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Updated on October 4, 2010

A Simplified Ratio Should Only Have Whole Numbers

A simplified ratio should only have whole numbers so lets look at a few examples;

Simplify these Fully:

2/5 : 3/4

At the moment we have fractions on both sides of the equation so we need to change these to whole numbers.

The first thing we need to do is look at the denominators (5 , 4), the bottom numbers in the equation, then we need to think what is a common denominator for these two numbers, that is a number that they both go into. Well that number is 20.

Now we will times(multiply) each side by the 20

So 2/5 X 20 = 20 ÷ 5 = 4

4 X 2 = 8

And 3/4 X 20 = 20 ÷ 4 = 5

5 X 3 = 15

Therefore our simplified ratio is 8 to 15 which is written as 8 : 15

(Answer) 8 : 15

Next we will do ratio dealing with decimals

2.5 : 0.05 (we see that the 0.05 has two decimal places so to make it a whole number we need to move the point two places to the right hand side for it to become a 5, which is a whole number.

Now we must do the same to the other side of the equation- if we take the 2.5 and move the point two places to the right hand side we seem to have a space 25? , we now fill that space with a (zero) 0 . Now that new whole number will become 250 .

Therefore now we have the equation;

250 : 5 (we can now divide both sides by 5)

250 ÷ 5 = 50

5 ÷ 5 = 1

Therefore our simplified ratio is 50 : 1

(Answer) 50 : 1



Now we are going to take a look at equivalent ratios;

If we take 2/3which is a fraction and look at it first,then if we multiply the top X 2 and the bottom X 2 we form an equivalent fraction;

2 X 2 = 4

3 X 2 = 6

 We had 2/and  we can change it to 4/6  , they are example of equivalent fractions.

Similiarly equivalent ratios 2 : 3, if we multiply the;

2 X 2 = 4

3 X 2 = 6

2 : 3 is the same as 4 : 6

This is an example of equivalent ratios.

Now complete the following ratios;

(i)  5   :    3

    25   :    ?

Therefore to find the missing value we divide;

25  ÷  5  =  5 (now we must multiply the 3 X 5 to find the missing value)

   3 X 5  = 15

So therefore the missing value is 15

5  :  3   is equivalent to   25  :  15


 (ii)    3    :   5   :   9

          ?    :   ?   :  27

This time we have two values missing

 So in order to solve this equation we must divide;

27  ÷  9  =  3 (now we must multiply the 3 X 3 and the 5 X 3 to find the missing values)

  3  X  3  =    9

  5  X  3   =  15

So therefore the missing values are 9 and 15

3 : 5 : 9 is equivalent to 9 : 15 : 27




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