Grade 3 Comparing Fractions with Same Numerator or Denominator

Visual Model 1

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

• A. \(\frac{2}{3}<\frac{2}{4}\) (bigger denominator = bigger fraction)
• B. \(\frac{2}{3}=\frac{2}{4}\) (both have numerator 2)
• C. \(\frac{2}{3}>\frac{2}{4}\)
• D. \(\frac{2}{4}>\frac{2}{3}\) (4 > 3, so \(\frac{2}{4}\) is larger)

Why it works: 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.

Answer: \(\frac{2}{3}>\frac{2}{4}\)

Visual Model 2

Question: The bars show two fractions. Which is larger?

• A. \(\frac{2}{6}\) (6 > 3)
• B. \(\frac{2}{3}\) (shaded area is larger)
• C. They are equal
• D. Cannot tell from the bars

Why it works: 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 \(\frac{2}{3} > \frac{2}{6}\).

Answer: \(\frac{2}{3}\) is larger

Example 1

Question: Using the bars, which is true?

• A. \(\frac{1}{2}>\frac{1}{3}\) (halves are larger pieces)
• B. \(\frac{1}{2}<\frac{1}{3}\) (2 < 3)
• C. \(\frac{1}{2}=\frac{1}{3}\)
• D. \(\frac{1}{3}>\frac{1}{2}\) (1 out of 3 is more than 1 out of 2)

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

Answer: \(\frac{1}{2}>\frac{1}{3}\)

Example 2

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

• A. \(\frac{4}{6}>\frac{4}{8}\) (same numerator, 6 > 8)
• B. \(\frac{4}{6}<\frac{4}{8}\) (8 > 6)
• C. \(\frac{4}{6}=\frac{4}{8}\)
• D. \(\frac{4}{8}>\frac{4}{6}\) (more pieces means more amount)

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

Answer: \(\frac{4}{6}>\frac{4}{8}\)

Example 3

Question: On the number line, the red dot is at the same position as which label?

• A. \(\frac{1}{2}\)
• B. \(\frac{3}{4}\)
• C. \(\frac{1}{4}\)
• D. Between \(\frac{1}{2}\) and \(\frac{3}{4}\)

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

Answer: \(\frac{3}{4}\)

Problem 1

Question: Which comparison is true?

• A. \(\frac{3}{5}>\frac{3}{4}\)
• B. \(\frac{3}{5}<\frac{3}{4}\)
• C. \(\frac{3}{4}<\frac{3}{5}\)
• D. \(\frac{3}{5}=\frac{3}{4}\)

Why it works: 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.

Answer: \(\frac{3}{5}<\frac{3}{4}\)

Problem 2

Question: Which comparison is true?

• A. \(\frac{3}{4}<\frac{3}{6}\)
• B. \(\frac{3}{4}=\frac{3}{6}\)
• C. \(\frac{3}{4}>\frac{3}{6}\) (same numerator, 4 < 6)
• D. \(\frac{3}{6}>\frac{3}{4}\) (6 > 4, so sixths are bigger)

Why it works: 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.

Answer: \(\frac{3}{4}>\frac{3}{6}\)