Calculate -3 1/2 + 1 1/4 Step by Step

Step by step

The question

Question: work out −3 and 1/2 + 1 and 1/4.

−312 + 114

1 Make one fraction

3 and 1/2 is a mixed number.

Each whole one is 2/2.

So we do 3 times 2, plus 1.

The bottom stays 2.

= −3 × 2 + 12 + 114

3 times 2 plus 1 is 7.

So it is 7/2.

= −72 + 114

1 and 1/4 is a mixed number.

Each whole one is 4/4.

So we do 1 times 4, plus 1.

The bottom stays 4.

= −72 + 1 × 4 + 14

1 times 4 plus 1 is 5.

So it is 5/4.

= −72 + 54

2 Make the bottoms the same

The bottom numbers are 2 and 4.

They are different, so we can't add the tops yet.

We count up in 2s and in 4s.

4 is the first number in both lists.

So 4 will be the new bottom.

In 2s: 2, 4

In 4s: 4

2 times 2 is 4.

So −7/2 gets times 2/2.

5/4 already has 4 at the bottom.

2 × 2 = 4

We multiply the top and the bottom by the same number.

= −72 × 22 + 54

2/2 is 1.

Times 1 does not change the size.

So the fraction stays the same, only the bottom changes.

22 = 1

Top times top.

Bottom times bottom.

= −7 × 22 × 2 + 54

7 times 2 is 14.

2 times 2 is 4.

Now both have 4 at the bottom.

= −144 + 54

3 Add the tops

The bottoms are the same, so the pieces are the same size.

We add the tops.

The bottom stays 4, because the size of the pieces does not change.

= −14 + 54

−14 plus 5 is −9.

= −94

4 Write as a mixed number

9 divided by 4 is 2, with 1 left over.

So it is 2 and 1/4.

= −214

So the answer is −2 and 1/4.

Let's look back.

First: make one fraction.

Then: make the bottoms the same.

Then: add the tops.

Last: write as a mixed number.

Answer