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Ratios and Percents

The ratios and percents are seen abundantly in arithmetic as well as in our day to day lives. You would have seen their usage quite commonly right from the cooking recipes to the games and sports. So, these two concepts are very important to know for all of us. By the end of this lesson, the students will be able to learn the following concepts :

1) Define ratios and percentages.
2) Tell relation between ratios and percents.
3) Know conversion between ratios and percentages.

Related Calculators
Ratio to Percent Percent Change
Calculate Ratio Ratio to Fraction
 

Definition

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Ratio

The ratio is defined as the result when a quantity or a number is divided by another quantity or number. A ratio indicates the relationship between two numbers. It tells how much quantity of the first number is contained in the second one. A ratio depicts relative sizes of two or more things. The ratios are one of the simplest mathematical tools which measure relationships hidden in given data to make meaningful conclusions. The colon symbol ":" is placed between two numbers in order to represent a ratio, such as x : y which is pronounced as "x is to y" or "x to y" or "x ratio y".

For example : If there are 3 mangoes and 2 oranges in a bag, then the ratio of mangoes to oranges will be 3 : 2.
Percent

A percent or percentage is defined as a number that represents certain parts of something among 100 parts. It is said to be a way of denoting a portion of the whole. The percentage is shown by placing a percent "%" sign after a number. Some authors do use abbreviations "pct" or "pc" to denote percentage.

If something is divided into 100 parts, then 70 % or 35% will be the 70 or 35 parts from them. They are shown in the following images below:

and

Relationship Between Ratio and Percent

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The ratio and percents are closely related to each other. A percentage is actually a kind of ratio and a ratio can be written as a percentage. A percentage is also called a ratio that is represented in terms of the fraction of 100. Similarly, a ratio can be expressed as a percentage.

For example :
If there are 4 marbles in which 1 is blue and remaining 3 are black, then the ratio of blue marbles to black marbles would be 1 : 3. So, the fraction denoting blue marbles is $\frac{1}{4}$ and that representing black marbles is $\frac{3}{4}$. We can say that 25% marbles are blue, while 75% are black.

Converting Percentages into Ratios

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How do you convert a percent value into ratio? In order to perform this conversion, you should follow the steps mentioned below.

Step 1 : Remove percent sign and divide the number by 100.

x % = $\frac{x}{100}$

Step 2 : Reduce into lowest terms.

x % = $\frac{x}{100}$ = $\frac{a}{b}$

Step 3 : Write the result in terms of ratio symbol.

x % = $\frac{x}{100}$ = $\frac{a}{b}$ = a : b

Converting Ratios into Percentages

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Wasn't it quite easy to convert a percent to ratio? Now, let's see how to convert ratios into percentages. Follow the steps written as under.

Step 1 : Write the ratio in the form of a fraction.

x : y = $\frac{x}{y}$

Step 2 : Choose a number to multiply the numerator and the denominator so that the denominator becomes 100 after multiplication.

x : y = $\frac{x\ \times\ z}{y\ \times\ z}$ = $\frac{xz}{100}$

Note :
 If there is no such number, just multiply 

Step 3 : Write it as percent by eliminating 100 from denominator and adding a percent sign at the end.

x : y = $\frac{x\ \times\ z}{y\ \times\ z}$ = $\frac{xz}{100}$ = xz %

Examples

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Let's see few examples based on conversions of ratios and percents.

Example 1 : Convert 88 percent into ratio?

Solution :
 88%

Step 1 : Divide by 100


88% = $\frac{88}{100}$

Step 2 : Reduce into lowest terms


$\frac{88}{100}$ = $\frac{44}{50}$ = $\frac{22}{25}$

Step 3 : Express as ratio

$\frac{22}{25}$ = 22 : 25
Example 2 : Express $\frac{11}{20}$ as percentage?

Solution :
 $\frac{11}{20}$

Step 1 :
Multiply numerator and denominator by 5, we get

$\frac{11\ \times\ 5}{20\ \times\ 5}$

= $\frac{55}{100}$

Step 2 :
 Express as percent

= 55%
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