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