GoalFind fractions that are equal to one half, such as 2/4, 3/6 and 4/8.
New words
half · one of 2 equal parts, written 1/2equal to · the same amountequivalent fractions · different fractions that show the same amount
Explanation
A half is 1 of 2 equal parts, written 1/2. But the same amount can have other names. Fold a strip into 4 equal parts and shade 2 of them: you have shaded the same amount as 1/2, so 2/4 = 1/2. In the same way, 3 of 6 equal parts make a half, and so do 4 of 8 equal parts. Fractions that show the same amount are called equivalent fractions. Here is a trick: in a fraction equal to one half, the top number is half of the bottom number. In 2/4, the 2 is half of 4. In 3/6, the 3 is half of 6. In 4/8, the 4 is half of 8. A fraction such as 3/8 is not a half, because half of 8 is 4, not 3.
Worked examples
Fold a strip into 2 equal parts and shade 1: that is 1/2. Now fold each part in half again. There are 4 equal parts and the shaded part is 2 of them, so 1/2 = 2/4.
A pizza is cut into 6 equal slices and Salma eats 3 of them. Half of 6 is 3, so she ate 3/6 of the pizza, and 3/6 = 1/2.
Is 3/8 equal to 1/2? The top bar shows 3/8 and the bottom bar shows 4/8. Half of 8 is 4, so only 4/8 is a half. The fraction 3/8 is less than a half.
Class activity
Half detective. On squared paper, draw four strips of the same length. Cut the first strip into 2 equal parts, the second into 4, the third into 6 and the fourth into 8. Shade one half of each strip. Under each strip write the fraction you shaded. What do you notice about the top number and the bottom number?
Practice
1
Write a fraction with 4 on the bottom that is equal to 1/2.
2/4, because 2 is half of 4.
2
A round pizza is cut into 8 equal slices and 4 slices are shaded. Write the fraction. Does it equal 1/2?
The fraction is 4/8. Yes, 4 is half of 8, so 4/8 = 1/2.
3
Is 3/6 equal to 1/2? How do you know?
Yes. The 3 is half of 6, so 3/6 = 1/2.
4
Mariam shaded the bar as shown. Did she shade a half?
No. She shaded 2 of 6 parts. Half of 6 is 3, so 2/6 is less than a half.
5
Find the missing numbers: 1/2 = ?/8 and 3/6 = 1/?.
1/2 = 4/8, because 4 is half of 8. And 3/6 = 1/2, so the missing number is 2.
