Questions: Fractions: Sixths and Eighths

Question 1

A pizza is cut into 8 equal slices. A second identical pizza is cut into 6 equal slices. Maya eats one slice from each pizza. Did she eat the same amount from each?

• A. Yes — she ate one slice from each, so she ate equal amounts from each pizza
• B. No — she ate more from the pizza cut into 6 slices, because each of those slices is larger
• C. No — she ate more from the pizza cut into 8 slices, because 8 is a larger number than 6
• D. Yes — the pizzas are the same size, so one slice from each must be equal

Answer: (B)

When the same whole is cut into more pieces, each piece is smaller. ⅙ > ⅛ because the pizza cut into only 6 pieces has larger slices than the one cut into 8. Option C reveals the key misconception: a larger denominator does NOT mean a larger piece — it means more cuts, so each piece is smaller.

Question 2

Which fraction represents the smallest amount?

• A. ½
• B. ⅙
• C. ⅛
• D. ⅓

Answer: (C)

When all numerators are 1, the fraction with the largest denominator is the smallest. ⅛ has denominator 8 — the whole is cut into the most pieces, so each piece is the smallest. The order from largest to smallest is: ½ > ⅓ > ⅙ > ⅛. This is counterintuitive because in regular counting, 8 > 6 > 3 > 2 — but as denominators, larger means smaller individual pieces.

Question 3

One-eighth of a pizza is larger than one-sixth of the same pizza.

• T. True
• F. False

Answer: False

⅛ < ⅙. When you cut the same whole into more pieces, each piece is smaller. Eight pieces are smaller than six pieces from the same pizza. Even though 8 > 6 as numbers, ⅛ < ⅙ as fractions — the denominator tells you how many equal pieces the whole was divided into, so more pieces means each piece is smaller.

Question 4

The denominator of a fraction tells you how many equal pieces the whole is divided into.

• T. True
• F. False

Answer: True

This is exactly what the denominator means. In ⅜, the denominator 8 tells you the whole was cut into 8 equal pieces. The numerator 3 tells you how many of those pieces you have. This is why comparing denominators — when numerators are the same — directly tells you which fraction is larger: a smaller denominator means fewer, bigger pieces.

Question 5

Why does a larger denominator mean a smaller fraction when the numerators are equal? Explain using a real-world example.

Model answer: Because when you divide a whole into more pieces, each piece is smaller. If you cut a candy bar into 2 equal pieces, each piece is ½ — large. If you cut the same candy bar into 8 equal pieces, each piece is ⅛ — much smaller. More cuts means smaller pieces. So even though 8 > 2 as numbers, ⅛ < ½ as fractions.

This is the central counterintuitive insight about fractions with the same numerator. Students used to thinking 'bigger number = bigger amount' must learn that the denominator works in reverse: it counts divisions, not quantities. The more divisions, the smaller each share. This understanding is essential before comparing fractions, placing them on number lines, or working with equivalent fractions.