## Dividing into a given ratio

To divide a quantity into a given ratio we need to calculate the multiplier that takes us from the number of parts to the required amount.

### When we have the total

When we know the total amount that we have, we can calculate the multiplier from the number of parts to the quantity by dividing the total amount by the total number of parts.

So multiplier = (Total amount)(Total number of parts)

Examples

Split $90 into the ratio 2:3:5

Total amount = $90

Total number of parts =

So multiplier =

Answer is

= $18:$27:$45

Mac is making a potion that will put warts on the noses of the girls she knows. It uses ground frogs legs, eel jelly and spiders eyes in the ratio of 5:3:4. She wishes to make 500g of the potion. How much does she need of each ingredient?

Multiplier = (Total amount)(Total number of parts) =

So multiply each number of parts by 41.667

She needs 208.33g of ground frogs legs, 125g of eel jelly and 166.67g of spider’s eyes.

### When we know the amount of a portion

When we the know the amount of a portion, we can calculate the multiplier by dividing the portion amount by the number of parts of that portion.

In short the multiplier = (Portion amount)(Portion parts)

Examples

An alloy is made up of metals A and B in the ratio of 3:5.

If there is 39kg of metel A how much is there of metal B?

Multiplier = (Portion amount)(Portion parts) = , since we know the details of A.

So there are of metal B

JiG has this strange idea that one day she will be able to fly and decides that if she can learn to run faster she might be able to fly sooner. Her running program consistes of running and walking and standing in the ratio of 4:2:1. If she plans to run for 30 minutes, how long will she be out for altogether?

Multiplier = (Portion amount)(Portion parts) =, since we have the information for running.

Walking will be 15 minutes (we multiplied 2 by 7.5)

Standing will be 7.5 minutes.

In total she will be out 52.5 minutes.

## Percentages

### What does Percent mean mathematically?

‘Per’ means divide by

‘Cent’ means 100

Examples

Write 37% as a decimal

Write 43% as a fraction

### Fractions of an amount

Mathematically ‘Of’ means

Examples

What is 52% of 76kg

(Note: % means and of means )

So 52% of 76kg = 39.52kg

Mad-dog wants to buy a pair of diamond encrusted drum sticks which $550. She doesn’t have enough money and decides to try and use charm to get the shop keeper to drop the price. After much negotiation he agrees that she will only have to pay 65% of the original price. How much does Mad-dog pay.

We require 65% of $550 = $357.50

### Percentage increase and decrease

If we have got all of something then we can say that we have got 100% of it. So if we want 10% more for example, that would mean that we want 110% of the original amount. Also, if we want 15% less for example, that would mean that we require 85% of the original amount.

Examples

Increase 28g by 30%

We want 130% of 28g.

(since 100% + 30% = 130%)

So answer is

Decrease $2200 by 17%

We want 83% of $2200.

(since 100% – 17% = 83%)

We require 83% of $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 =

### Percentage change

To calculate the percentage change we first find the fractional change and then change this to a percentage.

The fractional change =

So it follows that the Percentage change =

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 =

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

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

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?

, because 100% – 20% = 80%

, we divide by 80 on both sides to get 1%

, 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?

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?

The elephant costs $13043.48