B1/3, because cutting a whole into only 3 parts makes each part bigger
CThey are the same size because both have 1 in the numerator
DIt depends on how big the original whole is
When you cut a whole into more pieces, each piece gets smaller — not bigger. A whole cut into 3 parts gives larger pieces than a whole cut into 8 parts. So 1/3 > 1/8, even though 8 > 3. Option A is the most common misconception: treating the denominator like a whole number and thinking bigger denominator = bigger fraction. Option C misunderstands the numerator — having 1 of something does not make all fractions equal.
Question 2 Multiple Choice
Two identical pizzas are cut — yours into 6 equal slices, your friend's into 4 equal slices. You each take 1 slice. Who has more pizza?
AYou do, because 6 slices means more pizza total
BYour friend does, because 4 slices means each slice is larger
CYou both have the same — each of you has exactly 1 slice
DYour friend does, because 6 is a bigger number than 4
Both pizzas are the same size, but yours is divided into more pieces. More pieces sharing the same whole means each piece is smaller. Your friend's pizza has only 4 slices, so each slice is 1/4 of the pizza — a larger piece than your 1/6 slice. Option C is a common error: 'one slice' sounds equal, but the size of the slice depends on how many pieces the whole was divided into.
Question 3 True / False
1/2 is larger than 1/4 because dividing a whole into only 2 parts makes each part larger than dividing it into 4 parts.
TTrue
FFalse
Answer: True
Fewer cuts means bigger pieces. A whole cut in half produces two large pieces (each is 1/2 of the whole). The same whole cut into fourths produces four smaller pieces (each is 1/4). Because both have 1 in the numerator, we are comparing single pieces — and the half is visibly larger than the quarter.
Question 4 True / False
1/5 is larger than 1/3 because 5 is a larger number than 3.
TTrue
FFalse
Answer: False
This is the core misconception about unit fractions. A larger denominator means the whole was divided into more parts, so each part is smaller. 1/3 means the whole was divided into 3 parts — larger pieces. 1/5 means the whole was divided into 5 parts — smaller pieces. Therefore 1/3 > 1/5, opposite of what the denominator size alone would suggest.
Question 5 Short Answer
Why does a larger denominator mean a smaller unit fraction? Explain using the idea of dividing a whole into equal parts.
Think about your answer, then reveal below.
Model answer: The denominator tells you how many equal pieces the whole was cut into. The more pieces you cut a whole into, the smaller each piece must be — because all the pieces together still only make one whole. So a denominator of 8 means the whole was cut into 8 tiny pieces, while a denominator of 3 means it was cut into only 3 large pieces. One piece from the set of 8 is much smaller than one piece from the set of 3.
This is the key insight that unlocks fraction comparison. Students who treat fractions like whole numbers assume larger digits = larger value. But the denominator is a divisor: it tells you into how many equal shares the whole is being split. More shares = smaller individual share. Building this intuition with paper-folding or drawn diagrams makes it concrete before applying it abstractly.