 A fraction of a pie: What are fractions?

## We started with whole numbers

When we first thought about the number line, we counted only in whole numbers – we went straight from zero to one to two to three. But what if we wanted to stop in between the numbers?

## Halves and quarters

If we stop halfway between 0 and 1, we call that number a half – 1/2 – one out of two parts of a whole number. If we stop halfway between 0 and 1/2, we call that number a quarter – 1/4 – one out of four parts of a whole number. What if we stop halfway between 2 and 3? Then we call that number 2 1/2. Or we can call it 5/2 – five halves, instead of 2 1/2 whole numbers. Or we could call it 10/4 – ten quarters of a whole number. A number line is infinite in both directions.

## Numerator and denominator

When we write fractions this way, we call the top number the numerator and the bottom number the denominator.

## Decimals: another way to write fractions

Another way to write the numbers that come between whole numbers is as decimals. Decimals are just a different way to write down the same idea of halves and quarters. Instead of writing 50/100, we write 0.50, and instead of writing 25/100, we write 0.25.

## How do you add fractions?

How do you add fractions together? If the denominators are the same, it’s easy: just add the top numbers (the numerators) together: 1/8 + 2/8 = 3/8. But what about if the denominators aren’t the same?