Let us solve Exercise 2.3 from the NCERT book done in class 7. Understanding how to divide fractions and mixed numbers thoroughly is a crucial skill. Initially, you might find it a bit tricky, but it becomes straightforward once you grasp the concept. Remember that dividing by a fraction or a mixed number is the same as multiplying by its reciprocal (the number flipped upside down).
Examples with Explanations
1. Dividing a Fraction by a Whole Number
Example: 3/4 ÷ 2
Here, we convert the whole number 2 into a fraction (2/1) and multiply 3/4 by the reciprocal of 2/1, which is 1/2. The calculation becomes 3/4 × 1/2 = 3/8.
2. Dividing a Whole Number by a Fraction
Example: 3 ÷ 1/2
We multiply 3 by the reciprocal of 1/2, which is 2/1 or 2. The calculation becomes 3 × 2 = 6.
3. Dividing a Fraction by Another Fraction
Example: 2/3 ÷ 4/5
We multiply 2/3 by the reciprocal of 4/5, which is 5/4. The calculation is 2/3 × 5/4 = 10/12, which simplifies to 5/6.
4. Dividing a Mixed Number by a Whole Number
Example: 2 1/3 ÷ 3
First, convert the mixed number to an improper fraction (7/3). Then, multiply it by the reciprocal of 3 (1/3). The calculation is 7/3 × 1/3 = 7/9.
5. Dividing a Whole Number by a Mixed Number
Example: 3 ÷ 1 1/2
Convert 1(1/2) to 3/2 and multiply 3 by the reciprocal of 3/2, which is 2/3. The calculation is 3 × 2/3 = 2.
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Question and Answers for Class 7 Maths Exercise 2.3 Chapter 2 Fractions and Decimals
1. Find:
(i) 12 ÷ 3/4
(ii) 14 ÷ 5/6
(iii) 8 ÷ 7/3
(iv) 4 ÷ 8/3
(v) 3 ÷ 2(1/3)
(vi) 5 ÷ 3(4/7)
Solution
(i) 12 ÷ 3/4
= 12 × 4/3 [Dividing by a fraction is equivalent to multiplying by its reciprocal]
= 48/3
= 16
(ii) 14 ÷ 5/6
= 14 × 6/5
= 84/5
= 16.8
(iii) 8 ÷ 7/3
= 8 × 3/7
= 24/7
= 3(3/7)
(iv) 4 ÷ 8/3
= 4 × 3/8
= 12/8
= 1(1/2)
(v) 3 ÷ 2(1/3)
= 3 ÷ 7/3 [Converting the mixed number 2(1/3) into an improper fraction]
= 3 × 3/7
= 9/7
= 1(2/7)
(vi) 5 ÷ 3(4/7)
= 5 ÷ 25/7 [Converting the mixed number 3(4/7) into an improper fraction]
= 5 × 7/25
= 35/25
= 1(2/5)
2. Find the reciprocal of each of the following fractions. Classify the reciprocals as proper fractions, improper fractions and whole numbers.
(i) 3/7
(ii) 5/8
(iii) 9/7
(iv) 6/5
(v) 12/7
(vi) 1/8
(vii) 1/11
Solution
(i) Reciprocal of 3/7
= 7/3
Classified as: Improper Fraction
(ii) Reciprocal of 5/8
= 8/5
Classified as: Improper Fraction
(iii) Reciprocal of 9/7
= 7/9
Classified as: Proper Fraction
(iv) Reciprocal of 6/5
= 5/6
Classified as: Proper Fraction
(v) Reciprocal of 12/7
= 7/12
Classified as: Proper Fraction
(vi) Reciprocal of 1/8
= 8/1
= 8
Classified as: Whole Number
(vii) Reciprocal of 1/11
= 11/1
= 11
Classified as: Whole Number
3. Find:
(i) 7/3 ÷ 2
(ii) 4/9 ÷ 5
(iii) 6/13 ÷ 7
(iv) 4(1/3) ÷ 3
(v) 3(1/2) ÷ 4
(vi) 4(3/7) ÷ 7
Solution
(i) 7/3 ÷ 2
= 7/3 × 1/2 [Dividing by a whole number is the same as multiplying by its reciprocal]
= 7/6
= 1(1/6)
(ii) 4/9 ÷ 5
= 4/9 × 1/5
= 4/45
(iii) 6/13 ÷ 7
= 6/13 × 1/7
= 6/91
(iv) 4(1/3) ÷ 3
= 13/3 ÷ 3 [Converting the mixed number 4(1/3) into an improper fraction]
= 13/3 × 1/3
= 13/9
= 1(4/9)
(v) 3(1/2) ÷ 4
= 7/2 ÷ 4 [Converting the mixed number 3(1/2) into an improper fraction]
