 What you need to know

Things to remember:

• You can add and subtract different percentages to make the percentage you want.

What is 50% of 80?

Well, we have a couple of ways of doing this. First, we should look back at how we write percentages as fractions.

Percent                       Fraction                       Division

100%               $\dfrac{1}{1}$           $\div1$

50%                 $\dfrac{1}{2}$          $\div2$

25%                 $\dfrac{1}{4}$          $\div4$

20%                 $\dfrac{1}{5}$          $\div5$

10%                 $\dfrac{1}{10}$          $\div10$

5%                   $\dfrac{1}{20}$            $\div20$

2%                   $\dfrac{1}{50}$            $\div50$

1%                    $\dfrac{1}{100}$        $\div100$

So, how do we find the 50% of 80? Well, the table tells us we have to divide by 2!

$$50\% \text{ of }80 = 80\div2=40$$

Not too bad, right?

What is 2% of 400?

The table tells us that to find 2% we have to divide by 50.

$$2\% of 400 = 400\div50=8$$

How about if we have to find a percentage that isn’t in our table? Well, we can do that 3 steps.

What is 35% of 200?

Step 1: Think about what percentages in our table we can add or subtract to make the percentage in the question.

$$35\% = 25\% + 10\%$$

Step 2: Find these new percentage amounts.

$$25\% of 200 = 200\div4=50$$

$$10\% of 200 = 200\div10=20$$

Step 3: Add or subtract the percentages.

We need to add ours.

$$35\% = 25\% + 10\%$$

$$35\% of 200 = 50 + 20 = 70$$

Now for the quick and exciting method, which we’d usually do using a calculator.

What is 37% of 400?

What is 37% as a fraction?

$$37\% = \frac{37}{100}$$

So, this question can actually be rewritten as:

What is $\frac{37}{100}$ of 400?

But, we know how to do this in two steps:

Step 1: Divide the amount by the denominator.

$$400\div100=4$$

Step 2: Multiply the number in Step 1 by the numerator.

$$37\times4=148$$

$$37\% of 400 = 148$$

So, we can actually use these steps to find ANY percentage amount, even decimals!

What is 59 % of 300?

Step 1: Divide the amount by 100.

$$300\div100=3$$

Step 2: Multiply by your percentage.

$$3\times59=177$$

$$59\% of 300 = 177$$

Example Questions

Step 1: Think about what percentages in our table we can add or subtract to make the percentage in the question.

$45\% = 50\% - 5\%$

Step 2: Find these new percentage amounts.

$$50\% of 40 = 40\div2=20$$

$$5\% of 40 = 40\div20=2$$

Step 3: Add or subtract the percentages.

We need to add ours.

$$45\% = 50\% - 5\%$$

45\% of 40 = 20 -2 = 18 

Step 1: Divide the amount by 100.

$$700\div100=7$$

Step 2: Multiply by your percentage.

$$7\times87=609$$

$$87\% \text{ of } 700 = 609$$