Equal Parts

Four friends order one pizza and want to share it fairly. They cut it into 4 pieces. But if one piece is much bigger than the others, the sharing isn't fair. What do the pieces have to be like, and what do we call one of them?

Cutting into equal parts

For a fair share, the pizza must be cut into equal parts: pieces that are all the same size. Then each friend gets one of the 4 equal parts. We call that one quarter of the pizza, and we write it

• 1/4, said "one quarter".

A number written like this is called a fraction. It names a part of a whole. The parts must be equal: a bar cut into 4 pieces of different sizes is not cut into quarters.

The two numbers

A fraction has two numbers, one above the other (or with a slash between):

• the bottom number says how many equal parts the whole is cut into;
• the top number says how many of those parts you have.

So 3/4 means: cut into 4 equal parts, and take 3 of them. If three of the friends have eaten their slices, they have eaten 3/4 of the pizza, and 1/4 is left. The whole pizza is 4/4: all four quarters.

Mathematicians call the top number the numerator (the number that counts) and the bottom number the denominator (the number that names the size of the part).

Halves, thirds and quarters

Some fractions have their own names:

• cut into 2 equal parts, each is one half, 1/2;
• cut into 3, each is one third, 1/3;
• cut into 4, each is one quarter, 1/4.

After that, we say "fifths", "sixths", "tenths" and so on: 2/5 is "two fifths", 7/10 is "seven tenths".

Fractions are what the When It Doesn't Share Evenly lesson was waiting for. Two apples left over between 4 friends? Cut each apple into halves, and each friend gets 1/2 an apple more.

Try it at home

1. Fold a sheet of paper in half, then in half again. Open it. How many equal parts are there, and what is one of them called?
2. Colour 3 of the parts. What fraction of the sheet is coloured?
3. Cut an orange or a sandwich into what you think are equal parts. Are they really equal?

Answers: 4 parts, each one quarter; 3/4.

Words to know

• equal parts - pieces that are all the same size
• fraction - a number that names part of a whole, like 3/4
• bottom number (denominator) - how many equal parts the whole is cut into
• top number (numerator) - how many of those parts you have
• half, third, quarter - one of 2, 3 or 4 equal parts

Big idea

A fraction names part of a whole cut into equal parts. In 3/4, the 4 says the whole is cut into 4 equal parts, and the 3 says you have 3 of them. The parts must be equal, or it isn't a fraction of the whole.