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

BYes

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 dollars?

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

Find fractions, decimals, and percentages of amounts expressed as whole numbers, simple fractions, and decimals