= 7/2 × 1/4
= 7/8
(vi) 4(3/7) ÷ 7
= 31/7 ÷ 7 [Converting the mixed number 4(3/7) into an improper fraction]
= 31/7 × 1/7
= 31/49
4. Find:
(i) 2/5 ÷ 1/2
(ii) 4/9 ÷ 2/3
(iii) 3/7 ÷ 8/7
(iv) 2(1/3) ÷ 3/5
(v) 3(1/2) ÷ 8/3
(vi) 2/5 ÷ 1(1/2)
(vii) 3(1/5) ÷ 1(2/3)
(viii) 2(1/5) ÷ 1(1/5)
Solution
(i) 2/5 ÷ 1/2
= 2/5 × 2/1 [Dividing by a fraction is equivalent to multiplying by its reciprocal]
= 4/5
(ii) 4/9 ÷ 2/3
= 4/9 × 3/2
= 12/18
= 2/3
(iii) 3/7 ÷ 8/7
= 3/7 × 7/8
= 3/8
(iv) 2(1/3) ÷ 3/5
= 7/3 ÷ 3/5 [Converting the mixed number 2(1/3) into an improper fraction]
= 7/3 × 5/3
= 35/9
= 3(8/9)
(v) 3(1/2) ÷ 8/3
= 7/2 ÷ 8/3 [Converting the mixed number 3(1/2) into an improper fraction]
= 7/2 × 3/8
= 21/16
= 1(5/16)
(vi) 2/5 ÷ 1(1/2)
= 2/5 ÷ 3/2 [Converting the mixed number 1(1/2) into an improper fraction]
= 2/5 × 2/3
= 4/15
(vii) 3(1/5) ÷ 1(2/3)
= 16/5 ÷ 5/3 [Converting mixed numbers into improper fractions]
= 16/5 × 3/5
= 48/25
= 1(23/25)
(viii) 2(1/5) ÷ 1(1/5)
= 11/5 ÷ 6/5 [Converting mixed numbers into improper fractions]
= 11/5 × 5/6
= 11/6
= 1(5/6)
Extra Challenging MCQ Questions
1. What is the result of dividing 7/8 by 1/4?
Hint: Dividing by a fraction is equivalent to multiplying by its reciprocal.
a) 7/32
b) 7/2
c) 14/3
d) 28/3
Answer:
b) 7/2 – (7/8) × (4/1) = 28/8 = 7/2
2. Simplify: 5 ÷ 2 1/2
Hint: Convert the mixed number to an improper fraction and multiply by its reciprocal.
a) 2
b) 2 1/2
c) 5/2
d) 10/3
Answer:
a) 2 – 5 ÷ (5/2) = 5 × (2/5) = 2.
3. If 3/4 of a cake is divided equally among 6 people, what fraction of the whole cake does each person receive?
Hint: Divide the fraction by the number of people.
a) 1/8
b) 1/6
c) 1/12
d) 1/16
Answer:
a) 1/8 – (3/4) ÷ 6 = (3/4) × (1/6) = 3/24 = 1/8
4. What is the reciprocal of 1 2/3?
Hint: Convert the mixed number to an improper fraction and then find its reciprocal.
a) 3/5
b) 5/3
c) 3/2
d) 2/3
Answer:
a) 3/5 – 1 2/3 = 5/3. Reciprocal = 3/5
5. Which of the following fractions has a reciprocal that is a whole number?
Hint: A fraction whose reciprocal is a whole number has a numerator of 1.
a) 2/3
b) 3/4
c) 1/5
d) 5/2
Answer:
c) 1/5 – A fraction with numerator 1 works. Reciprocal of 1/5 = 5 (whole number)
6. Simplify: 4 ÷ 2/3
Hint: Multiply by the reciprocal of the divisor.
a) 6
b) 8/3
c) 12
d) 2 2/3
Answer:
a) 6 – (4) × (3/2) = 12/2 = 6
7. If a recipe requires 2/3 cup of sugar and you want to make half of the recipe, how much sugar do you need?
Hint: Multiply the fraction by 1/2.
a) 1/3 cup
b) 1/4 cup
c) 1/6 cup
d) 2/5 cup
Answer:
a) 1/3 cup – (2/3) × (1/2) = 2/6 = 1/3
8. What is the result of dividing 5/6 by 5?
Hint: Dividing by a whole number is the same as multiplying by its reciprocal.
a) 1/6
b) 5/36
c) 1/5
d) 6/5
Answer:
a) 1/6 – (5/6) ÷ 5 = (5/6) × (1/5) = 5/30 = 1/6
9. Which of the following is the reciprocal of 7/9?
Hint: The reciprocal of a fraction is obtained by swapping its numerator and denominator.
a) 9/7
b) 7/9
c) 1 2/7
d) 1 4/9
Answer:
a) 9/7 – Reciprocal = 9/7
10. Simplify: 3 1/2 ÷ 1 1/4
Hint: Convert mixed numbers to improper fractions and multiply by the reciprocal.
a) 2 4/5
b) 2 2/5
c) 2 1/3
d) 2 1/4
Answer:
a) 2 4/5 – (7/2) ÷ (5/4) = (7/2) × (4/5) = 28/10 = 14/5 = 2 4/5
