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
`20/20` (is `100%`) `=£340`
2. Write out what we know
`7/20=x`
3. Keep `%` on one side (or in this case fractions)
`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
`7/7` (is `100%`) `=£240`
2. Write out what we know
`8/7=x`
3. Keep the `%` on one side (or in this case fractions)
`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
`7/7` (is `100%`) `=28`
2. Write out what we know
`1/7=x`
3. Keep `%` on one side (or in this case fractions)
`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
`41/41` (is `100%`) `=£126.42`
2. Write out what we know
`37/41=x`
3. Keep `%` on one side (or in this case fractions)
`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`
