 # Benchmark Percentage of a Quantity

Lesson

Percentages are used for a variety of things, usually when we want to describe how much of something there is. For example, perhaps you only want $50%$50% of the juice in you cup or when the car dashboard says that the fuel tank is only $20%$20% full. However, $50%$50% of the water in a $100$100L swimming pool is obviously very different to $50%$50% of the $2$2L milk in your fridge. Let's take a look at how we can figure out how much there ACTUALLY is when we hear about percentages.

## Finding Percentages of a Quantity

We already know how to find a fraction of a quantity through multiplication. For example, we know to find $\frac{2}{3}$23 of $60$60 all we do is multiply the two numbers together, so $\frac{2}{3}\times60=40$23×60=40 is our answer. We can do the same with percentages as we know how to turn them into fractions with $100$100 as the denominator.

For example, we want to find what $25%$25% of $84$84 is, so let's multiply them together. $25%\times84$25%×84 can be rewritten as $\frac{25}{100}\times84$25100×84, and we can simplify the fraction and get $\frac{1}{4}\times84=\frac{84}{4}$14×84=844 = $21$21.

 $25%\times84$25%×84 $=$= $\frac{25}{100}\times84$25100​×84 $=$= $\frac{1}{4}\times84$14​×84 $=$= $\frac{84}{4}$844​ $=$= $21$21

#### Worked Examples

##### QUESTION 1

Consider the following:

1. Express $75%$75% as a fraction in simplest form.

2. Beth was given $20$20 minutes in which to solve a Rubik's Cube. She only needed $75%$75% of the time to finish it. How many minutes did she take?

##### QUESTION 2

'

Consider the following:

1. Express $60%$60% as a decimal.

2. Hence find $60%$60% of $90$90 kilograms.