What you need to know

Things to remember:

  • It doesn’t matter which number you choose as the percentage

x\% \text{ of } y = y\% \text{ of } x

We have two methods for finding percentage amounts:

Method 1: Add/multiply easier percentages.

To do use this method, you need to remember how to find some simple percentages.

Percentage                 Division

100%                           \div1

50%                             \div2

25%                             \div4

20%                             \div5

10%                             \div10

5%                               \div20

4%                               \div25

2%                               \div50

1%                               \div100

 

To do this method, we need to remember that we can add and subtract percentages to make other ones. This method is best when you don’t have a calculator.

9\%=5\%+4\%

28\%=20\%+10\%-2\%

Find 35% of 250

Step 1: Think about the percentages that add or multiply together to make your percentage.

 

35\%=25\%+10\%

 

Step 2: Find the value of these percentages

25\%\text{ of } 250 = 250\div4=62.5

10\%\text{ of } 250 = 250\div10=25

Step 3: Add/Subtract/Multiply

35\%=25\%+10\%

35\%\text{ of } 250=62.5+25=87.5

Multiplication works too.

Step 1: Think about the percentages that add or multiply together to make your percentage.

 

35\%=7\times5\%

 

Step 2: Find the value of these percentages

5\%\text{ of } 250 = 250\div20=12.5

Step 3: Add/Subtract/Multiply

35\%=7\times5\%

  35\%\text{ of } 250=7\times12.5=87.5

Our answers are the same.

 

Our second method is the most powerful can we can find any percentage amount in two steps. This is useful for decimal amounts and you have a calculator.

Method 2: Multiplying from 1%

Find 12.56% of 300.

 

Step 1: Divide the number you’re finding the percentage of by 100 to find 1%.

 

300\div100=3

1\%=3

 

Step 2: Multiply the value of 1% found in Step 1 by your starting percentage.

12.56\%=12.56\times1\%

12.56\%\text{ of }300=12.56\times3=37.68

We can now use these two methods to compare two percentage amounts.

Now that we have the strategies, we can look at some questions.

Which is bigger, 55% of 20 or 40% of 30?

 

Find 55% of 20

Method 1

Step 1: Think about the percentages that add or multiply together to make your percentage.

 

55\%=50\%+5\%

Step 2: Find the value of these percentages

50\%\text{ of }20=20\div2=10

5\%\text{ of }20=20\div20=1

Step 3: Add/Subtract/Multiply

55\%=50\%+5\%

55\%\text{ of }20=10 + 1 =11

Find 40% of 30

Method 2

Step 1: Divide the number you’re finding the percentage of by 100 to find 1%.

 

30\div100=0.3

1\%=0.3

 

Step 2: Multiply the value of 1% found in Step 1 by your starting percentage.

40\%=40\times1\%

40\%\text{ of }30=40\times0.3=12

Which is bigger, 70% of 55 or 55% of 70?

 

Find 70% of 55

Method 1

Step 1: Think about the percentages that add or multiply together to make your percentage.

 

70\%=50\%+20\%

Step 2: Find the value of these percentages

50\%\text{ of }55=55\div2=27.5

20\%\text{ of }55=55\div5= 11

Step 3: Add/Subtract/Multiply

70\%=50\%+20\%

70\%\text{ of }55= 27.5+11=38.5

Find 55% of 70

Method 2

Step 1: Divide the number you’re finding the percentage of by 100 to find 1%.

 

70\div100=0.7

1\%=0.7

 

Step 2: Multiply the value of 1% found in Step 1 by your starting percentage.

55\%=55\times1\%

55\%\text{ of }70=55\times0.7=38.5

So, these two percentages are the same. It is worth remembering that whenever you find a percentage of something, it is the same as using the number as the percent and the percent as the number.

55% of 20 = 20% of 55

78.5% of 24 = 24% of 78.5

13.35% of 72.8 = 72.8% of 13.35

Example Questions

Question 1: Which is bigger, 28% of 110 or 27% of 120?

Answer

28% of 110

 

Method 1

 

Step 1: Think about the percentages that add or multiply together to make your percentage.

 

 

28\%=25\%+2\%+1\%

 

Step 2: Find the value of these percentages

 

25\%\text{ of }110=110\div4=27.5

 

2\%\text{ of }110=110\div50=2.2

 

1\%\text{ of }110=110\div100=1.1

 

Step 3: Add/Subtract/Multiply

 

28\%=25\%+2\%+1\%

 

28\%\text{ of }110=27.5+2.2+1.1=30.8

 

27% of 120

 

Method 2

 

Step 1: Divide the number you’re finding the percentage of by 100 to find 1%.

 

 

120\div100=1.2

 

1\%=1.2

 

 

Step 2: Multiply the value of 1% found in Step 1 by your starting percentage.

 

27\%=27\times1\%

 

27\%\text{ of }120=27\times1.2=32.4

 

So, 27% of 120 is bigger than 28% of 110.

Question 2: Which is smaller, 13.6% of 25 or 25% of 13.6?

Answer

Neither is smaller, they’re equal! We have just swapped the numbers around.