# Numbers/Content/What Are Numbers/Fractions

## New Words

• Fraction
• Mixed Fraction
• Numerator
• Denominator

## Lesson

Often it is useful to use numbers for amounts that are only a part of a bigger amount. For example: you cut an apple into six parts and give one to a friend. How much of the apple do you have left? You have five parts of six. There is a special way to show this amount, using numbers.

### Fractions

A fraction is two numbers, one on top of the other, with a line in the middle, like this: $\displaystyle \frac{5}{6}$ . The higher number is the numerator. It shows how many parts. The lower number is the denominator. It shows you the amount of parts that make one thing. If the denominator is big, the parts are small.

 $\displaystyle \frac{2}{2}$ = $\displaystyle \frac{3}{3}$ = $\displaystyle \frac{4}{4}$ = When the numerator and denominator are the same, the fraction is equal to one. For positive fractions, when the numerator is less than the denominator, the fraction is less than one, and when the numerator is greater than the denominator, the fraction is greater than one (the opposite is true for negative fractions). The denominator can never be zero.

When a fraction is more than one, you can show it as a mixed fraction. Mixed fractions are a normal number followed by a fraction. For example, the fraction on the right of the equals sign is a mixed fraction.

$\displaystyle \frac{11}{6} = 1\frac{5}{6}$ .

### More, Less, and Equal

These are examples of equal fractions:

• $\displaystyle \frac{1}{1}=\frac{2}{2}=\frac{3}{3}$ • $\displaystyle \frac{1}{2}=\frac{2}{4}=\frac{3}{6}$

These are examples of more and less fractions:

• $\displaystyle \frac{2}{4} < \frac{3}{4}$ • $\displaystyle \frac{2}{3} > \frac{2}{4}$ • $\displaystyle \frac{2}{3} < \frac{3}{4}$ 