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

= 3/5 × 9/5

[Step II: Multiply the first fraction by that

= 27/25

[Step III: Is not required here since, we cannot simplify]

[Step I: Turn over the second fraction upside-down (it becomes a

= 2/3 × 1/8

= (2 × 1)/(3 × 8) [Step II: Multiply the first fraction by that

[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

Examples on division of fractions are explained here step by step:

**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

= 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

= 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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