Ratio is a comparison of two quantities. It is often used to compare two quatities. We often separate the two numbers in the ratio with the colon ( : ). There are many ways to write ratio one is a:b, second is a to b and third one is $\frac{a}{b}$. So from $\frac{a}{b}$ you can see that ratios can be written as fractions. So any number in the form of $\frac{a}{b}$ is known as ratio of two quatities. Example of ratio are $\frac{5}{7}$ is a ratio we can also write it as 5 : 7 and we can also write it in word form like five to seven. So basically ratios are the part of fractions.

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When first number and second number have the common factor then the ratio is not in simplest form. We need to divide both first and second number by greatest common factor to make the ratio to simplest form. Greatest common factor is the largest among the common factors of two or more non zero integers. Suppose you have ratio 12 :18 and you need to change it in simplest form first we will write all the common factors of 12 and 18

12 :- 1, 2, 3, 4, 6, 12 These all are the factors of 12

18 :- 1, 2, 3, 6, 9, 18 These all are the factors of 18

Common factor of 12 and 18 are 1, 2, 3, 6 and greatest among them is 6 so 6 will be our greatest common factor and to make the ratio in simplest form we need to divide both the numbers by 6

So 12 : 18 will become 2 : 3 and 12 : 18 is equal to 2 : 3.

An important thing related to ratios is ratio proportions. A proportion is the equality of two ratios. For example 6/9 and 8/12. You can use the multiplication property of equality to show an important property of all proportions.

If $\frac{a}{b}$ = $\frac{c}{d}$

Then, $(\frac{a}{b})$ × b ×d = $(\frac{c}{d})$ ×b ×d

We will get , a × d = b × c

The product ad and bc are called cross products of the proportion $\frac{a}{b}$ and $\frac{c}{d}$.

Below you could see simplifying ratios examples

6 : 12 , first will write factor of 6 and 12

6 :- 1, 2, 3, 6

12 :- 1, 2, 3, 4, 6, 12 highest common factor among 6 and 12 is 6 so gcf is 6

to make ratio in simplest form divide both the number by 6

so 6 : 12 will become 1 : 2

Write all the common factor of 20 and 15

20 :- 1, 2, 4, 5, 10, 20

15 :- 1, 3, 5, 15 so greatest common factor is 5

You can see ratios are equal so, s x 8 = 4 x 2

so, s = 1

Below you could see simplifying ratios practice problems

$\frac{a}{3}$ = $\frac{4}{6}$ ?

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