B1/3, because dividing a whole into fewer parts makes each part larger
CThey are equal because both fractions have 1 in the numerator
D1/6, because more pieces means a greater total
1/3 is larger. When you divide a whole into 3 equal parts, each part is bigger than when you divide the same whole into 6 equal parts. The denominator tells you how many cuts were made — more cuts means smaller pieces. The tempting wrong answer (1/6, because 6 > 3) is the classic misconception: applying whole-number reasoning ('bigger number = bigger') to fractions, where the relationship is inverted for unit fractions.
Question 2 Multiple Choice
One pizza is cut into 8 equal slices. An identical pizza is cut into 4 equal slices. If you take one slice from each pizza, which slice is larger?
AThe slice from the 8-piece pizza — there are more pieces, so each must be bigger
BThey are the same size because both are 'one slice'
CThe slice from the 4-piece pizza — fewer cuts means each piece is larger
DThe slice from the 8-piece pizza — 8 is greater than 4
1/4 of the pizza is a bigger piece than 1/8 of the same pizza. Cutting something into more pieces makes each piece smaller, not larger. Options A and D both fall for the misconception that a bigger denominator means a bigger fraction. Option B ignores that 'one slice' means different things depending on how many total slices there are.
Question 3 True / False
1/8 is greater than 1/4 because 8 is a greater number than 4.
TTrue
FFalse
Answer: False
This is the most common error with unit fractions. 8 > 4 as whole numbers, but 1/8 < 1/4 as fractions. The denominator tells you how many equal parts the whole was divided into — the more parts, the smaller each one. So 1/8 means one of eight tiny pieces, while 1/4 means one of four larger pieces. The fraction with the larger denominator is actually smaller.
Question 4 True / False
As the denominator of a unit fraction increases, the value of the fraction decreases.
TTrue
FFalse
Answer: True
This is the inverse relationship at the heart of comparing unit fractions. Going from 1/2 → 1/3 → 1/4 → 1/6 → 1/8, each fraction is smaller than the one before it, even though the denominators are getting larger. More equal parts means smaller pieces.
Question 5 Short Answer
Why is 1/10 smaller than 1/2, even though 10 is a larger number than 2? Explain using the idea of dividing a whole into parts.
Think about your answer, then reveal below.
Model answer: When you divide a whole into 10 equal parts, each part is much smaller than when you divide the same whole into only 2 equal parts. 1/10 means one of ten tiny pieces; 1/2 means one of two large pieces. The bigger the denominator, the more pieces the whole was cut into, which means each individual piece is smaller. So even though 10 > 2, the fraction 1/10 is far smaller than 1/2.
The key insight is the inverse relationship: denominator and piece size move in opposite directions for unit fractions. This is counterintuitive because students are used to larger numbers meaning larger amounts. The physical model (pizza slices, fraction strips) makes this relationship concrete and visible.