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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