## What you need to know

Things to remember:

• When dividing fraction, we use the KFC method (Keep, Flip, Change).
• We flip the fraction we are dividing, and then multiply with the first fraction.

When we divide fraction, it involves “flipping” one and then multiplying the new fraction with the old. Let’s just have a look back at how we multiply fractions.

$$\frac{7}{5}\times\frac{2}{9}=\frac{7\times2}{5\times9}=\frac{14}{45}$$

$$\frac{9}{12}\times\frac{11}{7}=\frac{11\times9}{12\times7}=\frac{99}{84}$$

So, to multiply fractions, we just multiply the tops and bottoms together. Division, however, is a little different…

What is $\dfrac{4}{9}\div\dfrac{5}{7}$?

To divide fractions, we keep the first one the same, flip the second one, and change the division into a multiplication. We call this the KFC method for short.

So, this division question has tuned into a multiplication question, which we know how to do!

$$\frac{4}{9}\times\frac{7}{5}=\frac{4\times7}{9\times5}=\frac{28}{45}$$

$$\frac{4}{9}\div\frac{5}{7}=\frac{28}{45}$$

So, we did this in 4 steps.

What is $\dfrac{8}{5}\div\dfrac{7}{3}$?

Step 1: Leave the fraction before the division alone.

Step 2: Flip the fraction after the division.

$$\frac{7}{3}\rightarrow\frac{3}{7}$$

Step 3: Change the division into a multiplication and multiply the fractions.

$$\div\rightarrow\times$$

$$\frac{8}{5}\times\frac{3}{7}=\frac{8\times3}{5\times7}=\frac{24}{35}$$

Step 4: Check to see if it simplifies

This doesn’t simplify, so our answer is:

$$\frac{8}{5}\div\frac{7}{3}=\frac{24}{35}$$

## Example Questions

#### Question 1: What is $\dfrac{6}{5}\div\dfrac{9}{4}$?

Step 1: Leave the fraction before the division alone.

Step 2: Flip the fraction after the division.

$$\frac{9}{4}\rightarrow\frac{4}{9}$$

Step 3: Change the division into a multiplication and multiply the fractions.

$$\div\rightarrow\times$$

$$\frac{6}{5}\times\frac{4}{9}=\frac{6\times4}{5\times9}=\frac{24}{45}$$

Step 4: Check to see if it simplifies

This one does simplify.

$$\frac{24}{45} =\frac{24\div3}{45\div3}=\frac{8}{15}$$

$$\frac{6}{5}\div\frac{9}{4}=\frac{8}{15}$$

#### Question 2: What is $\dfrac{13}{11}\div\dfrac{7}{5}$?

Step 1: Leave the fraction before the division alone.

Step 2: Flip the fraction after the division.

$$\frac{7}{5}\rightarrow\frac{5}{7}$$

Step 3: Change the division into a multiplication and multiply the fractions.

$$\div\rightarrow\times$$

$$\frac{13}{11}\times\frac{5}{7}=\frac{13\times5}{11\times7}=\frac{65}{77}$$

Step 4: Check to see if it simplifies

This one doesn’t simplify.

$$\frac{13}{11}\div\frac{7}{5}=\frac{65}{77}$$