In division of fractions or dividing fractions requires inverting the divisor, and then proceed the steps as in multiplication.
Reciprocal of a Fraction:
Two fractions are said to be the reciprocal or multiplicative inverse of each other, if their product is 1.
For example:
(i) 3/4 and 4/3 are the reciprocals of each other, because 3/4 × 4/3 = 1.
(ii) The reciprocal of 1/7 is 7/1 i.e.; 7, because 1/7 × 7/1 = 1
(iii) The reciprocal of 1/9 is 9, because 1/9 × 9 = 1
(iv) The reciprocal of 2³/₅ i.e., 13/5 is 5/13, because 2³/₅ × 5/13 = 1.
Reciprocal of 0 does not exist because division by zero is not possible.
Therefore, the reciprocal of a non-zero fraction a/b is the fraction b/a.
Division of fractions:
The division of a fraction a/b by a non-zero fraction c/d is defined as the product of a/b with the multiplicative inverse or reciprocal of c/d.
i.e. a/b ÷ c/d = a/b × d/c
How to divide fractions explain with examples?
There are 3 steps to divide fractions:
Step I: Turn over the second fraction (the one you want to divide by) upside-down (this is now a reciprocal).
Step II: Multiply the first fraction by that reciprocal.
Step III: Simplify the fraction (if possible to its lowest form) .
For example:
(i) 3/5 ÷ 5/9
[Step I: Turn over the second fraction upside-down (it becomes a reciprocal): 5/9 becomes 9/5.]
= 3/5 × 9/5
[Step II: Multiply the first fraction by that reciprocal: (3 × 9)/(5 × 5)]
= 27/25
[Step III: Is not required here since, we cannot simplify]
(ii) 2/3 ÷ 8
[Step I: Turn over the second fraction upside-down (it becomes a reciprocal): 8 = 8/1 becomes 1/8.]
= 2/3 × 1/8
= (2 × 1)/(3 × 8) [Step II: Multiply the first fraction by that reciprocal]
[Step III: Simplify the fraction]
= 1/12
(iii) 4 ÷ 6/7
[Step I: Turn over the second fraction upside-down (it becomes a reciprocal): 6/7 becomes 7/6.]
= 4/1 × 7/6
= (4 × 7)/(1 × 6) [Step II: Multiply the first fraction by that reciprocal]
[Step III: Simplify the fraction]
= 14/3
= 4²/₃
(iv) 4²/₃ ÷ 3¹/₂
= 14/3 ÷ 7/2
[Step I: Turn over the second fraction upside-down (it becomes a reciprocal): 7/2 becomes 2/7.]
= 14/3 × 2/7
= (14 × 2)/(3 × 7) [Step II: Multiply the first fraction by that reciprocal]
[Step III: Simplify the fraction]
= 4/3
1. Divide the fractions:
(i) 5/9 by 2/3
(ii) 28 by 7/4
(iii) 36 by 6²/₃
(iv) 14/9 by 11
Solution:
(i) 5/9 ÷ 2/3
= 5/9 × 3/2
= (5 × 3)/(9 × 2)
= (5 × 1)/(3 × 2)
= 5/6
(ii) 28 ÷ 7/4
= 28/1 ÷ 7/4
= 28/1 × 4/7
= (28 × 4)/(1 × 7)
= (4 × 4)/(1 × 1)
= 16/1
(iii) 36 ÷ 6²/₃
= 36 ÷ 20/3
= 36/1 ÷ 20/3
= 36/1 × 3/20
= (36 × 3)/(1 × 20)
= (9 × 3)/(1 × 5)
= 27/5
= 5²/₅
(iv) 14/9 ÷ 11
= 14/9 ÷ 11/1
= 14/9 × 1/11
= (14 × 1)/(9 × 11)
= 14/99
2. Simplify the fractions:
(i) 4/9 ÷ 2/ 3
(ii) 1⁴/₇ ÷ 5/7
(iii) 3³/₇ ÷ 8/21
(iv) 15³/₅ ÷ 1²³/₄₉
Solution:
(i) 4/9 ÷ 2/3
= 4/9 × 3/2
= (4 × 3)/(9 × 2)
