Equivalent fractions and comparing fractions (grade 4) · lesson

Multiply top and bottom

💡 Multiply the top and bottom by the same number to get an equal fraction.

Times the top and bottom by the same number. The pieces get smaller, but you get more of them. The amount stays the same.

To fill in a missing number, first find what changes one bottom into the other. Then do the same to the top.

If the bottom is the missing number, work from the tops instead. Find what changes one top into the other, then do the same to the bottom.

🧠 Let's work it out

Find the missing top: 2/3 = ?/12.

The bottom went from 3 to 12: 3 × 4 = 12.
So times the top by 4 too: 2 × 4 = 8.

What do you think comes next?

equivalent fractions: fractions that name the same amount
numerator: the top number of a fraction
denominator: the bottom number of a fraction

🔗 Equivalent fractions and comparing fractions · Khan Academy ↗

Divide top and bottom

💡 Divide the top and bottom by the same number to get an equal fraction with smaller numbers.

This works the other way too. Divide the top and bottom by the same number.

Find what turns one top into the other. Then divide the bottom by the same number.

🧠 Let's work it out

Find the missing bottom: 6/15 = 2/?.

The top went from 6 to 2: 6 ÷ 3 = 2.
Divide the bottom by 3 too: 15 ÷ 3 = 5.

What do you think comes next?

simplify: write a fraction with smaller numbers that name the same amount

Compare with a common bottom

💡 To compare two fractions, rewrite them with the same bottom number and compare the tops.

You can't compare tops when the pieces are different sizes. So give both fractions the same bottom.

Multiply the two bottoms to find a bottom both can use. If one bottom already goes into the other, like 4 and 8, just use the bigger one. Then rewrite each fraction and compare the tops.

🧠 Let's work it out

Which is greater, 1/3 or 2/5?

Use fifteenths: 1/3 = 5/15.
And 2/5 = 6/15.
6 is more than 5.

What do you think comes next?

common denominator: a bottom number two fractions share

Check against one half

💡 A fraction is more than 1/2 when its top is more than half of its bottom.

Find half of the bottom number. Then look at the top.

If the top is more than that, the fraction is more than 1/2. If it is less, the fraction is less than 1/2. If it is equal, the fraction is 1/2.

🧠 Let's work it out

Is 5/9 more or less than 1/2?

Half of 9 is 4.5.
5 is more than 4.5.
So 5/9 is more than 1/2.

What do you think comes next?

benchmark: an easy number, like 1/2, used to compare