Understanding unit fractions
I can explain what a unit fraction like 1/4 means and show it with a model.
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If you share a sandwich equally with three friends, how much does each person get?
A fraction describes equal parts of one whole. The bottom number, the denominator, tells how many equal parts the whole is split into.
A unit fraction has a numerator of 1. It names exactly one of those equal parts: 1/4 is one part when the whole is split into 4 equal parts.
The parts must be equal in size. Cutting a rectangle into 4 pieces of different sizes does not make fourths.
More parts means smaller parts. That is why 1/8 is smaller than 1/3, even though 8 is bigger than 3.
Worked examples
Naming one part
- Count the equal parts: there are 5.
- The denominator is 5.
- One part is shaded, so the fraction is 1/5 — one fifth.
Comparing unit fractions
- Both bars are the same whole.
- The top bar is split into 3 parts; the bottom into 6.
- Each sixth is half the size of a third, so 1/3 > 1/6.
Explore
Keep the numerator at 1 and increase the denominator. Watch how one part gets smaller as the whole is split into more equal parts.
Guided practice
Use the hints as much as you like. You can try each question as many times as you need.
0 of 2 solved
What unit fraction is shaded?
Choose the symbol: 1/3 ? 1/8
Independent practice
Answers are checked exactly — equivalent fractions count unless a question asks for a particular form.
0 of 4 solved
A pizza is cut into 6 equal slices. You eat 1 slice. What fraction of the pizza did you eat?
How many copies of 1/5 make one whole?
Choose the symbol: 1/10 ? 1/2
Which picture shows 1/4?
Common mistakes
Thinking 1/8 is bigger than 1/4 because 8 is bigger than 4.
Why it happens: The denominator counts parts. More parts of the same whole means each part is smaller.
What to do: Draw two same-sized bars and split them. Compare the size of one part, not the number.
Calling any 1 of 4 pieces “one fourth”, even when the pieces are not equal.
Why it happens: A fraction only describes equal shares of the whole.
What to do: Before naming a fraction, check that every part is the same size.
Lesson check
Three practice questions to check your understanding. Hints and retries are allowed, so this counts as practice — not mastery.
0 of 3 solved
A ribbon is cut into 8 equal pieces. What fraction is one piece?
Choose the symbol: 1/7 ? 1/5
How many 1/9 pieces fill one whole?
Show mastery on your own
Ready? Answer 4 new questions with no hints and one try each. This is the only way a lesson is marked as mastered.
Start mastery check