In this post we will **learn about fractional ratios** with examples.

Then we will move on to learn methods to convert fractional ratio into simple whole number ratio.

In order to understand this chapter, you should have basic knowledge about ratios, fractions and LCM concept.

**What are fractional ratios?**

The **ratios presented in the form of fraction numbers** are called **fractional ratios**.

Given below are some examples of fractional ratios:

\mathtt{( a) \ \frac{1}{2} \ :\ \frac{3}{4}}\\\ \\ \mathtt{( b) \ \frac{2}{5} \ :\ \frac{3}{7}}\\\ \\ \mathtt{( c) \ \frac{4}{7} \ :\ \frac{2}{9}}\\\ \\ \mathtt{( d) \ \frac{1}{3} \ :\ \frac{4}{11}}\

Note that all the above ratio involve fraction numbers which make things confusing and complicated. Therefore it is required to simplify the ratios into whole numbers so that the data look understandable and presentable.

**Converting fractional ratios into whole number ratios**

Here we will learn two methods:

(a) Fractional ratio conversion using LCM

(b) Fractional ratio conversion with direct division

**Fractional Ratio conversion using LCM method**

Given below are steps to convert ratio from fraction into whole number form.

(a) Find the **LCM of the ratio denominators**

(b) **Multiply each fraction with LCM** numbers.

(c) Simplify the fraction.

**Note:**

Multiplication of any number on both side of the ratio will not affect the ratio.

Let us look at some of the examples for our understanding.

**Example 01**

Simplify the fractional ratio; \mathtt{\frac{1}{3} \ :\ \frac{1}{7}}

**Solution**

Here the ratios are in form of fractions.

In order to convert the ratio into whole numbers, follow the below steps:

**(a) Take LCM of denominators**

LCM ( 3, 7 ) = 21

**(b) Multiply the ratios with LCM = 21**

\mathtt{\Longrightarrow \ \frac{1}{3} \times 21\ :\ \frac{1}{7} \ \times 21}\\\ \\ \mathtt{\Longrightarrow \ \frac{21}{3} \ :\ \frac{21}{7}}\\\ \\ \mathtt{\Longrightarrow \ 7\ :\ 3}\

**Hence, the simplified version of the ratio is 7 : 3.**

**Example 02**

Simplify the fractional ratio into whole number ratio

\mathtt{\frac{3}{11} \ :\ \frac{2}{5}}

**Solution**

Follow the below process:**(a) Find LCM of the denominator**

LCM ( 11, 5 ) = 55**(b) Multiply the ratios with number 55**

\mathtt{\Longrightarrow \ \frac{3}{11} \times 55\ :\ \frac{2}{5} \ \times 55}\\\ \\ \mathtt{\Longrightarrow \ \frac{3\ \times 55}{11} \ :\ \frac{2\ \times \ 55}{5}}\\\ \\ \mathtt{\Longrightarrow \ 3\ \times 5\ :\ 2\ \times 11}\\\ \\ \mathtt{\Longrightarrow \ 15\ :\ 22}

**The ratios is simplified to 15 : 22**.

**Example 03**

Convert the below fractional ratio into whole number ratio.

\mathtt{\frac{7}{3} \ :\ \frac{1}{6}}

**Solution**

Do the following steps:

(a) **Find LCM of both the denominators**

LCM (3, 6) = 6

(b) **Multiply the ratios with number 6** on both sides.

\mathtt{\Longrightarrow \ \frac{7}{3} \times 6\ :\ \frac{1}{6} \ \times 6}\\\ \\ \mathtt{\Longrightarrow \ \frac{7\ \times 6}{3} \ :\ \frac{1\ \times \ 6}{6}}\\\ \\ \mathtt{\Longrightarrow \ 7\ \times 2\ :\ 1\ \times 1}\\\ \\ \mathtt{\Longrightarrow \ 14\ :\ 1}

Hence, the **fraction is simplified to 14 : 1**.

**Example 04**

Simplify the below fractional ratio into whole number form.

