Solving the Ratio

Ratio is the spoken language of arithmetic. It is a way of comparing two or more quantities having the same units. The quantities may be separate entities or they may be different parts of a whole. We can right the ratio of ” a”  and ” b ” in three ways:

Word form – a is to b
Colon form –   a:b
Fraction form –  a/b

Problem:
                   Multiply:  2/6 × 3/4

Step 1: Multiply both numerator and denominator

Example: 
                           2/6 × 3/4  = 2×3/ 6×4

Step 2:  Get the common factor of both numerators and denominators

Example:
                          2×3 / 2×3×4

Step 3:  Group them according to their common factor.

Example:
                          2/3 × 3/3 × 1/4

Step 4:  Simplify the numerator and denominator with common factor. Then multiply

Example:
                            1 × 1 × 1/4

Step 5:   Answer
Example: 
                       1/4

Step 6:  Whole computation
Multiply :  2/6 × 3/4

           2/6 × 3/4  =  2×3/6×4
                            = 2 × 3 / 2× 3 × 4
                            = 2/2 × 3/3 × 1/4
                            = 1 × 1 × 1/4
                            = 1/4