# Fractions of an amount

This has to be read in conjunction with % because you tackle fractions in the same way i.e.

- Write out what `100%` is
- Write out what we know
- Keep `%` on one side
- Put the divide sign in

**Example 1**

What is `7/20` of `£340`?

1. Write out what `100%` is

`100%` is `20/20`

2. Write out what we know

`7/20=x`

3. Keep `%` on one side

`20/20=340`

`7/20=x`

4. Put the divide sign in

`(20/20)/(7/20)=340/x`

Simplify the equation

`(20timescancel20)/(cancel20times7)=(£340)/x`

`20/7=(£340)/x`

Multiply `x` on both sides to get `x` on its own.

`xtimes20/7=(£340cancelx)/cancelx`

`xtimes20/7=£340`

Multiply `7` on both sides to get `x` on its own.

`cancel7timesx20/cancel7=£340times7`

`x20=£340times7`

Divide both sides by `20` to get `x` on its own

`(x20)/20=(£340times7)/20`

`x=(34cancel0times7)/(2cancel0)`

`x=17times7`

`x=£119`

**Example 2**

Increase `£240` by `1/7`

1. Write out what `100%` is

`100%` is `7/7`

2. Write out what we know

`8/7=x`

3. Keep the `%` on one side

`7/7=£240`

`8/7=x`

4. Put the divide sign in

`(7/7)/(8/7)=240/x`

Now just work out the calculation by simplifying first

`(7timescancel7)/(cancel7times8)=240/x`

`7/8=240/x`

Multiply both sides by `x` to get `x` on its own

`x7/8=(240timescancelx)/cancelx`

`x7/8=240`

Multiply both sides by `8` to get `x` on its own

`cancel8x7/cancel8=240times8`

`x7=240times8`

Divide both sides by `7` to get `x` on its own

`(xtimescancel7)/cancel7=(240times8)/7`

`x=(240times8)/7`

`x=£274.28`

**Answer:** Increase `£240` by `1/7` is `£274.28`

**Example 3**

What is `1/7` of `28`

1. Write out what `100%` is

`100%` is `7/7`

2. Write out what we know

`1/7=x`

3. Keep `%` on one side

`7/7=28`

`1/7=x`

4. Put the divide sign in

`(7/7)/(1/7)=28/x`

Simplify

`(7timescancel7)/(cancel7times1)=28/x`

`7=28/x`

Multiply by `x` to get `x` on its own

`7timesx=(28timescancelx)/cancelx`

`7x=28`

Divide both sides by `7` to get `x` on its own.

`(cancel7x)/cancel7=28/7`

`x=28/7`

`x=4`

**Answer:** `1/7` of `28` is `4`

**Example 4**

What is `37/41` of `£126.42`

1. Write out what `100%` is

`100%` is `41/41`

2. Write out what we know

`37/41=x`

3. Keep `%` on one side

`41/41=£126.42`

`37/41=x`

4. Put the divide sign in

`(41/41)/(37/41)=(£126.42)/x`

Simplify

`41/cancel41timescancel41/37=(£126.42)/x`

`41/37=(£126.42)/x`

Multiply by `x` to get `x` on its own

`41/37timesx=(£126.42timescancelx)/cancelx`

`41/37x=£126.42`

Multiply both sides by `37` to get `x` on its own

`(cancel37times41x)/cancel37=£126.42times37`

`41x=£126.42times37`

Divide both sides by `41` to get `x` on its own

`(cancel41x)/cancel41=(£126.42times37)/41`

`x=(£126.42times37)/41`

`x=£114.08`

**Answer:** `37/41` of `£126.42` is `£114.08`