Step by step
The question
Question: work out 3 and 1/4 − 1 and 5/6.
1 Write as fractions
3 and 1/4 is a mixed number.
Each whole one is 4/4.
So the top is 3 × 4 + 1.
The bottom stays 4.
1 and 5/6 is a mixed number.
Each whole one is 6/6.
So the top is 1 × 6 + 5.
The bottom stays 6.
3 × 4 + 1 is 13.
1 × 6 + 5 is 11.
So we have 13/4 − 11/6.
2 Make the bottoms the same
The bottom numbers are 4 and 6.
The bottom tells the size of the pieces.
These pieces are different sizes, so we can't take away the tops yet.
We need one bottom number that works for both.
We count up in 4s and 6s.
In 4s: 4, 8, 12.
In 6s: 6, 12.
12 is the first number in both lists.
So 12 works for both.
12 will be the new bottom.
To make 4 into 12, we multiply by 3: 4 × 3 = 12.
To make 6 into 12, we multiply by 2: 6 × 2 = 12.
We multiply the bottom by 3: 4 × 3.
We did it to the bottom, so we must do it to the top too: 13 × 3.
We multiply the bottom by 2: 6 × 2.
We did it to the bottom, so we must do it to the top too: 11 × 2.
Top and bottom times the same number: the fraction keeps its size.
13 × 3 is 39.
4 × 3 is 12.
11 × 2 is 22.
6 × 2 is 12.
Now both have 12 at the bottom.
3 Take away the tops
The bottoms are the same, so the pieces are the same size.
We take away the tops: 39 − 22.
The bottom stays 12, because the size of the pieces does not change.
39 − 22 is 17.
The bottom stays 12.
4 Write as a mixed number
17/12 means 17 ÷ 12.
How many 12s fit in 17?
We can fit 1: 12 × 1 = 12.
17 take away 12 leaves 5: 17 − 12 = 5.
1 whole, and 5 left over out of 12.
So the answer is 1 and 5/12.
Let's look back.
First: write as fractions.
Then: make the bottoms the same.
Then: take away the tops.
Last: write as a mixed number.