Dividing Fractions
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.
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For example, the reciprocal of ¾ is 4/3. |
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Find the reciprocal of 3 ¾
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The reciprocal of 3 ¾ is 4/15. |
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I. Division of a fraction by a whole number:
For example:
(i) Divide 3/5 by 12
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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
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= 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
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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
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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
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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
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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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