Testinar Grade 4 math

Comparing Fractions

Students will compare fractions with different numerators and denominators using benchmarks, models, and common denominators.

CH03-02 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 comparison is correct?

    1. \(\frac{2}{3}<\frac{1}{2}\)
    2. \(\frac{2}{3}=\frac{1}{2}\)
    3. \(\frac{2}{3}>\frac{1}{2}\)
    4. \(\frac{2}{3}<\frac{3}{6}\)

  2. Compare: \(\frac{1}{4}\) and \(\frac{3}{4}\).

    1. \(\frac{1}{4}>\frac{3}{4}\)
    2. Cannot compare
    3. \(\frac{1}{4}=\frac{3}{4}\)
    4. \(\frac{1}{4}<\frac{3}{4}\)

  3. Which inequality is true?

    1. \(\frac{5}{8}>\frac{7}{8}\)
    2. \(\frac{5}{8}<\frac{1}{2}\)
    3. \(\frac{5}{8}=\frac{7}{8}\)
    4. \(\frac{5}{8}<\frac{7}{8}\)

  4. Is \(\frac{3}{5}\) greater than or less than \(\frac{1}{2}\)?

    1. Greater than \(\frac{1}{2}\)
    2. Less than \(\frac{1}{2}\)
    3. Equal to \(\frac{1}{2}\)
    4. Cannot determine

  5. Look at the fraction bars below. Which comparison is correct?

    Comparing Fractions visual for G4-C03-T02-Q005
    1. \(\frac{3}{4}<\frac{2}{4}\)
    2. \(\frac{2}{4}>\frac{3}{4}\)
    3. \(\frac{3}{4}=\frac{2}{4}\)
    4. \(\frac{3}{4}>\frac{2}{4}\)

  6. Which fraction is less than \(\frac{1}{2}\)?

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

  7. Two pizzas are the same size. Ava ate \(\frac{1}{3}\) of one pizza. Sam ate \(\frac{1}{4}\) of another. Who ate more?

    Comparing Fractions visual for G4-C03-T02-Q007
    1. Ava ate more
    2. Sam ate more
    3. They ate the same
    4. Cannot determine

  8. Compare: \(\frac{3}{8}\) and \(\frac{3}{10}\).

    1. \(\frac{3}{8}<\frac{3}{10}\)
    2. Cannot compare
    3. \(\frac{3}{8}=\frac{3}{10}\)
    4. \(\frac{3}{8}>\frac{3}{10}\)
Teacher and parent reference

Answer key and explanations

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

    To compare, find a common denominator: \(\frac{2}{3}=\frac{4}{6}\) and \(\frac{1}{2}=\frac{3}{6}\). Since \(4>3\), we have \(\frac{2}{3}>\frac{1}{2}\).

  2. D. \(\frac{1}{4}<\frac{3}{4}\)

    Same denominators? Just compare the numerators! Since \(1<3\), \(\frac{1}{4}<\frac{3}{4}\).

  3. D. \(\frac{5}{8}<\frac{7}{8}\)

    The denominators match, so look at the numerators. Since \(5<7\), \(\frac{5}{8}<\frac{7}{8}\).

  4. A. Greater than \(\frac{1}{2}\)

    Compare to \(\frac{1}{2}\): Convert to tenths: \(\frac{3}{5}=\frac{6}{10}\) and \(\frac{1}{2}=\frac{5}{10}\). Since \(6>5\), \(\frac{3}{5}>\frac{1}{2}\).

  5. D. \(\frac{3}{4}>\frac{2}{4}\)

    The bars show us! The blue bar for \(\frac{3}{4}\) is longer than the coral bar for \(\frac{2}{4}\). Bigger shaded area means bigger fraction.

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

    Check each against \(\frac{1}{2}\): \(\frac{3}{5}>\frac{1}{2}\), \(\frac{3}{6}=\frac{1}{2}\), \(\frac{4}{6}>\frac{1}{2}\). But \(\frac{2}{5}<\frac{1}{2}\) because \(\frac{2}{5}=\frac{4}{10}<\frac{5}{10}=\frac{1}{2}\).

  7. A. Ava ate more

    Same numerator, different denominators: larger denominator means smaller pieces. Since thirds are bigger than fourths, \(\frac{1}{3}>\frac{1}{4}\).

  8. D. \(\frac{3}{8}>\frac{3}{10}\)

    Same numerator (3) means compare denominators: eighths are bigger pieces than tenths, so \(\frac{3}{8}>\frac{3}{10}\).

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