Step by step
The question
Question: work out 2 and 2/3 ÷ 1 and 1/9.
1 Write as fractions
2 and 2/3 is a mixed number.
Each whole one is 3/3.
So the top is 2 × 3 + 2.
The bottom stays 3.
1 and 1/9 is a mixed number.
Each whole one is 9/9.
So the top is 1 × 9 + 1.
The bottom stays 9.
2 × 3 + 2 is 8.
1 × 9 + 1 is 10.
So we have 8/3 ÷ 10/9.
2 Flip and multiply
To divide by a fraction, we multiply by its flip.
Keep the first number: 8/3.
Change divide to times: ÷ becomes ×.
Turn the second fraction upside down: 10/9 becomes 9/10.
So we have 8/3 times 9/10.
3 Multiply tops and bottoms
To multiply fractions, we do top times top, and bottom times bottom.
Top times top: 8 × 9.
Bottom times bottom: 3 × 10.
8 × 9 is 72.
3 × 10 is 30.
4 Simplify
To make it simpler, we need a number that goes into the top and the bottom.
What goes into 72 and 30?
We list the numbers that go into each.
Into 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.
Into 30: 1, 2, 3, 5, 6, 10, 15, 30.
6 is the biggest one in both lists.
We divide the top and the bottom by 6.
The fraction keeps its size.
72 divided by 6 is 12.
30 divided by 6 is 5.
So it is 12/5.
So the answer is 12/5.
Let's look back.
First: write as fractions.
Then: flip and multiply.
Then: multiply tops and bottoms.
Last: simplify.