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Dividing into a given ratio

November 4, 2010 Leave a comment

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)\div(Total number of parts)

Examples

Split $90 into the ratio 2:3:5

Total amount = $90

Total number of parts = 2+3+5=10

So multiplier = \frac{90}{10}=9

Answer is 2 \times 9:3 \times 9:5 \times 9

= $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)\div(Total number of parts) = \frac{500}{12}=41.667

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)\div(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)\div(Portion parts) = \frac{39}{3}=13, since we know the details of A.

So there are 5 \times 13 = 65kg 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)\div(Portion parts) =\frac{30}{4}=7.5, 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.

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Categories: Proportion

Percentages

November 3, 2010 Leave a comment

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


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 = 65 \div 100 \times 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 130 \div 100 \times 28g=36.4g


Decrease $2200 by 17%

 

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

Categories: Number