Testinar Grade 7 math

Dividing Integers and Rational Numbers

Students will build Grade 7 mastery of dividing integers and rational numbers using models, equations, and test-style reasoning.

CH03-06 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 \(-36\div(-9)\)?

    1. \(-4\)
    2. \(-3\)
    3. \(3\)
    4. \(4\)
  2. What is \(48\div(-6)\)?

    1. \(-8\)
    2. \(-1\)
    3. \(1\)
    4. \(8\)
  3. Evaluate \(-72\div8\).

    1. \(-9\)
    2. \(-8\)
    3. \(8\)
    4. \(9\)
  4. What is \(\frac{3}{4}\div\frac{1}{2}\)?

    1. \(\frac{3}{8}\)
    2. \(\frac{2}{3}\)
    3. \(\frac{3}{2}\)
    4. \(2\)
  5. Compute \(\frac{5}{6}\div\frac{5}{9}\).

    1. \(\frac{25}{54}\)
    2. \(\frac{3}{2}\)
    3. \(\frac{25}{30}\)
    4. \(\frac{3}{1}\)
  6. Which division expression equals \(2\)?

    1. \(\frac{1}{3}\div\frac{1}{3}\)
    2. \(\frac{2}{5}\div\frac{4}{5}\)
    3. \(\frac{4}{7}\div\frac{2}{7}\)
    4. \(\frac{3}{8}\div\frac{3}{4}\)
  7. Divide \(2\frac{1}{4}\div\frac{3}{4}\).

    1. \(2\)
    2. \(2\frac{2}{3}\)
    3. \(3\)
    4. \(4\)
  8. What is \(-\frac{2}{3}\div\frac{4}{5}\)?

    1. \(-\frac{5}{6}\)
    2. \(-\frac{8}{15}\)
    3. \(\frac{8}{15}\)
    4. \(\frac{5}{6}\)
Teacher and parent reference

Answer key and explanations

  1. D. \(4\)

    Negative divided by negative is positive. Calculate the magnitude: \(36\div9=4\). Apply sign rule: \((-)\div(-)=(+)\). Thus \(-36\div(-9)=4\).

  2. A. \(-8\)

    Positive divided by negative is negative: \(48\div(-6)=-8\).

  3. A. \(-9\)

    Negative divided by positive is negative: \(-72\div8=-9\).

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

    Multiply by the reciprocal: \(\frac{3}{4}\div\frac{1}{2}=\frac{3}{4}\times\frac{2}{1}=\frac{6}{4}=\frac{3}{2}\).

  5. B. \(\frac{3}{2}\)

    \(\frac{5}{6}\div\frac{5}{9}=\frac{5}{6}\times\frac{9}{5}=\frac{45}{30}=\frac{3}{2}\).

  6. C. \(\frac{4}{7}\div\frac{2}{7}\)

    \(\frac{4}{7}\div\frac{2}{7}=\frac{4}{7}\times\frac{7}{2}=\frac{4}{2}=2\).

  7. C. \(3\)

    Convert: \(2\frac{1}{4}=\frac{9}{4}\). Then \(\frac{9}{4}\div\frac{3}{4}=\frac{9}{4}\times\frac{4}{3}=\frac{9}{3}=3\).

  8. A. \(-\frac{5}{6}\)

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

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