Fraction of a set

So far we've taken a fraction of a shape: half a pizza, a quarter of a square.

But we can also take a fraction of a group of objects: half of 8 apples, a quarter of 12 marbles.

How "half of" works

½ of 8 apples = 4 apples.

How do we get there?

1. Split the group into 2 equal halves.
2. 8 apples ÷ 2 = 4 apples in each half.

If we want a half, we take one of the two halves: 4 apples.

How "a quarter of" works

¼ of 12 marbles = 3 marbles.

1. Split 12 marbles into 4 equal quarters.
2. 12 ÷ 4 = 3 marbles in each quarter.

If we want a quarter, we take one of the four quarters: 3 marbles.

How "three quarters of" works

¾ of 12 = 9.

1. 12 ÷ 4 = 3 marbles in each quarter.
2. We want 3 quarters, so 3 × 3 = 9 marbles.

In other words: divide first, then take as many copies as the top number says.

More examples

• ½ of 10 = 10 ÷ 2 = 5.
• ½ of 6 = 6 ÷ 2 = 3.
• ¼ of 8 = 8 ÷ 4 = 2.
• ¼ of 20 = 20 ÷ 4 = 5.

Pay attention to the numbers

To take "½ of X", X must split into 2 equal parts. So X has to be an even number.

• ½ of 6 ✓ (6 ÷ 2 = 3)
• ½ of 7 ✗ (7 doesn't split equally)

For "¼ of X", X must split into 4 equal parts. So X has to be a multiple of 4 (4, 8, 12, 16, 20…).

In real life

• "Eat half of your apple" → 1/2 of 1 apple.
• "A quarter of the class is sick today" → if class is 24, that's 6 children.
• "Three quarters of the pizza is gone" → ¾ of 8 slices = 6 eaten, 2 left.

Summary

• A fraction can be taken of a group, not only of a shape.
• ½ of X = X ÷ 2.
• ¼ of X = X ÷ 4.
• ¾ of X = (X ÷ 4) × 3.
• The number X has to split equally into the right number of parts.