Multiplication of Rational Numbers

Multiplication of rational numbers is similar to multiplying fractions. A rational number is any number that can be written in the form  pq, where  q≠0. When we multiply rational numbers, we multiply their numerators together and their denominators together and then simplify the result to its lowest form. This concept is very useful in solving real-life problems involving parts of a whole, ratios, and scaling quantities.

Table of Contents

• Definition
• Solved Examples

Definition

Multiplication of rational numbers means finding the product of two or more rational numbers by multiplying their numerators and denominators separately.

Rule

For two rational numbers:

pq×rs=p×rq×s

So,

• Multiply numerators p × r
• Multiply denominators q × s
• Simplify the result to the lowest form

Solved Examples

Example 1: Find  23×45 

Solution:
Multiply numerators: 2 × 4 = 8
Multiply denominators: 3 × 5 = 15

23×45=815

 

Example 2: Find  −37×149 

Solution:
Multiply numerators: -3 × 14 = -42
Multiply denominators: 7 × 9 = 63

−4263=−23

Example 3: Find  56×310 

Solution:
Multiply numerators: 5 × 3 = 15
Multiply denominators: 6 × 10 = 60

1560=14