We will discuss here about dividing fractions by a whole number, by a fractional number or by another mixed fractional number.

First let us recall how to find reciprocal of a fraction, we interchange the numerator and the denominator.

Find the reciprocal of 3 ¾

**I. Division of a fraction by a whole number:
**

For example:

(i) Divide 3/5 by 12

Solution: 3/5 ÷ 12 = 3/5 ÷ 12/1 = 3/5 × 1/12
= (3 × 1)/(5 × 12) = 3/60 = 1/20 |
Step I: Find the reciprocal of the whole number and multiply with the fractional number as usual. Step II: Express the product in its lowest terms. |

(ii) Solve: 5/7 ÷ 10

= 5/7 ÷ 10/1
= 5/7 × 1/10 = (5 × 1)/(7 × 10) = 5/70 |
Step I: Find the reciprocal of the whole number and multiply with the fractional number as usual. Step II: Express the product in its lowest terms. |

**II. Division of a fractional number by a fractional number:**

For example:

(i) Divide 7/8 by 1/5

Solution: 7/8 ÷ 1/5 = 7/8 × 5/1 = (7 × 5)/(8 × 1)
= 35/8 = 4 3/8 |
Step I: Find reciprocal of 1/5. Step II: Multiply 7/8 by it.
Step III: Express the product in its simplest form. |

(ii) Divide: 5/9 ÷ 10/18

Solution: 5/9 ÷ 10/18 = 5/9 × 18/10 = (5 × 18)/(9 × 10)
= 90/90 = 1 |
Step I: Find reciprocal of 1/5. Step II: Multiply 7/8 by it.
Step III: Express the product in its simplest form. |

**III. Division of a mixed number by another mixed number:**

For example:

(i) Divide 2 ¾ by 1 2/3

Solution: 2 ¾ ÷ 1 2/3 = 11/4 ÷ 5/3 = 11/4 × 3/5
= (11 × 3)/(4 × 5) = 33/20 = 1 13/20 |
Express the mixed numbers as improper fractions and multiply as usual. |

(ii) Divide: 2 4/17 ÷ 1 4/17

Solution: 2 4/17 ÷ 1 4/17 = 38/17 ÷ 21/17 = 38/17 × 17/21
= (38 × 17)/(17 × 21) = 646/357 = 38/21 = 1 17/21 |
Express the mixed numbers as improper fractions and 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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