In a/b, the numerator is the top number (a) and the denominator the bottom one (b). The denominator says into how many equal parts a whole is divided; the numerator says how many of those parts are taken. In 5/7, the whole is divided into 7 equal parts and 5 are taken, which is read “five sevenths.” Together they are called the terms of the fraction.
The word that confuses most is “denominator.” Its value counts parts, it does not measure their size: the more parts, the smaller each one is. Each part measures 1/b of the whole.
| Change | Example | Effect on the value |
|---|---|---|
| Denominator doubled | 1/4 becomes 1/8 | It is cut in half |
| Numerator doubled | 1/8 becomes 2/8 | It doubles |
| Both doubled | 3/4 becomes 6/8 | It does not change |
The table holds for a positive numerator and denominator and the same reference whole. Further down is what changes with negative signs.
What each term counts
A drawing is enough to see it. A bar that represents the whole is divided into 7 parts of equal length, and 5 are shaded. The 7 comes from counting all the parts of the bar and the 5 from counting the shaded ones. If the parts are not equal, the denominator stops making sense: a figure with five regions of very different areas does not let you say that two of them are 2/5 of the area.
The whole matters too. A fourth of a yard is 9 inches and a fourth of two yards is 18. The fraction is the same, but the amount depends on the whole you chose.
With a set of objects it works the same way. For 2/3 of 18 buttons, the denominator asks you to form 3 equal groups of 6 buttons and the numerator asks you to take 2 groups: 12 buttons.
Worked example: doubling both terms of 3/4
A pizza has four equal slices and three have been eaten. If you cut each slice in half, how do you write what was eaten, and does the amount change?
- Write what you already have. There are 4 equal parts and 3 eaten: 3/4.
- Cut each part in two. Now there are 4 × 2 = 8 equal parts, so the denominator is 8.
- Count the eaten pieces again. Each eaten slice is two pieces, so 3 × 2 = 6 pieces: the numerator is 6.
- Simplify to compare. The GCF of 6 and 8 is 2, and 6/8 = 3/4.
Result: 6/8 and 3/4 are the same amount.
Check: 3 ÷ 4 = 0.75 and 6 ÷ 8 = 0.75. There are twice as many pieces, but each one is half the size.
If you only doubled the numerator, 6/4 would equal 1.5 and the amount would be a different one. To generate more pairs like this, use the equivalent fractions tool.
What happens with the negative sign
A fraction is written with the sign in front, or in the numerator, and with a positive denominator. So 2/(−5) = −2/5, and if both terms are negative the value is positive: (−2)/(−5) = 2/5. A negative denominator does not mean “negative parts,” only that the sign has moved somewhere else.
With negatives, the rule of comparing by piece size flips. With numerator 1, −1/3 is less than −1/4, because it sits farther to the left on the number line. Normalize the sign before comparing and do not apply “bigger denominator, smaller value” blindly.
Why the denominator cannot be zero
A fraction is a division, and you cannot share something into zero parts. That is why 7/0 has no value. The numerator can be zero: 0/7 = 0, because no part is taken. The case 0/0 has no defined value, and the guide on why the denominator cannot be zero proves it with the quotient equation.
Practice
- In 11/15, which is the numerator and which is the denominator?
- Which is greater, 3/10 or 3/7?
- Write 4/(−9) with a positive denominator.
- Scale up 2/3 by multiplying both terms by 5.
Show the answers
- The numerator is 11 and the denominator is 15.
- 3/7, because sevenths are larger than tenths.
- −4/9.
- 10/15, which goes back to 2/3 when divided by 5.
Sources and where to go next
The English Wikipedia article Fraction describes a simple fraction as having an integer numerator and a non-zero integer denominator, and says the denominator cannot be zero (consulted October 17, 2026).
For the general idea of a fraction, start with what are fractions. The fraction glossary defines each term in one line, and the simplify fractions tool normalizes the sign and reduces with the GCF.