Testinar Grade 4 math

Equivalent Fractions

Students will generate and recognize equivalent fractions using visual models and multiplicative reasoning.

CH03-01 Fraction Equivalence and Comparison
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. Which fraction is equivalent to \(\frac{2}{3}\)?

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

  2. Look at the two fraction bars. Both bars are the same length. Which fraction should replace the question mark?

    Equivalent Fractions visual for G4-C03-T01-Q002
    1. \(\frac{1}{4}\)
    2. \(\frac{4}{4}\)
    3. \(\frac{3}{4}\)
    4. \(\frac{2}{4}\)

  3. What fraction is equivalent to \(\frac{1}{2}\)?

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

  4. Which fraction is in simplest form and equivalent to \(\frac{6}{8}\)?

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

  5. Look at the two circle models. They are the same size. Which fraction should replace the question mark?

    Equivalent Fractions visual for G4-C03-T01-Q005
    1. \(\frac{2}{8}\)
    2. \(\frac{1}{8}\)
    3. \(\frac{4}{8}\)
    4. \(\frac{3}{8}\)

  6. Multiply the numerator and denominator of \(\frac{3}{5}\) by 2. What fraction do you get?

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

  7. Which of these is NOT equivalent to \(\frac{1}{3}\)?

    1. \(\frac{2}{6}\)
    2. \(\frac{3}{9}\)
    3. \(\frac{2}{5}\)
    4. \(\frac{4}{12}\)

  8. Which fraction equals \(\frac{3}{4}\)?

    1. \(\frac{6}{8}\)
    2. \(\frac{6}{12}\)
    3. \(\frac{2}{5}\)
    4. \(\frac{5}{8}\)
Teacher and parent reference

Answer key and explanations

  1. D. \(\frac{4}{6}\)

    To find an equivalent fraction, multiply both the numerator and denominator by the same number. Here, multiply by 2: \(\frac{2}{3}=\frac{2\times2}{3\times2}=\frac{4}{6}\). Both pieces are twice as many, but they"re the same size!

  2. D. \(\frac{2}{4}\)

    The shaded parts in both bars cover the same length, even though the second bar has more pieces. When you divide each half into 2 more pieces, \(\frac{1}{2}\) becomes \(\frac{2}{4}\)—same amount, more pieces.

  3. C. \(\frac{3}{6}\)

    Multiply both top and bottom by 3: \(\frac{1}{2} = \frac{1\times3}{2\times3} = \frac{3}{6}\). This gives you more pieces, but they still cover the same amount!

  4. A. \(\frac{3}{4}\)

    To simplify, divide both top and bottom by the same number. Here, divide by 2: \(\frac{6}{8} = \frac{6\div2}{8\div2} = \frac{3}{4}\). This gives you fewer, bigger pieces.

  5. A. \(\frac{2}{8}\)

    The shaded wedges in both circles are the same size. The first circle is split into 4 pieces (1 shaded), the second into 8 pieces (2 shaded). They cover the same amount: \(\frac{1}{4} = \frac{2}{8}\).

  6. A. \(\frac{6}{10}\)

    Multiply the numerator and denominator by 2: \(\frac{3}{5} = \frac{3\times2}{5\times2} = \frac{6}{10}\).

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

    Check each option: \(\frac{1}{3} = \frac{2}{6} = \frac{3}{9} = \frac{4}{12}\). All equivalent! But \(\frac{2}{5}\) is different because when you cross-multiply, \(2 \times 3 = 6\) but \(5 \times 1 = 5\).

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

    Multiply both the numerator and denominator by 2: \(\frac{3}{4} = \frac{3\times2}{4\times2} = \frac{6}{8}\).

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