# Calculating percentage

In the example:
"10% of 50 cars = 5 cars", we have three numbers involved:
- The starting number. (50 cars)
- The percentage. (10%)
- The result. (5 cars)

**We can find any one of them if we know the other two**.

The three cases are described below. They each use the applet below to illustrate the techniques.

## 1. Calculating the result

Given the percentage and starting number (10% of 50 cars). How many cars is that?
- First, write the percentage as a fraction. Put the percentage on the top and a hundred on the bottom
- Then multiply the starting number of cars by the fraction:

### Try this

- In the applet above, uncheck the right box under the result to hide it.
- Drag both orange dots to create a new problem.
- Calculate the result
- Check the box to see how you did.

## 2. Calculating the percentage

Given the starting number (50 cars) and the result (5 cars). What percentage is that?
- First, write the relationship as a fraction. Put the result (5) on the top and the starting number on the bottom:
This would be read as "5 out of 50 cars".
- Then convert the fraction to a percentage by multiplying by 100:

### Try this

- In the applet above, uncheck the middle box under the percentage to hide it.
- Drag both orange dots to create a new problem.
- Calculate the percentage
- Check the box to see how you did.

## 3. Calculating the starting number

Given the result and the percentage, find the original starting number.
For example if I have 5 cars and I know that is 10% of the total, how many cars are there in total?
- We know that 10% of the total is 5, so first find what 1% would have been. It would be a tenth of the 5 cars so
write a fraction with the result on the top and the percentage on the bottom.
If 5 is 10% of the total, then 1% would be one tenth of that

- If that is 1% of the total, then the total must be 100 times that, so multiply by 100 to get the total number of cars:

### Try this

- In the applet above, use the oiptions menu to uncheck the "Base number" to hide it.
- Drag both orange dots to create a new problem.
- Calculate the starting number.
- Check the box in the options menu to see how you did.

## Other fractions, percents, ratios topics

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