GSEB Class 7 Maths Solutions Chapter 2 Fractions and Decimals Exercise 2.4

Question 1. Find:
(i) \( 12 \div \frac { 3 }{ 4 } \)
(ii) \( 14 \div \frac { 5 }{ 6 } \)
(iii) \( 8 \div \frac { 7 }{ 3 } \)
(iv) \( 4 \div \frac { 8 }{ 3 } \)
(v) \( 3 \div 2\frac { 1 }{ 3 } \)
(vi) \( 5 \div 3\frac { 4 }{ 7 } \)
Answer:
(i) \( 12 \div \frac { 3 }{ 4 } = 12 \times \frac { 4 }{ 3 } = \frac { 4 \times 4 }{ 1 } = 16 \)
(ii) \( 14 \div \frac { 5 }{ 6 } = 14 \times \frac { 6 }{ 5 } = \frac { 14 \times 6 }{ 5 } = \frac { 84 }{ 5 } = 16\frac { 4 }{ 5 } \)
(iii) \( 8 \div \frac { 7 }{ 3 } = 8 \times \frac { 3 }{ 7 } = \frac { 8 \times 3 }{ 7 } = \frac { 24 }{ 7 } = 3\frac { 3 }{ 7 } \)
(iv) \( 4 \div \frac { 8 }{ 3 } = 4 \times \frac { 3 }{ 8 } = \frac { 1 \times 3 }{ 2 } = \frac { 3 }{ 2 } = 1\frac { 1 }{ 2 } \)
(v) \( 3 \div 2\frac { 1 }{ 3 } = 3 \div \frac { 7 }{ 3 } = 3 \times \frac { 3 }{ 7 } = \frac { 9 }{ 7 } = 1\frac { 2 }{ 7 } \)
(vi) \( 5 \div 3\frac { 4 }{ 7 } = 5 \div \frac { 25 }{ 7 } = 5 \times \frac { 7 }{ 25 } = \frac { 7 }{ 5 } = 1\frac { 2 }{ 5 } \)
In simple words: To divide by a fraction, you flip the second fraction upside down (find its reciprocal) and then multiply. If you have a mixed number, change it to an improper fraction first before flipping.

Exam Tip: Remember to convert any mixed numbers into improper fractions before finding the reciprocal or performing division. Simplification should always be the last step.

Question 2. Find the reciprocal of each of the following fractions. Classify the reciprocals as proper fractions, improper fractions and whole numbers.
(i) \( \frac { 3 }{ 7 } \)
(ii) \( \frac { 5 }{ 8 } \)
(iii) \( \frac { 9 }{ 7 } \)
(iv) \( \frac { 6 }{ 5 } \)
(v) \( \frac { 12 }{ 7 } \)
(vi) \( \frac { 1 }{ 8 } \)
(vii) \( \frac { 1 }{ 11 } \)
Answer:
(i) The reciprocal of \( \frac { 3 }{ 7 } \) is \( \frac { 7 }{ 3 } \); (improper fraction)
(ii) The reciprocal of \( \frac { 5 }{ 8 } \) is \( \frac { 8 }{ 5 } \); (improper fraction)
(iii) The reciprocal of \( \frac { 9 }{ 7 } \) is \( \frac { 7 }{ 9 } \); (proper fraction)
(iv) The reciprocal of \( \frac { 6 }{ 5 } \) is \( \frac { 5 }{ 6 } \); (proper fraction)
(v) The reciprocal of \( \frac { 12 }{ 7 } \) is \( \frac { 7 }{ 12 } \); (proper fraction)
(vi) The reciprocal of \( \frac { 1 }{ 8 } \) is 8; (whole number)
(vii) The reciprocal of \( \frac { 1 }{ 11 } \) is 11; (whole number)
In simple words: To find the reciprocal of a fraction, just flip the top and bottom numbers. Then, check if the new fraction has a bigger top number (improper), a smaller top number (proper), or is a whole number.

Exam Tip: A proper fraction has a numerator smaller than its denominator. An improper fraction has a numerator larger than or equal to its denominator. If the denominator is 1, it's a whole number.

