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Introduction to Ratio

what you'll learn...

overview

In this page, specifying ratio of two quantities is explained. For example, the number 24$24$ is double of 12$12$. These two quantities are in the ratio 2$2$ to 1$1$. The symbols :$:$ is introduced to specifying a ratio, eg 2:1$2 : 1$.

relation between numbers

Comparing two numbers $p = 120$ and $q = 240$

Apart from saying $q$ is greater, the following helps to understand the numbers better.

"$q$ is double of $p$". If $p$ is multiplied by $2$, we get $q$.

$120 \times 2 = 240$

ratio

The comparison in magnitude is specified by ratio.
Ratio of $p$ to $q$ is $120 : 240$. To convey the comparison in magnitude, the common-factors are canceled.

$120 : 240$
(by dividing the two numbers by common factor $120$.
$\Rightarrow 1 : 2$

The ratio of $p$ and $q$ is $1 : 2$. This comparison is easier to understand.

The word "ratio" means: relation between two amounts giving the number of times one quantity is to the other quantity.

Two numbers are in ratio $2 : 3$, the $:$ is pronounced as is-to.

summary

Ratio : comparison of two quantities given as "magnitude of one" to "magnitude of another".

terms

Consider an example $2 : 3$ ratio. This is given as two numbers.

The first number ($2$ in the example) is called the first term.

The other number ($3$ in the example) is called the second term

Given two ratios $2 : 3$ and $3 : 2$. These two ratios do not represent the same.

In a ratio, the order of the number is important.

In a basket, there are $20$ apples and $30$ oranges.

The ratio of apples to oranges is $2 : 3$. It is not $3 : 2$.

The ratio of oranges to apples is $3 : 2$.

The ratio $2 : 3$ is not same as $3 : 2$.

examples

Time required to travel by train is $1$ hour and time required to travel the same distance by car is $50$mins. What is the ratio of the two time periods?

The answer is "$6 : 5$". Note that the quantities have to be converted to the same units to workout the ratio.

Simplify the ratio $30 : 90$

The answer is "$1 : 3$". The two terms of a ratio can be divided by any common factors to simplify the ratio.

Simplify the ratio $\frac{1}{6} : \frac{1}{12}$

The answer is "$2 : 1$". The two terms of a ratio can be multiplied by a number to simplify the ratio given in fractions.

In a basket, the ratio of apples to oranges is $1 : 3$. All the following is correct about the given basket.

For every $1$ apple there are $3$ oranges

For every $2$ apples there are $6$ oranges

For every $9$ oranges there are $3$ apples

In a basket, the ratio of apples to oranges is $1 : 3$. If the number of oranges in the basket is $27$, how many apples are in the basket?

Solution:

Number of apples in the basket $= \frac{1}{3}$ of number of oranges.
The number of oranges $= 27$

The number of apples
$= \frac{1}{3} \times 27$
$= 9$

The answer is "$9$".

In a basket, there are $40$ apples. Divide the apples to a brother and a sister in $2 : 3$ ratio. How much does the brother get?

The total number of apples is $40$
The ratio is $2 : 3$

Number of apples brother get is
$= \frac{2}{2 + 3} \times 40$
$= 16$ apples

The answer is "$16$ apples".

In a basket, there are $120$ apples. Divide the apples to a brother and a sister in $\frac{1}{3} : \frac{1}{5}$ ratio. How much does the brother get?

The total number of apples is $120$
The ratio is $\frac{1}{3} : \frac{1}{5}$

Number of apples brother get is
$= 120 \times \frac{1}{3} \div \left(\frac{1}{3} + \frac{1}{5}\right)$
$= 40 \div \frac{8}{15}$ apples
$= 40 \times \frac{15}{8}$ apples
$= 75$ apples

The answer is "$75$ apples".

In a basket, there are $120$ apples. Divide the apples to a brother and a sister such that they get $\frac{1}{3}$ and $\frac{1}{5}$ respectively. How many does the brother get? Note that this is a problem in fractions.

The total number of apples is $120$
Brother gets $\frac{1}{3}$ of the apples

Number of apples brother get is
$= 120 \times \frac{1}{3}$
$= 40$ apples

The answer is "$40$ apples".

summary

Ratio : comparison of two quantities given as "magnitude of one" to "magnitude of another".

Outline