What Is a Fraction?
A fraction represents a part of a whole. It is written as two numbers separated by a line:
3/4 (three-fourths)
The top number (numerator) tells you how many parts you have. The bottom number (denominator) tells you how many equal parts the whole was divided into.
3/4 means: the whole was divided into 4 equal parts, and you have 3 of them.
Three meanings of fractions
Fractions actually mean three related things:
1. Part of a whole: 3/4 of a pizza = the pizza is cut into 4 equal slices, you have 3.
2. A division: 3/4 = 3 ÷ 4 = 0.75. The fraction bar is a division symbol.
3. A number on the number line: 3/4 is a point between 0 and 1, three-fourths of the way from 0 to 1.
Understanding all three meanings gives your child a complete picture of what fractions are.
Key fraction facts
- 1/2 = one half: the most fundamental fraction
- Fractions equal to 1: 4/4 = 3/3 = 2/2 = 1 (when numerator equals denominator)
- Fractions greater than 1: 5/4 = 1 1/4 (when numerator is larger than denominator)
- Equivalent fractions: 1/2 = 2/4 = 3/6 = 4/8 (same value, different representation)
The numerator-denominator relationship
A common source of confusion:
- Bigger denominator = smaller pieces: 1/8 < 1/4 (eighths are smaller than fourths)
- Bigger numerator = more pieces: 5/8 > 3/8 (more eighths means a larger amount)
Fractions connect to everything
Fractions are foundational to:
- Decimals: 3/4 = 0.75
- Percents: 3/4 = 75%
- Ratios: 3 out of 4 = ratio of 3:4
- Division: 3/4 = 3 ÷ 4
- Probability: a 3 in 4 chance = 3/4
Related concepts
- How to Teach Fractions: full teaching guide
- Equivalent fractions: same value, different form
- Comparing fractions: which is bigger?
- Fractions on a number line: fractions as numbers
- Why kids struggle with fractions: common difficulties