Multiplication of Rational Numbers

To learn multiplication of rational numbers let us recall how to multiply two fractions. The product of two given fractions is a fraction whose numerator is the product of the numerators of the given fractions and whose denominator is the product of the denominators of the given fractions.

In other words, product of two given fractions = product of their numerators/product of their denominators

Similarly, we will follow the same rule for the product of rational numbers.

Therefore, product of two rational numbers = product of their numerators/product of their denominators.

Thus, if a/b and c/d are any two rational numbers, then

a/b × c/d = a × c/b × d

Solved examples on multiplication of rational numbers:

1. Multiply 2/7 by 3/5

Solution:

2/7 × 3/5

= 2 × 3/7 × 5

= 6/35

2. Multiply 5/9 by (-3/4)

Solution:

5/9 × (-3/4)

= 5 × -3/9 × 4

= -15/36

= -5/12

3. Multiply (-7/6) by 5

Solution:

(-7/6) × 5

= (-7/6) × 5/1

= -7 × 5/6 × 1

= -35/6

4. Find each of the following products:

(i) -3/7 × 14/5

(ii) 13/6 × -18/91

(iii) -11/9 × -51/44

Solution:

(i) -3/7 × 14/5

= {(-3) × 14/(7 × 5)

= -6/5

(ii) 13/6 × -18/91

= {13 × (-18)}/(6 × 91)

= -3/7

(iii) -11/9 × 51/44

= {(-11) × (-51)}/(9 × 44)

= 17/12

5. Verify that:

(i) (-3/16 × 8/15) = (8/15 × (-3)/16)

(ii) 5/6 × {(-4)/5 + (-7)/10} = {5/6 × (-4)/5} + {5/6 × (-7)/10}

Solution:

(i) LHS = ((-3)/16 × 8/15) = {(-3) × 8}/(16 × 15) = -24/240 = -1/10

RHS = (8/15 × (-3)/16) = {8 × (-3)}/(15 × 16) = -24/240 = -1/10

Therefore, LHS = RHS.

Hence, ((-3)/16 × 8/15) = (8/15 × (-3)/16)

(ii) LHS = 5/6 × {-4/7 + (-7)/10} = 5/6 × [{(-8) + (-7)}/10}

= 5/6 × (-15)/10

= 5/6 × (-3)/2 = {5 × (-3)}/(6 × 2) = -15/12 = -5/4

RHS = {5/6 × -4/5} + {5/6 ×(-7)/10}

= {5 × (-4)/(6 × 5) + { 5 × (-7)}/(6 × 10) = -20/30 + (-35)/60

= (-2)/3 + (-7)/12

= {(-8) + (-7) }/ 12 = (-15)/12 = (-5)/4

Therefore, LHS = RHS

Hence, 5/6 × (-4/5 + (-7)/10) = {5/6 × (-4)/5} + (5/6 × (-7)/10)

Rational Numbers

What is Rational Numbers?

Is Every Rational Number a Natural Number?

Is Zero a Rational Number?

Is Every Rational Number an Integer?

Is Every Rational Number a Fraction?

Positive Rational Number

Negative Rational Number

Equivalent Rational Numbers

Equivalent form of Rational Numbers

Rational Number in Different Forms

Properties of Rational Numbers

Lowest form of a Rational Number

Standard form of a Rational Number

Equality of Rational Numbers using Standard Form

Equality of Rational Numbers with Common Denominator

Equality of Rational Numbers using Cross Multiplication

Comparison of Rational Numbers

Rational Numbers in Ascending Order

Representation of Rational Numbers on the Number Line

Addition of Rational Number with Same Denominator

Addition of Rational Number with Different Denominator

Addition of Rational Numbers

Properties of Addition of Rational Numbers

Subtraction of Rational Number with Different Denominator

Subtraction of Rational Numbers

Properties of Subtraction of Rational Numbers

Simplify Rational Expressions Involving the Sum or Difference

Multiplication of Rational Numbers

Properties of Multiplication of Rational Numbers

Rational Expressions Involving Addition, Subtraction and Multiplication

Division of Rational Numbers

Rational Expressions Involving Division

Properties of Division of Rational Numbers

To Find Rational Numbers

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

Recent Articles

1. Arranging Numbers | Ascending Order | Descending Order |Compare Digits

Sep 15, 24 04:57 PM

We know, while arranging numbers from the smallest number to the largest number, then the numbers are arranged in ascending order. Vice-versa while arranging numbers from the largest number to the sma…

2. Counting Before, After and Between Numbers up to 10 | Number Counting

Sep 15, 24 04:08 PM

Counting before, after and between numbers up to 10 improves the child’s counting skills.

3. Comparison of Three-digit Numbers | Arrange 3-digit Numbers |Questions

Sep 15, 24 03:16 PM

What are the rules for the comparison of three-digit numbers? (i) The numbers having less than three digits are always smaller than the numbers having three digits as:

4. 2nd Grade Place Value | Definition | Explanation | Examples |Worksheet

Sep 14, 24 04:31 PM

The value of a digit in a given number depends on its place or position in the number. This value is called its place value.

5. Three Digit Numbers | What is Spike Abacus? | Abacus for Kids|3 Digits

Sep 14, 24 03:39 PM

Three digit numbers are from 100 to 999. We know that there are nine one-digit numbers, i.e., 1, 2, 3, 4, 5, 6, 7, 8 and 9. There are 90 two digit numbers i.e., from 10 to 99. One digit numbers are ma

Rational Numbers - Worksheets

Worksheet on Rational Numbers

Worksheet on Lowest form of a Rational Number

Worksheet on Standard form of a Rational Number

Worksheet on Equality of Rational Numbers

Worksheet on Comparison of Rational Numbers

Worksheet on Representation of Rational Number on a Number Line

Worksheet on Properties of Addition of Rational Numbers

Worksheet on Rational Expressions Involving Sum and Difference

Worksheet on Multiplication of Rational Number

Worksheet on Division of Rational Numbers

Worksheet on Finding Rational Numbers between Two Rational Numbers

Worksheet on Word Problems on Rational Numbers

Objective Questions on Rational Numbers