Question 3. Find:
(i) \( \frac { 7 }{ 3 } \div 2 \)
(ii) \( \frac { 4 }{ 9 } \div 5 \)
(iii) \( \frac { 6 }{ 13 } \div 7 \)
(iv) \( 4\frac { 1 }{ 3 } \div 3 \)
(v) \( 3\frac { 1 }{ 2 } \div 4 \)
(vi) \( 4\frac { 4 }{ 7 } \div 7 \)
Answer:
(i) \( \frac { 7 }{ 3 } \div 2 = \frac { 7 }{ 3 } \times \frac { 1 }{ 2 } = \frac { 7 }{ 6 } \)
(ii) \( \frac { 4 }{ 9 } \div 5 = \frac { 4 }{ 9 } \times \frac { 1 }{ 5 } = \frac { 4 }{ 45 } \)
(iii) \( \frac { 6 }{ 13 } \div 7 = \frac { 6 }{ 13 } \times \frac { 1 }{ 7 } = \frac { 6 }{ 91 } \)
(iv) \( 4\frac { 1 }{ 3 } \div 3 = \frac { 13 }{ 3 } \div 3 = \frac { 13 }{ 3 } \times \frac { 1 }{ 3 } = \frac { 13 }{ 9 } = 1\frac { 4 }{ 9 } \)
(v) \( 3\frac { 1 }{ 2 } \div 4 = \frac { 7 }{ 2 } \div 4 = \frac { 7 }{ 2 } \times \frac { 1 }{ 4 } = \frac { 7 }{ 8 } \)
(vi) \( 4\frac { 4 }{ 7 } \div 7 = \frac { 31 }{ 7 } \div 7 = \frac { 31 }{ 7 } \times \frac { 1 }{ 7 } = \frac { 31 }{ 49 } \)
In simple words: When you divide a fraction by a whole number, remember that the whole number can be written as a fraction with 1 under it. Then, flip that whole number fraction and multiply.

Exam Tip: Always remember that dividing by a number is the same as multiplying by its reciprocal. This is a fundamental concept in fraction arithmetic.

Question 4. Find:
(i) \( \frac { 2 }{ 5 } \div \frac { 1 }{ 2 } \)
(ii) \( \frac { 4 }{ 9 } \div \frac { 2 }{ 3 } \)
(iii) \( \frac { 3 }{ 7 } \div \frac { 8 }{ 7 } \)
(iv) \( 2\frac { 1 }{ 3 } \div \frac { 3 }{ 5 } \)
(v) \( 3\frac { 1 }{ 2 } \div \frac { 8 }{ 3 } \)
(vi) \( 2\frac { 2 }{ 5 } \div 1\frac { 1 }{ 2 } \)
(vii) \( 3\frac { 1 }{ 5 } \div 1\frac { 2 }{ 3 } \)
(viii) \( 2\frac { 1 }{ 5 } \div 1\frac { 1 }{ 5 } \)
Answer:
(i) \( \frac { 2 }{ 5 } \div \frac { 1 }{ 2 } = \frac { 2 }{ 5 } \times \frac { 2 }{ 1 } = \frac { 2 \times 2 }{ 5 \times 1 } = \frac { 4 }{ 5 } \)
(ii) \( \frac { 4 }{ 9 } \div \frac { 2 }{ 3 } = \frac { 4 }{ 9 } \times \frac { 3 }{ 2 } = \frac { 2 \times 1 }{ 3 \times 1 } = \frac { 2 }{ 3 } \)
(iii) \( \frac { 3 }{ 7 } \div \frac { 8 }{ 7 } = \frac { 3 }{ 7 } \times \frac { 7 }{ 8 } = \frac { 3 \times 1 }{ 1 \times 8 } = \frac { 3 }{ 8 } \)
(iv) \( 2\frac { 1 }{ 3 } \div \frac { 3 }{ 5 } = \frac { 7 }{ 3 } \div \frac { 3 }{ 5 } = \frac { 7 }{ 3 } \times \frac { 5 }{ 3 } = \frac { 35 }{ 9 } = 3\frac { 8 }{ 9 } \)
(v) \( 3\frac { 1 }{ 2 } \div \frac { 8 }{ 3 } = \frac { 7 }{ 2 } \div \frac { 8 }{ 3 } = \frac { 7 }{ 2 } \times \frac { 3 }{ 8 } = \frac { 21 }{ 16 } = 1\frac { 5 }{ 16 } \)
(vi) \( 2\frac { 2 }{ 5 } \div 1\frac { 1 }{ 2 } = \frac { 12 }{ 5 } \div \frac { 3 }{ 2 } = \frac { 12 }{ 5 } \times \frac { 2 }{ 3 } = \frac { 4 \times 2 }{ 5 \times 1 } = \frac { 8 }{ 5 } = 1\frac { 3 }{ 5 } \)
(vii) \( 3\frac { 1 }{ 5 } \div 1\frac { 2 }{ 3 } = \frac { 16 }{ 5 } \div \frac { 5 }{ 3 } = \frac { 16 }{ 5 } \times \frac { 3 }{ 5 } = \frac { 48 }{ 25 } = 1\frac { 23 }{ 25 } \)
(viii) \( 2\frac { 1 }{ 5 } \div 1\frac { 1 }{ 5 } = \frac { 11 }{ 5 } \div \frac { 6 }{ 5 } = \frac { 11 }{ 5 } \times \frac { 5 }{ 6 } = \frac { 11 }{ 6 } = 1\frac { 5 }{ 6 } \)
In simple words: When dividing two fractions, simply flip the second fraction (find its reciprocal) and then multiply them together. If you have mixed numbers, convert them into improper fractions first.

Exam Tip: After multiplying fractions, always look for opportunities to simplify the resulting fraction by canceling common factors in the numerator and denominator before converting to a mixed number if needed.