Testinar Grade 3 math

Comparing Fractions with Same Numerator or Denominator

Students will compare fractions with the same numerator or denominator and justify the comparison.

CH04-05 Fractions
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 true?

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

  2. Compare \(\frac{2}{3}\) and \(\frac{2}{4}\). Which is true?

    Comparing Fractions with Same Numerator or Denominator visual for G3-C04-T05-Q002
    1. \(\frac{2}{3}<\frac{2}{4}\) (bigger denominator = bigger fraction)
    2. \(\frac{2}{3}=\frac{2}{4}\) (both have numerator 2)
    3. \(\frac{2}{3}>\frac{2}{4}\)
    4. \(\frac{2}{4}>\frac{2}{3}\) (4 > 3, so \(\frac{2}{4}\) is larger)

  3. The bars show two fractions. Which is larger?

    Comparing Fractions with Same Numerator or Denominator visual for G3-C04-T05-Q003
    1. \(\frac{2}{6}\) (6 > 3)
    2. \(\frac{2}{3}\) (shaded area is larger)
    3. They are equal
    4. Cannot tell from the bars

  4. Which comparison is true?

    1. \(\frac{3}{4}<\frac{3}{6}\)
    2. \(\frac{3}{4}=\frac{3}{6}\)
    3. \(\frac{3}{4}>\frac{3}{6}\) (same numerator, 4 < 6)
    4. \(\frac{3}{6}>\frac{3}{4}\) (6 > 4, so sixths are bigger)

  5. Using the bars, which is true?

    Comparing Fractions with Same Numerator or Denominator visual for G3-C04-T05-Q005
    1. \(\frac{1}{2}>\frac{1}{3}\) (halves are larger pieces)
    2. \(\frac{1}{2}<\frac{1}{3}\) (2 < 3)
    3. \(\frac{1}{2}=\frac{1}{3}\)
    4. \(\frac{1}{3}>\frac{1}{2}\) (1 out of 3 is more than 1 out of 2)

  6. Compare \(\frac{4}{6}\) and \(\frac{4}{8}\). Which is true?

    Comparing Fractions with Same Numerator or Denominator visual for G3-C04-T05-Q006
    1. \(\frac{4}{6}>\frac{4}{8}\) (same numerator, 6 > 8)
    2. \(\frac{4}{6}<\frac{4}{8}\) (8 > 6)
    3. \(\frac{4}{6}=\frac{4}{8}\)
    4. \(\frac{4}{8}>\frac{4}{6}\) (more pieces means more amount)

  7. On the number line, the red dot is at the same position as which label?

    Comparing Fractions with Same Numerator or Denominator visual for G3-C04-T05-Q007
    1. \(\frac{1}{2}\)
    2. \(\frac{3}{4}\)
    3. \(\frac{1}{4}\)
    4. Between \(\frac{1}{2}\) and \(\frac{3}{4}\)

  8. Lily has \(\frac{3}{8}\) of a chocolate bar. Noah has \(\frac{3}{4}\) of the same size chocolate bar. Who has more?

    1. Lily (8 > 4)
    2. Noah (3/4 is larger)
    3. They have the same amount
    4. Cannot tell without the bar's size
Teacher and parent reference

Answer key and explanations

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

    When comparing fractions with the same numerator (3), look at the denominator: fifths are bigger pieces than fourths. So \(\frac{3}{5}\) (3 large pieces) is less than \(\frac{3}{4}\) (3 slightly larger pieces). Key rule: smaller denominator = bigger pieces.

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

    Strategy: same numerator (2), so compare denominators. Thirds are bigger pieces than fourths (a whole divided by 3 gives bigger parts than divided by 4). Visual check: the blue bar (2/3) covers more area than the bar would if it were 2/4. Rule: when numerators match, smaller denominator wins.

  3. B. \(\frac{2}{3}\) (shaded area is larger)

    Visual reasoning: same numerator (2), so both take 2 pieces. But \(\frac{2}{3}\) divides the whole into 3 parts (each third is large), while \(\frac{2}{6}\) divides into 6 parts (each sixth is small). Comparing shaded amounts: 2 large pieces > 2 small pieces, so \(\frac{2}{3} > \frac{2}{6}\).

  4. C. \(\frac{3}{4}>\frac{3}{6}\) (same numerator, 4 < 6)

    Same numerator (3), different denominators: fourths are bigger pieces than sixths (the bar is cut into fewer, larger pieces). Three fourths covers more area than three sixths.

  5. A. \(\frac{1}{2}>\frac{1}{3}\) (halves are larger pieces)

    Same numerator (1): both fractions take 1 piece from their bar. But the first bar is divided in half (larger piece), the second in thirds (smaller piece). One half > one third. Visually: the green shaded area is larger in the first bar.

  6. A. \(\frac{4}{6}>\frac{4}{8}\) (same numerator, 6 > 8)

    Same numerator (4): sixths are bigger pieces than eighths. Comparing the shaded areas: 4 sixths covers more than 4 eighths. The fewer pieces the denominator divides into, the bigger each piece.

  7. B. \(\frac{3}{4}\)

    The dot is positioned at the third quarter mark on the number line, which is \(\frac{3}{4}\). This is greater than \(\frac{1}{2}\).

  8. B. Noah (3/4 is larger)

    Same numerator (3), different denominators, same chocolate bar: fourths are larger pieces than eighths. So \(\frac{3}{4}\) is more than \(\frac{3}{8}\). Noah has more because he has 3 larger pieces.

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