**Comparing Percentages** *KS3 Revision*

## 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?

*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?

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