Fractions overview

​What is a fraction?
A fraction represents part of a whole. Here are some fraction models.

​Fractions of a set
Fractions can also represent parts of a set or group. For example, 3 4 of these circles are shaded in.

​Fraction words: numerator and denominator
In a fraction, the denominator tells you how many equal parts the whole is split into. The numerator tells you how many of those parts you have. The denominator is the bottom number, and the numerator is the top number.

For example, in the fraction 5/6 , 6 is the denominator. The model shows 6 equal parts in the whole. The numerator is 5. The model shows 5 equal parts shaded.

​Fraction names

When you split a whole into equal parts, those parts have names. Here are some of those names.

​Equivalent fractions
Sometimes, two fractions show the same amount. Those fractions are called equivalent fractions. For example, the fractions 1/4 and 2/8 are equivalent. They show the same part of a whole.

​To find an equivalent fraction without a model, multiply or divide the top and bottom of a fraction by the same number.
For example, if you multiply the top and bottom of 2/8 by 3, you get the equivalent fraction 6/24 . If you divide the top and bottom of 2/8 by 2, you get the equivalent fraction 1/4 .

​Comparing fractions
You can compare two fractions to see which fraction is greater. If the fractions have the same denominator, then the greater fraction has the greater numerator. For example, 4/5 is greater than 3/5.

​If two fractions have the same numerator, the fraction with the smaller denominator is the greater fraction. For example, 3/4 is greater than 3/6 .

​You can also compare fractions with unlike denominators by writing the fractions using a common denominator.

​Adding fractions

You can add fractions. Look at the models to see how to add fractions with like denominators.

​You can also add fractions with unlike denominators by making equivalent fractions with like denominators.

​Subtracting fractions

You can subtract fractions, too. Look at the models to see how to subtract fractions with like denominators.

​You can also subtract fractions with unlike denominators by making equivalent fractions with like denominators.

​Multiplying fractions

You can also multiply fractions. To multiply fractions, multiply the numerators, and then multiply the denominators. Let's try it with 2/3 × 1/5 .

​You can multiply a fraction and a whole number by writing the whole number as a fraction with a denominator of 1.

​Dividing fractions

If you need to divide by a fraction, you can multiply by its reciprocal instead. You can find the reciprocal of a fraction by switching the numerator and denominator. Let's try it for 1/4 ÷ 3/7 . The reciprocal of 3/7 is 7/3 .

​You can divide fractions by whole numbers and divide whole numbers by fractions using the same steps. Just be sure to write the whole number as a fraction with a denominator of 1.

​Simplest form

When you solve problems with fractions, you may want to write your answer in simplest form. A fraction is in simplest form if the top and bottom have no common factors other than 1. In other words, you cannot divide the top and bottom any further and have them still be whole numbers. Simplest form can also be called lowest terms.

For example, the fraction 2/7 is in simplest form. There's no number that divides both 2 and 7, other than 1.

The fraction 6/15 is not in simplest form. You can divide both the numerator and denominator by 3.

​The fraction 6/15 is equivalent to 2/5 . There's no number that divides both 2 and 5, other than 1. So, the simplest form of 6/15 is 2/5 .

​An improper fraction is a fraction where the numerator is greater than or equal to the denominator. For example, 13/4 is an improper fraction, since 13 is larger than 4.