Simplify (5/6 - 1/3)/(1/4 + 1/2) Step by Step

Step by step

The question

Question: simplify this fraction.

On top: 5/6 − 1/3.

At the bottom: 1/4 + 1/2.

A fraction with fractions inside is called a complex fraction.

56 − 1314 + 12

1 Find the common bottom

The small fractions have bottoms 6, 3, 4 and 2.

The smallest thing they all go into is 12.

12 is in the 6 and 3 and 4 and 2 times tables.

small bottoms: 6, 3, 4, 2

common bottom: 12

2 Times 12 on top and bottom

12/12 is 1.

Times 1 does not change the value.

1212 = 1

We multiply the top and the bottom by 12.

Then the small fractions go away.

= 12 × (56 − 13)12 × (14 + 12)

3 Multiply every part

Every part times 12.

12 times 5/6: the bottom 6 goes into 12, so we get 10.

12 times 1/3: the bottom 3 goes into 12, so we get 4.

12 × 56 = 10

12 × (−13) = −4

12 × 14 = 3

12 × 12 = 6

So we get (10 − 4)/(3 + 6).

No more small fractions!

= 10 − 43 + 6

Like terms go together: 6/9.

= 69

4 Simplify

Every part, on the top and the bottom, can be divided by 3.

So we divide the top and the bottom by it.

÷ 3: 6 → 2

÷ 3: 9 → 3

So the answer is 2/3.

= 23

5 Check

Let's check the long way: work out the top and the bottom first.

The top is 1/2, the bottom is 3/4.

top: 56 − 26 = 12, bottom: 14 + 24 = 34

Then top divided by bottom: times the flip.

We get 2/3 again.

It works!

12 ÷ 34 = 12 × 43 = 23

Let's look back.

First: find the common bottom.

Then: times 12 on top and bottom.

Then: multiply every part.

Then: simplify.

Last: check.

Answer