# RATIO AN WHOLE NUMBERS

## 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**

**EQUIVALENT RATIOS:**

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

If we take ^{2}/_{3}_{}which 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}/_{3 }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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