Commercial Arithmetics : Introduction to Ratio

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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 $q$ .

$120 xx 2 = 240$

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 $120$ .
$rArr 1:2$

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 $1/6:1/12$

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 $= 1/3$ of number of oranges.
The number of oranges $= 27$

The number of apples
$= 1/3 xx 27$
$= 9$

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
$= 2/(2+3) xx 40$
$=16$ apples

The answer is " $16$ apples".

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

The total number of apples is $120$
The ratio is $1/3:1/5$

Number of apples brother get is
$= 120 xx 1/3 -: (1/3+1/5)$
$=40 -: 8/15$ apples
$=40 xx 15/8$ 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 $1/3$ and $1/5$ respectively. How many does the brother get? Note that this is a problem in fractions.

The total number of apples is $120$
Brother gets $1/3$ of the apples

Number of apples brother get is
$= 120 xx 1/3$
$=40$ apples

The answer is " $40$ apples".

summary

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

Outline

The outline of material to learn "commercial arithmetics" is as follows.

Note: Click here for the detailed ouline of commercial arthmetics.

• Ratio, Proportion, Percentage

→ Comparing Quantities

→ Introduction to Ratio

→ Ration & Fraction Differences

→ ProportionsP

→ Percentages

→ Conversion to percentage

• Unitary Method

→ Introduction to Unitary Method

→ Direct Variation

→ Inverse Variation

→ DIV Pair

• Simple & Compound Interest

→ Story of Interest

→ Simple Interest

→ Compound Interest

• Rate•Span=Aggregate

→ Understanding Rate-Span

→ Speed • Time=Distance

→ Work-rate • time = Work-amount

→ Fill-rate • time = Filled-amount

• Profit-Loss-Discount-Tax

→ Profit-Loss

→ Discount

→ Tax

→ Formulas