How do you multiply, divide and reduce fractions?

Question

3/4 X 5/6

2/7 ÷ 5/14

Answer 1

3/4 x 5/6...

Multiply the numerators: 3 x 5 = 15.

Multiply the denominators: 4 x 6 = 24.

Find the common factors of the numerator and denominator of your new fraction. (15/24)

Since both 15 and 24 have a factor of 3 (meaning they are both divisible by 3) we can divide both numbers by 3 to get a new reduced fraction.

15 ÷ 3 = 5.

24 ÷ 3 = 8.

So our answer is 5/8.

2/7 ÷ 5/14...

Since this is division, we must Keep, Change, Flip.

Keep 2/7 as is.

Change the division sign to a multiplication sign.

Flip the second fraction to its reciprocal. (5/14 flips to 14/5)

We now have 2/7 x 14/5.

Now, we multiply the numerators and denominators just as we did in the first problem.

2 x 14 and

7 x 5

Before we continue though, we can actually cross reduce BEFORE multiplying to make it easier on ourselves.

We check if the opposing numerators and denominators have common factors.

2 and 5 do not have common factors, but 7 and 14 have a common factor of 7.

We can divide both 7 and 14 by their common factor of 7.

7 ÷ 7 = 1.

14 ÷ 7 = 2.

This gives us the new reduced problem of 2/1 x 2/5.

We multiply the numerators, 2 x 2 = 4.

And the denominators 1 x 5 = 5.

Our answer is 4/5.

Answer 2

For multiplying fractions, you multiply numerators and denominators

For 3/4 x 5/6

3 x 5 = 15 and 4 x 6 =24

So, the fraction will be 15/24

To simplify the fraction, you need to find a factor of the numerator and denominator, in this case we will use 3

Divide the numerator and denominator by 3 (15/3 = 5 and 24/3 = 8)

So, the simplified fraction is 5/8

To divide fractions, you multiply by the reciprocal of one of the fractions

For the 2/7 divided by 5/14

So, we will do 2/7 times 14/5

Following the steps above we get 28/35

A common factor is 7, so we can simplify this to 4/5

Answer 3

Hello,

For the first, just multiply the numerators and denominators straight across:

3/4 * 5/6

3*5 = 15

4*6= 24

3/4 * 5/6 = 15/24

Now, to reduce that, you need the greatest common factor for 15 and 24. This is 3, so divide:

15/3 = 5

24/3 = 8

15/24 = 5/8

Now, to divide fractions, you multiply by the reciprocal, or opposite:

(2/7) / (5/14) = 2/7 * 14/5

Now, multiply straight across again:

2/7 * 14/5 = 28/35

Again, look for the greatest common factor for numerator and denominator. This is 7, so:

28/7 = 4

35/7 = 5

28/35 = 4/5

I hope this helps.