Step by step
The question
Question: work out 2/3 ÷ 4/9.
1 Flip and multiply
To divide by a fraction, we multiply by its flip.
Keep the first number: 2/3.
Change divide to times: ÷ becomes ×.
Turn the second fraction upside down: 4/9 becomes 9/4.
So we have 2/3 times 9/4.
2 Multiply tops and bottoms
To multiply fractions, we do top times top, and bottom times bottom.
Top times top: 2 × 9.
Bottom times bottom: 3 × 4.
2 × 9 is 18.
3 × 4 is 12.
3 Simplify
To make it simpler, we need a number that goes into the top and the bottom.
What goes into 18 and 12?
We list the numbers that go into each.
Into 18: 1, 2, 3, 6, 9, 18.
Into 12: 1, 2, 3, 4, 6, 12.
6 is the biggest one in both lists.
We divide the top and the bottom by 6.
The fraction keeps its size.
18 divided by 6 is 3.
12 divided by 6 is 2.
So it is 3/2.
Can we make it simpler?
No number goes into both 3 and 2, except 1.
So it stays like this.
So the answer is 3/2.
Let's look back.
First: flip and multiply.
Then: multiply tops and bottoms.
Last: simplify.