In plain words
What does the top number of a fraction mean?
The top number, the numerator, counts how many of the equal parts you have. In 3/5, the whole is cut into 5 equal parts and the 3 says you have three of them.
- The big idea
- The top number counts how many of the equal parts we have. In 3/5, we have 3 of the 5 equal parts.
- The common confusion
- The top number counts all the parts, or the parts left over, instead of the parts we have. It often sounds like this: “The top number is how many pieces there are altogether.”
Why it works
The top number of a fraction is called the numerator. It counts how many of the equal parts we have, or are talking about.
In 3/5, the bottom number says the whole is cut into 5 equal parts, and the top number says we have 3 of them. To show 3/5, shade 3 of 5 equal parts.
The numerator does not count all the parts; that is the job of the bottom number. Three shaded parts next to five unshaded parts make 8 parts in all, which shows 3/8, not 3/5.
Any 3 of the 5 equal parts make 3/5, whether they sit side by side or not, because all the parts are the same size.
Another way to see it: 3/5 is three fifths, 1/5 + 1/5 + 1/5. The numerator counts how many fifths there are. When it reaches 5, as in 5/5, we have the whole.
A worked example
A pizza is cut into 8 equal slices and you eat 3. You ate 3/8 of the pizza, and 5/8 is left. The bottom number is 8 both times, because the pizza is still made of 8 equal slices; the top number counts the slices we are talking about.
Why this confusion is so common
Children are used to counting everything in sight, so it feels natural to count all the parts, or to count shaded and unshaded parts as two separate numbers. A fraction asks for two counts that work together: the parts we have, out of the equal parts that make the whole. Saying the unit out loud (“three fifths”) helps, because it names what is being counted.
Try this away from the screen
Use an egg carton with 6 cups as the whole. Put an egg, a ball of paper or a pebble in 4 of the cups and ask what fraction of the carton is full (4/6) and what fraction is empty (2/6). Then swap roles and let your child set a challenge for you.
Helpful things to say
| Instead of | Try |
|---|---|
| “Put the shaded ones on top and the unshaded ones on the bottom.” | “How many equal parts make the whole? How many of those parts do we have?” |
| “3/5 means 3 and 5.” | “3/5 means three fifths: three parts, each one fifth of the whole.” |
Practice questions
For grown-ups helping out: the answers are tucked away so learners can try first.
Shade 4/6 of this circle.
Show the answer
Answer: shade parts of the circle so that 4/6 of it is shaded. The circle has 6 equal parts, matching the bottom number. The top number says to shade 4 of them.
A pizza is cut into 8 equal slices. Sam eats 3 slices. What fraction of the pizza is left?
Show the answer
Answer: 5/8. 8 equal slices make the whole pizza, so the bottom number is 8. 5 slices are left, so the top number is 5: 5/8 of the pizza is left.
What fraction of the rectangle is shaded?
Show the answer
Answer: 3/4. 4 equal parts make the rectangle and 3 of them are shaded, so 3/4 of the rectangle is shaded.
Drag the point to 4/5 on this number line.
Show the answer
Answer: place the point at 4/5. The space from 0 to 1 is cut into 5 equal parts, each 1/5. The top number says to count 4 of those parts from 0.
Questions people ask
What does the numerator tell you?
The numerator (the top number) tells how many of the equal parts you have. In 3/5, the whole is cut into 5 equal parts and you have 3 of them.
Can the numerator be bigger than the denominator?
Yes. 7/4 means seven fourths. Four fourths make one whole, so 7/4 is one whole and three fourths more. Fractions like this are greater than 1.
Does it matter which parts are shaded?
No, as long as the parts are equal. Any 3 of 5 equal parts show 3/5, whether they are next to each other or spread out.
What does a numerator of 0 mean?
0/5 means none of the 5 equal parts, so it is worth zero.
Words to know
- Numerator
- The top number of a fraction. It counts how many of the equal parts we have.
- Denominator
- The bottom number of a fraction. It tells how many equal parts make one whole.
- Unit fraction
- A fraction with 1 on top, such as 1/2, 1/3 or 1/8. It is one equal part of the whole.
- Fraction
- A number that describes equal parts of a whole. Every fraction also has its own point on the number line.
Curriculum connections
We don’t assume any particular curriculum. For teachers in the United States, here’s how this slice lines up with the Common Core State Standards:
- 3.NF.A.1
Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
- 4.NF.B.3
Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
- 3.NF.A.2.b
Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.
Related slices
The Bottom Number
What does the bottom number of a fraction mean?
What the bottom number of a fraction counts: all the equal parts that make one whole. · About 3 minutes
The Bigger Numerator Trap
Which is bigger, (three eighths) or (two thirds)?
Why 2/3 is bigger than 3/8, even though 3 is bigger than 2. · About 3 minutes
Same Bottom, Compare the Top
How do you compare fractions with the same denominator?
Why 5/7 is bigger than 2/7: the pieces are the same size, so the one with more pieces is bigger. · About 3 minutes
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