percentages and ratio

to convert PERCENTAGE TO FRACTION  write the fraction over 100 then cancel down , For an example ;                    25% = 25/100 = 1/4

to convert PERCENTAGE TO A DECIMAL divide the percentage amount by 100  for example  25%= 25 divided by 100= 0.25

to convert FRACTION TO DECIMAL   divide the denominator by the numerator  for example

3/25 =  3 divided by 25  is equal to 0.12  BUT if you don't have a calculator work it out in this way:

When you change a terminating DECIMAL TO FRACTION, the denominator will be 10, or 100, or 1000 or… (depending on the number of decimal places). EG;

0.5 means 'five tenths', so 0.5 = ⁵/₁₀ = ¹/₂

0.45 means '45 hundredths', so 0.45 = ⁴⁵/₁₀₀ = ⁹/₂₀

0.240 means '240 thousandths', so 0.240 = ²⁴⁰/₁₀₀₀ = ⁶/₂₅

When you change a DECIMAL TO A PERCENTAGE you  need to be /100 so  multiply the decimal by 100 then put the percentage sign  FOR EXAMPLE: 

  0.32 X 100 = 32 THEN ADD THE PERCENT SIGN  32%

To convert a  FRACTION TO A PERCENTAGE   you need to be over 100 again so x fraction to make denominator 100

and then add % sign EXAMPLE  3/4 TIMES DENOMINATOR BY 25 TO GET OVER 100  THEN DO THE SAME TO THE TOP  TO GET 75/100 WHICH IS 75%

Percentage of a quantity

It's often useful to be able to find a percentage of a quantity. For example, you might be told that bus fares are going up by 5% and you need to know how much more you will need each week.

Here are a couple of ways you could do it:

Find 1% of the quantity by dividing it by 100.

Find x% of a quantity by multiplying 1% of the quantity by x.

to do this as a written method  turn to a fraction with your percentage 

put a times sign in the middle take the other number and put it after the  times sign 

you will end up with this;

16  x 90      is equal to     4 x 18     is equal to   72                        

100                                    5                            5          

then cancel down by using common factors to make the sum easier before working it out by hand 72 divided by 5 = 14.4

It is possible to look at the difference between two numbers and work out the percentage increase or the percentage decrease. This is known as percentage change. Often goods are bought for one price and then sold on for another. The percentage change can be calculated to find out the profit or loss an item has made.

 To increase or decrease an amount by a percentage, use the multiplier method. This type of calculation is most convenient when used with a calculator but it is vital to use it when dealing with compound interest questions.

Firstly, consider what the overall percentage would be after the figure has had its percentage increase or decrease added or subtracted. Then convert this amount to a decimal, before finally multiplying by the number in question. eg;

 INCREASE BY                                                                   DECREASE BY

4%  = X 1.04                                                                            4%  = X 0.96

  15% = x 1.15                                                                         15% = x  0.85

2 1/2 % = x 1.025                                                                  1/2 % = x 0.995

Sometimes a question will ask you to work backwards and find the original price of something after the price has increased. If you are given a quantity after a percentage increase or decrease, and you need to find the original amount, use this method:

Example 1

A radio sells for £63, after a 40% increase in the cost price. Find the cost price.  Solution;

Start with the original amount as 100%.   :             Cost price = 100%

We are told the selling price is a 40% in the cost price.  :So the selling price is 100% + 40% = 140% of the cost price.

We know that the selling price is £63, so 140% = £63.

Now calculate 1%:

140% = £63

1% = £63/140

1% = £0.45

The cost price is 100%, so multiply £0.45 by 100.

Cost price = 0.45 × 100 = £45.