 # Fractions of an amount

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

1. Write out what 100% is
2. Write out what we know
3. Keep % on one side

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

(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

(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

(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

(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