Computing Ratio

A relation obtained by comparing two quantities similar in some sense is called a ratio. Ratio can be expressed in terms of fraction, that is,  a:b is equal to a/b For example 25 is 1/4^th of the hundred, Therefore, the ratio of 25 to 100is ¼. We write it in ratio as 1:4.

Facts for computing ratio:

The numbers a and b in a ratio a:b are called the term of the ratio. Here, a is called the first terms and b is called the second term of the ratio

Computing Nature of ratio:
A ratio is purely a number: it has no unit attached to it.

Computing Comparison of ratio:
Since, the ratio a:b represents what multiple are part a is of b, it is also equal to a/b.
Accordingly ratio a : b is said greater than a ratio c : d if, a/b > c/d ( b and d >0)
Or  ad – bc > 0

Computing simplest form of ratio:
Since, a/b=ma/mb for every non-zero number m, therefore the ratios a:b and ma:mb are the same.
If,a/b is in its lowest terms, the ratio a:b is said to be in its simplest form.

Computing Composition of ratios:
Two or more ratios can be compounded.
For example: the ratio compounded of the ratios.

1. 2:3 and 4:5 is 2 * 4 : 3 * 5
2. a : b  and c : d is ac : bd

Note: The ratio a : B and B : a are generally different.
For example: the ratio 3:4 is ¾ where as, the ratio, 4:3 is 4/3 and surely ¾ is not equal to 4/3

Example problem for computing ratio:

Example:

In red and green tiles, the ratio of red tiles to green tiles is 2:3. If there is 90 green tiles, how many red tiles are there?

Solution:

Step 1: Assign variables:

Let x = red tiles

Write the items in the ratio as a fraction.

Red / green = 2/3 = x / 90

Step2: Do the cross multiplication

2 * 90 = 3 * x

3 * x = 2 * 90

3x = 180

3x / 3 = 180 / 3

X = 60

Example 2:

The length and width of the rectangle is 4:3 whose perimeter is 350.Find the are of the rectangle.
Solution:
Take the ratio 4:3
Consider 4x be the length and 3x be the width.
Perimeter of the rectangle is =350
That is, 2(l+w)= 350
2(4x+3x)= 350
2*7x=350
14x=350
X=25
Therefore,
The length of the rectangle is 4x= 4*25=100.
The width of the rectangle is 3x=3*25=75

Area of the rectangle = length * width = 100 * 75 = 7500