Percentages

Lesson

We know that percentages are used to describe parts of wholes, and that **whole** is represented as $1$1 or $100%$100% as a percentage. This is important when we come to talk about **complementary percentages**, which are percentages that add together to give a whole.

Let's say we knew that $30%$30% of a class is made up of people who wear glasses, how do we know what percentage does NOT wear glasses? Well, we know that glasses-wearers and non-wearers are the only two possible groups, so together they must make a whole = $100%$100%. That means the percentage of people who don't wear glasses is $100%-30%=70%$100%−30%=70%. This can be represented in the following **pie chart**:

We can use what we've learnt above to help calculate things when shopping! Let's say I wanted to buy a car for $\$12000$$12000 and I had to pay a $15%$15% deposit. Now I want to know is: how much do I have to pay after already putting down a deposit?

There are two ways to do this.

One way is to figure out how much the deposit is worth and then taking it away from $\$12000$$12000

To find out the value of the deposit, we would multiply the two amounts:

$12000\times15%$12000×15% | $=$= | $\frac{12000\times15}{100}$12000×15100 |

$=$= | $120\times15$120×15 | |

$=$= | $1800$1800 |

So the deposit is $\$1800$$1800.

That means there is $\$12000-\$1800=\$10200$$12000−$1800=$10200 left to be paid.

What is the other way? Well we know that $15%$15% of the price is the deposit, therefore the part left to pay must be $100%-15%=85%$100%−15%=85%.

$85%\times12000$85%×12000 | $=$= | $\frac{85\times12000}{100}$85×12000100 |

$=$= | $85\times120$85×120 | |

$=$= | $\$10200$$10200 |

Wow, we get the same answer but working differently with percentages first!

Both methods are valid, so have a think about how you might use one or the other in different problems.

We want to increase $1300$1300 by $40%$40% by following the steps outlined below.

First find $40%$40% of $1300$1300.

Add the percentage increase to the original amount to find the amount after the increase.

Calculate $140%$140% of $1300$1300.

Is increasing an amount by $40%$40% equivalent to finding $140%$140% of that amount?

Yes

ANo

B

Steph is going to buy a hat that is marked as $25%$25% off. The original price was $£36$£36.

What is the value of the discount in pounds?

What is the price that Steph will pay for the hat?