Introduction to Ratio

overview

In this page, specifying **ratio** of two quantities is explained. For example, the number 2424 is double of 1212. These two quantities are in the ratio 22 to 11. The symbols :: is introduced to specifying a ratio, eg 2:12:1.

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.

120×2=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.*

⇒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 50mins. 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 16:112

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 =13 of number of oranges.

The number of oranges =27

The number of apples

=13×27

=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

=22+3×40

=16 apples

The answer is "16 apples".

In a basket, there are 120 apples. Divide the apples to a brother and a sister in 13:15 ratio. How much does the brother get?

The total number of apples is 120

The ratio is 13:15

Number of apples brother get is

=120×13÷(13+15)

=40÷815 apples

=40×158 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 13 and 15 respectively. How many does the brother get? Note that this is a problem in fractions.

The total number of apples is 120

Brother gets 13 of the apples

Number of apples brother get is

=120×13

=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__

→ Proportions__P__

→ __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__