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## Percentages

### What does Percent mean mathematically?

‘Per’ means divide by

‘Cent’ means 100

Examples

Write 37% as a decimal

$37\% = 37 \div 100 = 0.37$

Write 43% as a fraction

$43\% = 43 \div 100 = \frac{43}{100}$

### Fractions of an amount

Mathematically ‘Of’ means $\times$

Examples

What is 52% of 76kg

(Note: % means $\div 100$ and of means $\times$)

So 52% of 76kg = $52 \div 100 \times 76kg=$ 39.52kg

We want 83% of $2200. (since 100% – 17% = 83%) We require 83% of$2200 $= 83$ $\div 100 \times 2200 =$ $1826 Bruce is training for a fighting match. At present she can hit with a power of 472. To stand a chance of winning she needs to increase her power by 12%. What power does she require. 112% of 472 = $112 \div 100 \times 472 = 529$ ### Percentage change To calculate the percentage change we first find the fractional change and then change this to a percentage. The fractional change = $\frac{Actual change}{Original amount}$ So it follows that the Percentage change = $\frac{Actual change}{Original amount}\times 100\%$ Examples Jack buys a collection of books for$8000 and 1 year later she sells them for $8750. What is the percentage change in its value. Actual change =$750

Percentage change = $\frac{750}{8000} \times 100\% = 9.375\%$

### Finding the value before a percentage increase or decrease

If something has had a given percentage ($x$) taken off it, then we need to realise that we have (100 – $x$)%.

The method we will use will be to find 1% and then multiply up to get 100%, the original amount.

Examples

A car’s value is reduced by 20% to $4500. What was the original price? $80\% \rightarrow 4500$, because 100% – 20% = 80% $1\%\rightarrow 56.25$, we divide by 80 on both sides to get 1% $100\%\rightarrow 5625$, we multiply by 100 on both sides to get 100% So the original price was$5625

Chewy sees a shop with a sale on.  The sign says 15% off everything.  She sees a brown mohair jumper and decides that she must have it.  If the jumper costs $120 in the sale, how much was it originally? $85\% \rightarrow 120$ $1\%\rightarrow 1.4118$ $100\%\rightarrow 141.18$ So the original price was$141.18

Luce goes to a pet shop that is saying that it will pay the GST.  When she enters the shop she sees an elephant for sale with a price tag of $15000. Luce has always wanted an elephant and decides to buy it. How much does it cost? $115\% \rightarrow 15000$ $1\%\rightarrow 130.4348$ $100\%\rightarrow 13043.48$ The elephant costs$13043.48