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Multiplication of Rational Numbers

Rational numbers are defined as one of the basis of mathematics. Otherwise called as the fractions. It also used to denote the ratio of the two quantities. It consists of both the numerator and the denominator numbers. But the denominator number will not equal to the value of 0. For example, $\frac{x}{y}$ is called as the rational numbers.

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How to Multiply Rational Numbers

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The explanation for the rational numbers are shown below the following,

  • By using the rational numbers we can able to do all the arithmetic operations.
  • All the rules are same as the normal method, but the only difference is in this we are using the rational numbers.

Steps for multiplication of rational numbers:

The steps are given below,

  • In the 1st step, we have to write the given rational numbers.
  • In the 2nd step, we have to multiply the number terms present in the rational numbers.
  • In the 3rd step, we have to multiply the denominator terms present in the rational numbers.
  • In the 4th step,Then finally we have to simplify the following terms.

Multiplying Rational Numbers Examples

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Solved Examples

Question 1: Multiply the given rational numbers, $\frac{2}{4}$ × $\frac{6}{9}$
Solution:
 
Step 1: Write the given numbers,

$\frac{2}{4}$ × $\frac{6}{9}$

Step 2: In the next step, we have to first multiply the numerator terms.

2 × 6 = 12

Step 3: In the next step, we have to multiply the denominator terms.

4 × 9 = 36

Step 4: In this step, we have to simplify the obtained result, we get,

$\frac{12}{36}$

= $\frac{1}{3}$

This is the required solution.
 

Question 2: Multiply the given rational numbers, $\frac{5}{4}$ × $\frac{3}{7}$
Solution:
 
Step 1: Write the given numbers,

$\frac{5}{4}$ × $\frac{3}{7}$

Step 2: In the next step, we have to first multiply the numerator terms.

5 × 3 =15

Step 3: In the next step, we have to multiply the denominator terms.

4 × 7 =28

Step 4: In this step, we have to simplify the obtained result, we get,

$\frac{15}{28}$

This is the required solution.
 

Question 3: Multiply the given rational numbers, $\frac{2}{4}$ × $\frac{6}{9}$
Solution:
 
Write the given numbers,

$\frac{2}{4}$ × $\frac{6}{9}$

Step 2: In the next step, we have to first multiply the numerator terms.

2 × 6 = 12

Step 3: In the next step, we have to multiply the denominator terms.

4 × 9 = 36

Step 4: In this step, we have to simplify the obtained result, we get,

$\frac{12}{36}$

= $\frac{1}{3}$

This is the required solution.
 

Question 4: Multiply the given rational numbers, $\frac{5}{4}$ × $\frac{3}{7}$
Solution:
 
Step 1: Write the given numbers,

$\frac{5}{4}$ × $\frac{3}{7}$

Step 2: In the next step, we have to first multiply the numerator terms.

5 × 3 =15

Step 3: In the next step, we have to multiply the denominator terms.

4 × 7 =28

Step 4: In this step, we have to simplify the obtained result, we get,

$\frac{15}{28}$

This is the required solution.
 

Multiplying Rational Numbers Practice

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Practice Problems

Question 1: Multiply the given rational numbers, $\frac{4}{3}$ × $\frac{2}{3}$

Question 2: Multiply the given rational numbers, $\frac{3}{2}$ × $\frac{5}{4}$

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