\mathtt{\frac{1}{3} \ :\ \frac{1}{4} \ :\ \frac{1}{5}}

**Solution**

Follow the below steps:**(a) Take LCM of the denominators**

LCM ( 3, 4, 5) = 60

**(b) Multiply the ratios with the LCM**

\mathtt{\Longrightarrow \ \frac{1}{3} \times 60\ :\ \frac{1}{4} \times 60\ :\ \frac{1}{5} \ \times 60}\\\ \\ \mathtt{\Longrightarrow \ \frac{1\ \times 60}{3} \ :\ \frac{1\ \times \ 60}{4} \ :\ \frac{1\ \times \ 60}{5}}\\\ \\ \mathtt{\Longrightarrow \ 1\times 20\ :\ 1\ \times \ 15\ :\ 1\ \times \ 12}\\\ \\ \mathtt{\Longrightarrow \ 20\ :\ 15\ :\ 12}\

**Hence the ratio is simplified to 20 : 15 : 12.**

**Example 05**

Simplify the below factional ratio

\mathtt{\frac{25}{4} \ :\ \frac{21}{7}}

**Solution****(a) Find LCM of the denominators**

LCM ( 4, 7 ) = 28

**(b) Multiply the ratios with LCM = 28**

\mathtt{\Longrightarrow \ \frac{25}{4} \times 28\ :\ \frac{21}{7} \times 28\ }\\\ \\ \mathtt{\Longrightarrow \ \frac{25\ \times 28}{4} \ :\ \frac{21\ \times \ 28}{7} \ }\\\ \\ \mathtt{\Longrightarrow \ 25\times 7\ :\ 21\ \times \ 4\ }\\\ \\ \mathtt{\Longrightarrow \ 175\ :\ 84\ }\

**Hence, the fractional fraction is simplified to 175 : 84**

**Fractional Ratio conversion using direct **

Follow the below steps:

(i) **Divide the first fraction with other given fraction**.

(ii) **Convert the division into multiplication** by changing the reversing the digits of second fraction

(ii) **Eliminate the common factors** and you will have your solution.

Given below are some examples for your understanding.

**Example 01**

Simplify the below fractional ratio into whole numbers ratio.

\mathtt{\frac{3}{5} \ :\ \frac{5}{9}}

**Solution**

Follow the below steps:**(a) Divide the first fraction with other fraction**

\mathtt{\frac{3}{5} \ \div \ \frac{5}{9}}

(b) **Convert division into multiplication** by changing the order of second fraction.

**(c) Simplify the fractions**

\mathtt{\ \frac{3\ \times \ 9}{5\ \times \ 5} \ \Longrightarrow \frac{27}{25} \ }

(d) Now **convert the fraction into ratio** form.

27 / 25 ⟹ 27 : 25

Hence, the given **fractional ratio has been reduced to 27 : 25**.

**Example 02**

Simplify the fractional ratio into simple ratio using division method

\mathtt{\frac{2}{18} \ :\ \frac{3}{15}}

**Solution**

(a) **Convert the ratio in the form of division**

\mathtt{\frac{2}{18} \ \div \ \frac{3}{15}}

(b)** Convert the division into multiplication** by by reversing numerator and denominator of second fraction.

\mathtt{\frac{2}{18} \ \times \ \frac{15}{3}}

(c)** Simplify the fractions**

(d)** Convert the fraction back to ratio**

The fraction 5/9 can be written as 5 : 9.

Hence, **ratio 5 : 9 is the simplified form** of the above ratio.

**Example 03**Simplify the given fractional ratio using division method

\mathtt{\frac{4}{20} \ :\ \frac{6}{25}}

**Solution**

(a)

**Convert the ratio in form of division**

\mathtt{\frac{4}{20} \ \div \ \frac{6}{25}}

(b) **Convert the division into multiplication** by reversing the second fraction

\mathtt{\frac{4}{20} \ \times \ \frac{25}{6} \ }

(c) **Simplify the fraction**

**(d) Now convert the fraction into ratio**

5 / 6 ⟹ 5 : 6

Hence the ratio has been simplified to 5 : 6