A fraction is a number written a/b, with b not equal to zero: the denominator b says into how many equal parts a whole is divided and the numerator a says how many of those parts are taken. With 3/4 you take three of four parts. The same fraction is the share 3 ÷ 4 = 0.75 and a point on the number line.
| Reading | Question it answers | Example |
|---|---|---|
| Part of a whole | How many equal parts are taken? | 3 of the 4 parts of a bar |
| Sharing | How much does each group get? | 3 pies among 4 people: 3 ÷ 4 |
| Point on the line | Where does it sit relative to 0 and 1? | Three quarters of the way from 0 to 1 |
The three readings give the same value. Use the first for amounts between 0 and 1, the second when something is shared, and the third to compare, or for values greater than 1 and negative ones.
What the numerator and denominator count
The denominator sets how many equal parts the whole is divided into, and each part measures 1 divided by that number. The numerator counts how many parts are taken. If the denominator goes up, the parts get smaller: an eighth of a pizza is less than a fourth of the same pizza.
The whole has to be the same and the parts must be equal. If you cut a bar into four unequal pieces and take three, you do not have three fourths of the bar. The denominator is never 0, but the numerator can be 0, and then the fraction equals 0.
Throughout this page, “fraction” means a common fraction: a number written a/b where a and b are both integers, the way the English Wikipedia article on fractions defines it.
Worked example: sharing three pies among four people
Worked example: 3 pies among 4 people
There are 3 identical pies for 4 people. Each person gets the same amount. What part of a pie does each one get?
- Write the sharing. There are 3 pies shared equally among 4 people.
- Cut each pie into 4 equal parts. That gives 12 pieces, and each piece is a fourth of a pie.
- Share. Each person takes one piece from each pie, which is 3 pieces of a fourth.
- State the result. Three fourths of a pie, which as a decimal is 0.75.
Result: each person gets 3/4 of a pie.
Check: 4 people with 3/4 each add up to 12/4 = 3 pies, exactly the number there were.
Each bar is a pie. A, B, C and D are the four people; each one gets the pieces with their letter.
A fraction can be greater than 1 or negative
When the numerator is greater than the denominator, the fraction is greater than 1. With 7/4 you need one complete whole, which is 4/4, and three fourths of another identical whole, so 7/4 = 1 3/4. If the numerator and denominator are the same, the fraction equals exactly 1. “Improper” describes that way of writing it and does not point to any mistake.
A negative fraction sits to the left of 0 on the line. The number −1/2 is half a step from 0, and −2/4 occupies the same point because dividing both terms by 2 gives −1/2.
Practice with your own numbers
Practice
- Five quarts of water are shared equally between two pitchers. How much is in each one, as a fraction and as a mixed number?
- What is 0/8 worth?
- Write 9/4 as a mixed number.
Show the answers
- 5 ÷ 2 = 5/2 quarts, which is 2 1/2 quarts.
- 0, because no part is taken.
- 9/4 = 8/4 + 1/4 = 2 1/4.
Where to go next
The guide to numerator and denominator looks at what happens when you change one of the two terms. To tell proper, improper and mixed fractions apart, see the types of fractions. If you want to see how many meanings a fraction has in different problems, continue with the meanings of a fraction.
To draw a fraction, use visual fractions or read the guide to drawing them, and to place it among others, the fraction number line. The guide to reading and writing fractions teaches how to say them aloud, and the glossary defines each term. When you want to calculate, the fraction calculator returns the result with its steps.
Sources
The English Wikipedia article Fraction defines a fraction as representing a part of a whole or any number of equal parts, defines a common fraction as a rational number a/b where a and b are both integers, says the denominator cannot be zero, and says that fractions can represent ratios and division, with the numerator as the dividend and the denominator as the divisor (consulted October 17, 2026). It was used only for those definitions; the rest of the page is our own elementary arithmetic examples.