= (2 × 1)/(3 × 1)
= 2/3
(ii) 1⁴/₇ ÷ 5/7
= 11/7 × 7/5
= (11 × 7)/(7 × 5)
= 11/5
(iii) 3³/₇ ÷ 8/21
= 24/7 ÷ 8/21
= 24/7 × 21/8
= (24 × 21)/(7 × 8)
= (3 × 3)/(1 × 1)
= 9
(iv) 15³/₇ ÷ 1²³/₄₉
= 108/ 7 ÷ 72/49
= 108/7 × 49/72
= (108 × 49)/(7 × 72)
= (3 × 7)/(1 × 2)
= 21/2
3. Simplify the dividing fractions:
(i) (16/5 ÷ 8/20) + (15/5 + 3/35)
(ii) (3/2 ÷ 4/5) + (9/5 × 10/3)
Solution:
(i) (16/5 ÷ 8/20) + (15/5 + 3/35)
= (16/5 × 20/8) + (15/5 × 35/3)
= (16 × 20)/(5 × 8) + (15 × 35)/(5 × 3)
= (3 × 7)/(1 × 2)
= 21/2
3. Simplify the dividing fractions:
(i) (16/5 ÷ 8/20) + (15/5 + 3/35)
(ii) (3/2 ÷ 4/5) + (9/5 × 10/3)
Solution:
(i) (16/5 ÷ 8/20) + (15/5 + 3/35)
= (16/5 × 20/8) + (15/5 × 35/3)
= (16 × 20)/(5 × 8) + (15 × 35)/(5 × 3)
= 15/8 + 6/1
= 15/8 + (6 × 8)/(1 × 8)
= 15/8 + 48/8
= (15 + 48)/8
= 63/8
= 7⁷/₈
1. The cost of 5²/₅ kg of sugar is $ 101¹/₄, find its cost per kg.
Solution:
Cost of 5²/₅ kg of sugar kg of sugar = $ 101¹/₄
Cost of 27/5 kg of sugar = $ 405/4
Cost of 1 kg of sugar
= $ (405/4 ÷ 27/5)
= $ (405/4) × (5/27)
= $ (405 × 5)/(4 × 27)
= $ 75/4
= $ 18³/₄
Hence, the cost of 1 kg of sugar is $ 18³/₄.
2. The product of two numbers is 20⁵/₇. If one of the numbers is 6²/₃, find the other.
Solution:
Product of two numbers = 20⁵/₇ = 145/7
One of the numbers is = 6²/₃ = 20/3
The other number = (Product of the numbers ÷ One of the numbers)
= 145 /7 ÷ 3/20
= 145/7 × 3/20
= (145 × 3)/ (7 × 20)
= (29 × 3)/(7 × 4)
= 87/28
= 3³/₂₈
Hence, the other number is 3³/₂₈.
3. By what number should 5⁵/₆ be multiplied to get 3¹/₃?
Solution:
Product of two numbers = 3¹/₃ =10/3
One of the numbers = 5⁵/₆ = 35/6
The other number = Product of the numbers ÷ One of the numbers
The other number = 10/3 ÷ 35/6
= 10/3 × 6/35
= (2 × 2)/(1 × 7)
= 4/7
Hence, required number is 4/7.
4. If the cost of a notebook is $ 8³/₄, how many notebooks can be purchased for $ 131¹/₄?
Solution:
Cost of one note book = $ 8³/₄ = $ 35/4
Total amount $ 131¹/₄ = $ 525/4
Therefore, number of notebooks = total amount/cost of one note book
= 525/4 ÷ 35/4
= 525/4 × 4/35
= (525 × 4)/(4 × 35)
= 15
Hence, 15 notebooks can be purchased for $ 131¹/₄
5. A bucket contains 24³/₄ litres of water. How many 3/4 litre jugs can be filled from the bucket to get it emptied?
Solution:
Volume of water in the bucket = 24³/₄ litres = 99/4litres
Capacity of jug = 3/4 litre
Therefore, number of jugs that can be filled to get the bucket emptied
= 99/4 ÷ 3/4
= 99/4 × 4/3
= (99 × 4)/(4 × 3)
= 33
Hence, 33 jugs of 3/4 litre can be filled to get the bucket emptied.
● Fractions
Addition and Subtraction of Fractions
● Fractions - Worksheets
Worksheet on Multiplication of Fractions
Worksheet on Division of Fractions
7th Grade Math Problems
From Division of Fractions to HOMEPAGE
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