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A pie with a piece cut out

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?

The number line
Whole numbers
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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.

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.

Who invented a way to write fractions?
Where did Arabic numbers come from?

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.

More about decimals

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?

What’s a common denominator?
More about addition

Then you need to find a common denominator, make the denominators the same, and then add the numerators together. One way to find a common denominator is to multiply the denominators together.

So to add 1/4 and 1/3, you find that 12 is a common denominator for them. Convert 1/4 to 3/12 and 1/3 to 4/12, and then add 3/12 + 4/12 = 7/12.

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