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 $£114.08$