Question

How do you add 9/4 + 2/8. Explain the steps

Answer 1

`(5)/(2)`

Explanation:

`(9)/(4) +(2)/(8)`

1. Since the denominators (bottom numbers) are different, you have to find the lowest common denominator
Your denominators are 4 and 8. The goal is to find the least common multiple. (LCM) this is the lowest number that both 4 and 8 can go into. Here that is 8.

`(9)/(4) +(2)/(8)`

To find the LCM you can write out the multiples like this

4: 4,8,12,16...

8: 8,16,24

Since they both have 8, this is your lcm

2. Now look at the difference between the denominators in the original problem.

`(9)/(4) +(2)/(8)`

The other bottom number is 4 so you need to see how many times you'd have to multiply 4 to get 8. Here that is 2. Because 4x2 is 8.

3. Now multiply both numbers on the left by 2. (because of step 2)

9x2= 19 and 4x2=8

Now you have
`(18)/(8) +(2)/(8)`

4. Now do the other side. The denominator is already 8 so you don't have to change anything. (this is because you would just do everything times 1 like you did 2 in the last step.)

5. Now you can just add the 2 fractions across.

`(18)/(8) +(2)/(8)` 18+2= 20 and 8+8=16

This gives you:
`(20)/(8)`

6. Now simplify. To simplify, find the highest common factor (HCF). to do that you find the highest number that goes into both 20 and 8.

20: 1,2,4,5,20

8: 1,2,4,8

The highest number that goes into both is 4.

Noe divide both numbers of
`(20)/(8)` by 4.

This gives you

`(5)/(2)`