\frac{6}{5}\)

    \(\frac{4}{5}\times\frac{3}{2}=\frac{12}{10}=\frac{6}{5}\).

  7. B. \(8\)

    You are counting how many \(\frac{1}{4}\)-cup servings fit inside \(2\) cups---that’s a division problem: \(2\div\frac{1}{4}\). Rewrite as \(2\times 4\), which equals \(8\) servings.

  8. C. \(4\frac{2}{3}\)

    Change \(3\frac{1}{2}\) to \(\frac{7}{2}\), then divide by multiplying by \(\frac{4}{3}\): \(\frac{7}{2}\times\frac{4}{3}=\frac{28}{6}\), which simplifies to \(\frac{14}{3}\) or \(4\frac{2}{3}\) lengths along the trail.

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