Dividing fractions questions with solutions is provided for students to practice. Practising these questions will improve their understanding of fractions and help them score well in examinations. The questions presented here are designed for students in grades 3 to 6, helping them understand various questions regarding the division of fractions.
Fractions represent a part of whole, generally represented as numerator and denominator. Dividing fractions is equivalent to multiplying the dividend fraction by the reciprocal of the divisor fraction.
Suppose we have to divide m/n by p/q, then,
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m/n ÷ p/q = m/n × q/p; where q/p is the reciprocal of p/q |
Learn more about How to divide fractions?
Dividing Fractions Questions with Solution
Below are some practice questions on the division of fractions with detailed solutions.
Question 1: Evaluate the following:
(i) ¾ ÷ ⅞
(ii) 23/21 ÷ 19/7
(iii) ½ ÷ ⅚
Solution:
(i) ¾ ÷ ⅞
= ¾ × 8/7
= 6/7
(ii) 23/21 ÷ 19/7
= 23/21 × 7/19
= 23/57
(iii) ½ ÷ ⅚
= ½ × 6/5
= ⅗
Question 2: Divide the following:
(i) ⅔ by 14
(ii) 4/15 by 11/15
(iii) 23/14 by 1/7
Solution:
(i) ⅔ by 14
⅔ ÷ 14 = ⅔ × 1/14
= 1/21.
(ii) 4/15 by 11/15
4/15 ÷ 11/15
= 4/15 × 15/11
= 4/11.
(iii) 23/14 by 1/7
23/14 ÷ 1/7
= 23/14 × 7
= 23/2 = 11½ .
Also Check:
- Dividing Fractions Puzzle Worksheets
- Fractions Questions
- Multiplication of Fractions
- Dividing Fractions Calculator
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Dividing Mixed Fractions: Step I: Convert the mixed fractions into improper fractions. Step II: Divide the improper fractions as usual. Step III: Again convert the answer into a mixed fraction (if the answer is in improper fraction). |
Question 3: Divide the following:
Solution:
= 2.
Question 4: Divide the following:
(i) 2 by 2 ⅕
(ii) 4 by 225/7
(iii) 77 by 211/13
Solution:
(i) 2 by 2 ⅕
(ii) 4 by 225/7
(iii) 77 by 211/13
Refer:
- Convert Mixed to Improper Fraction
- Improper to Mixed Number Calculator
- Mixed to Improper Fraction Calculator
Question 5: Evaluate the following:
(i) 0.025 ÷ 0.625
(ii) 34.56 ÷ 0.002
(iii) 27.03 ÷ 0.3
Solution:
(i) 0.025 ÷ 0.625
= 25/1000 ÷ 625/1000
= 25/1000 × 1000/625
= 25/625
= 1/25
= 0.04
(ii) 34.56 ÷ 0.002
= 3456/100 ÷ 2/1000
= 3456/100 × 1000/2
= 34560/2
= 17280
(iii) 27.03 ÷ 0.3
= 2703/100 ÷ 3/10
= 2703/100 × 10/3
= 2703/30
= 901/10
= 90.1
Question 6: Fill in the blanks:
(i) 3/2 × ___ = ¾
(ii) 57/8 × ___ = 9⅖
(iii) ___ × 7½ = 3
Solution:
(i) 3/2 × ___ = ¾
¾ ÷ 3/2 = ¾ × ⅔ = ½
∴ 3/2 × ½ = ¾
(ii) 57/8 × ___ = 9⅖
9⅖ ÷ 57/8 = 47/5 ÷ 47/8
= 47/5 × 8/47
= 8/5
∴ 57/8 × 8/5 = 9⅖
(iii) ___ × 7½ = 3
= 3 ÷ 7½ = 3 ÷ 15/2
= 3 × 2/15 = ⅖
∴ ⅖ × 7½ = 3
Question 7: Small paper strips of width 2½ cm and length 2 cm have to be cut-out from a sheet of paper of dimension 15½ cm × 2 cm. How many such strips can be cut-out?
Solution:
Width of each paper strip = 2½ cm
Length of each paper strip = 2 cm
Thus, the sheet of paper has to be cut along the length 5½ cm in strips.
Number of strips = 15½ ÷ 2½ = 31/2 ÷ 5/2
= 31/2 × ⅖ = 31/5 = 6⅕
Therefore, 6 whole strips can be cut-out.
Question 8: Sarah needs to divide a cake of 2⅔ kg cake into three equal parts. How much each part of the cake will weigh?
Solution:
Total weight of cake = 2⅔ kg
Weight of each part of cake after dividing in three equal parts = 2⅔ ÷ 3
= 8/3 ÷ 3 = 8/3 × ⅓ = 8/9 kg.
Question 9: A wall of length 6⅔ m and width 31/7 m has to be painted. If each can of paint covers 5 m2 of wall and the cost of each can is ₹ 105. Find the cost of painting the whole wall.
Solution:
Area of wall = 6⅔ × 31/7 = 20/3 × 22/7 = 440/21 m2
Number of paint can needed = 440/21 ÷ 5 = 440/21 ÷ 5
= 440/21 × 1/5 = 88/21 = 44/21
Therefore, 5 cans of paint is required
Total cost = 88/21 × 105 = 88 × 5 = ₹ 440.
Question 10: Find the length of the rectangle whose area is 9⅘ m2 and breadth 4⅕ m.
Solution:
Let l be the length of the rectangle.
Area of rectangle = l × 4⅕ = 9⅘
⇒ l = 9⅘ ÷ 4⅕ = 49/5 ÷ 21/5
⇒ l = 49/5 × 5/21 = 7/3
∴ the length of the rectangle is 7/3 m.
Related Articles: |
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Video Lesson on Fractions
Practice Questions on Dividing Fractions
1. Evaluate the following:
(i) ⅔ ÷ ⅘
(ii) 4/7 ÷ 9/21
(iii) 45/7 ÷ 3½
(iv) 196/7 ÷ 13½
(v) 0.023 ÷ 2.3
(vi) 34.5 ÷ 6/7
(vii) 2 ÷ ⅘
(viii) ⅞ ÷ 13
(ix) ⅚ ÷ 96/5
(x) 12 ÷ ¾
2. Find the height of the triangle whose base is 5⅗ cm and the area is 28/35 cm2.
3. Three times more sugar is needed to make a large size pudding than a small one. If 3⅕ kg sugar is needed to make a large size pudding, how much sugar is needed to make a small size pudding?
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