Understanding Fractions

What Are Fractions?#

A fraction is a number that represents part of a whole or part of a set. You use fractions every day — when you eat half a sandwich, share a pizza into slices, or divide a bag of apples among friends.

Equal Parts Are Essential#

The most important thing to understand about fractions is that the parts must be equal. If you cut a pizza into unequal pieces, you cannot name the pieces as fractions.

Example: A circle cut into 4 equal pieces — each piece is one-fourth (1/4). If the pieces are unequal, they are not fourths.

The Parts of a Fraction#

A fraction is written with two numbers separated by a line:

$\frac{3}{4}$43​

• The numerator (top number) tells how many parts you have: 3
• The denominator (bottom number) tells how many equal parts the whole is divided into: 4

A helpful memory trick: the Denominator is Down (at the bottom).

Types of Fractions You Will Learn#

Unit fractions have 1 as the numerator:

• 1/2 — one half (whole divided into 2 equal parts, you have 1)
• 1/3 — one third (whole divided into 3 equal parts, you have 1)
• 1/4 — one fourth (whole divided into 4 equal parts, you have 1)
• 1/6 — one sixth
• 1/8 — one eighth

Non-unit fractions have a numerator greater than 1:

• 2/3 — two thirds
• 3/4 — three quarters
• 5/8 — five eighths

Fractions of a Set#

Fractions can also describe part of a set (group of objects).

Example: 4 cats, 1 is black. What fraction of the cats are black? Answer: 1/4 (one out of four cats is black)

Fractions of sets work the same way: numerator = how many have the property, denominator = total in the set.