Ratio Definition

In certain cases, comparing two amounts by division is quite efficient. A ratio is a comparison or reduced form of two quantities of the same sort. We use the colon “:” symbol to denote the ratio.

Proportion Definition

A proportion denotes that the two ratios are equal. The proportion establishes the equivalence of two fractions or ratios. In proportion, two sets of numbers that increase or decrease in the same ratio are satopicId to be directly proportionate.

For example, a train moving 100 km per hour takes 6 hours to traverse 600 km. 

In other words, speed = distance / time.

Speed = 600 km / 6 hr = 100 km/r

How are ratio and proportion related?

The ratio denotes comparison between values whereas the proportion focuses on equality of two ratios.

Methods to transform or convert ratios in their simplest form

The following procedures need be followed in order to convert the supplied ratio to Simplest Form: –

1. Calculate the numerator and denominator HCFs.

2. Taking the HCF of both integers and divtopicIding them

Example:

Convert 28: 32 into its simplest form

For finding HCF of 28 and 32.

Various factors of 28 can be written as 1, 2, 4, 7, ...

Various factors of 32  can be written as  1, 2, 4, 8, ….

Explanation: The highest common factor from the multiples of two numbers is 4.

Example: Convert the ratio 28:32 in its simplest form.

Since, 28/4:32/4 = ⅞

Or simplest method to find the ratio in the simplest form is:

Find the biggest number which is divisible by both 28 and 32. That seems to be 4.

reason : 4 x 7 = 28 and 4 x 8 = 32

Types of proportion:

The proportion may be classed as follows:

Direct Ratio

Inverse Ratio

Proportion in continued form or continued proportion 

Proportionate Proportion

The direct proportion defines the connection between two quantities in which when one number increases, the other quantity increases as well. In the same way, if one amount falls in terms of a value, the other quantity reduces as well. As a result, the direction proportion is expressed as ab if "a" and "b" are two quantities.

Inverse Proportion 

The inverse proportion indicates a connection between two variables in which an increase in one item causes the other to decrease. Similarly, if one quantity decreases, the other amount increases. As a result, a  ∝ (1/b) represents the inverse proportion of a to b, say "a" and "b."

Continued Proportion

ConstopicIder the following two ratios: a: b and c: d.

We next transform the means to a single term/number in order to get the continuous proportion for the two specified ratio terms. In essence, this would be the LCM.

The LCM of b and c for the given ratio is bc.

Now let us constopicIder a:b.

Therefore, multiplying and divtopicIding bc by a:b, we get.

a x bc              ac

-------     =        ---

b x bc              bc

Similarly, for c:d, we get:

c         c x bc      bc

--  =    --------  =  ---

d        d  x bc      db

As a result, the continuous proportion may be expressed as ca: bc: bd.