Fractions Made Easy: What Numerators and Denominators Mean

Read the two numbers as a pair

In 3/4, the denominator 4 says the whole is split into four equal parts. The numerator 3 says we are considering three of those parts. The slash is not decoration: it means three divided by four.

A useful picture is a strip divided into four equal boxes with three shaded. The same picture can represent a length, a serving, a probability, or a point on a number line.

Compare fractions with the same denominator

If two fractions have the same denominator, compare their numerators. Five eighths is greater than three eighths because both count eighth-size pieces and five is more than three.

If the denominators differ, rename the fractions with a common denominator. For 1/2 and 3/8, turn 1/2 into 4/8. Now both fractions describe eighths, so 4/8 is greater than 3/8.

Add parts of the same size

When denominators match, add only the numerators and keep the denominator: 2/7 + 3/7 = 5/7. You are combining two sevenths with three sevenths, so the pieces stay sevenths.

With unlike denominators, first find a common denominator. For 1/3 + 1/4, twelfths work: 1/3 is 4/12 and 1/4 is 3/12. The sum is 7/12.

Simplify without changing the amount

A fraction is simplified when the numerator and denominator have no common factor greater than one. Divide both by the same number, because removing equal groups from the top and bottom keeps the value unchanged.

For 12/18, divide both numbers by 6 to get 2/3. A quick check is to multiply 2/3 by 6/6 and see that it returns to 12/18.

Use a number line to check your sense

Fractions between zero and one should land between those points on a number line. A fraction greater than one, such as 5/4, should land just past one. This estimate catches many sign, denominator, and simplification errors before a calculator does.