We will discuss here about multiplying fractions by a whole number, by a fractional number or by another mixed fractional number.
I. Multiplication of fractional number by a whole number:
For example:
(i) Multiply 2/3 by 7 Solution: 2/3 × 7 = (2 × 7)/3 = 14/3 = 4 2/3 
We simply multiply the numerator of the fractional number by the whole number. The denominator remains the same. 
(ii) Multiply 2 3/5 by 6 Solution: 2 3/5 × 6 = (2 × 5 + 3)/5 × 6 = (10 + 3)/5 × 6
= 13/5 × 6 = (13 × 6)/5 = 78/5 = 15 3/5 
We change the mixed numbers into improper fractions and then simply multiply the numerator of the fractional number by the whole number. The denominator remains the same. 
II. Multiplication of fractional number by another fractional number:
For example:
(i) Multiply 2/5 by 4/5 Solution:
2/5 × 4/5 = (2 × 4)/(5 × 5) = 8/25 
Step I: We multiply the numerators. Step II: We multiply the denominators.
Step III: We write the fraction in the simplest form. 
(ii) Multiply 8/9 by 7/10 Solution:
8/9 × 7/10 = (8 × 7)/(9 × 10) = 56/90 
We simply multiply the numerators of the fractional numbers and then multiply the denominators of the fractional numbers. Write the fraction in the simplest form. 
III. Multiplication of a mixed number by another mixed number:
For example:
(i) Multiply 2 1/3 by 1 ¾ Solution:
2 1/3 × 1 ¾ = 7/3 × 7/4 = 49/12 = 4 1/12 
We change the mixed numbers into improper fractions and then we multiply as usual. 
(ii) Multiply 1 7/9 by 3 5/11 Solution:
1 7/9 × 3 5/11 = 16/9 × 38/11 = (16 × 38)/(9 × 11) = 608/99 = 6 14/99 
We change the mixed numbers into improper fractions and then we multiply as usual. 
Related Concept
● Representation of a Fraction
● Properties of Equivalent Fractions
● Comparison of Like Fractions
● Comparison of Fractions having the same Numerator
● Conversion of Fractions into Fractions having Same Denominator
● Conversion of a Fraction into its Smallest and Simplest Form
● Addition of Fractions having the Same Denominator
● Subtraction of Fractions having the Same Denominator
● Addition and Subtraction of Fractions on the Fraction Number Line
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