Maharashtra Board Class 6 Maths Chapter 4 Operations on Fractions Set 9 Solutions

Question 1. Convert into improper fractions:
(i) \( 7\frac{2}{5} \)
(ii) \( 5\frac{1}{6} \)
(iii) \( 4\frac{3}{4} \)
(iv) \( 2\frac{5}{9} \)
(v) \( 1\frac{5}{7} \)
Answer:
(i) \[ 7\frac{2}{5} = 7 + \frac{2}{5} = \frac{7}{1} + \frac{2}{5} = \frac{7 \times 5}{1 \times 5} + \frac{2}{5} = \frac{35}{5} + \frac{2}{5} = \frac{35+2}{5} = \frac{37}{5} \]
(ii) \[ 5\frac{1}{6} = 5 + \frac{1}{6} = \frac{5}{1} + \frac{1}{6} = \frac{5 \times 6}{1 \times 6} + \frac{1}{6} = \frac{30}{6} + \frac{1}{6} = \frac{30+1}{6} = \frac{31}{6} \]
(iii) \[ 4\frac{3}{4} = 4 + \frac{3}{4} = \frac{4}{1} + \frac{3}{4} = \frac{4 \times 4}{1 \times 4} + \frac{3}{4} = \frac{16}{4} + \frac{3}{4} = \frac{16+3}{4} = \frac{19}{4} \]
(iv) \[ 2\frac{5}{9} = 2 + \frac{5}{9} = \frac{2}{1} + \frac{5}{9} = \frac{2 \times 9}{1 \times 9} + \frac{5}{9} = \frac{18}{9} + \frac{5}{9} = \frac{18+5}{9} = \frac{23}{9} \]
(v) \[ 1\frac{5}{7} = 1 + \frac{5}{7} = \frac{1}{1} + \frac{5}{7} = \frac{1 \times 7}{1 \times 7} + \frac{5}{7} = \frac{7}{7} + \frac{5}{7} = \frac{7+5}{7} = \frac{12}{7} \]
In simple words: To convert a mixed fraction to an improper fraction, multiply the whole number by the denominator, add the numerator, and place the result over the original denominator. This process combines the whole and fractional parts into a single fraction.

🎯 Exam Tip: Mastering mixed to improper fraction conversion is fundamental for operations like addition and subtraction of fractions. Ensure your multiplication and addition steps are accurate to avoid errors.

Question 2. Convert into mixed numbers:
(i) 30/7
(ii) 7/4
(iii) 15/12
(iv) 11/8
(v) 21/4
(V) 20/7
Answer:
(i) \( \frac{30}{7} \)
Divide 30 by 7: The quotient is 4 and the remainder is 2.
So, \( \frac{30}{7} = 4\frac{2}{7} \)
(ii) \( \frac{7}{4} \)
Divide 7 by 4: The quotient is 1 and the remainder is 3.
So, \( \frac{7}{4} = 1\frac{3}{4} \)
(iii) \( \frac{15}{12} \)
Divide 15 by 12: The quotient is 1 and the remainder is 3.
So, \( \frac{15}{12} = 1\frac{3}{12} \)
(iv) \( \frac{11}{8} \)
Divide 11 by 8: The quotient is 1 and the remainder is 3.
So, \( \frac{11}{8} = 1\frac{3}{8} \)
(v) \( \frac{21}{4} \)
Divide 21 by 4: The quotient is 5 and the remainder is 1.
So, \( \frac{21}{4} = 5\frac{1}{4} \)
(V) \( \frac{20}{7} \)
Divide 20 by 7: The quotient is 2 and the remainder is 6.
So, \( \frac{20}{7} = 2\frac{6}{7} \)
In simple words: To convert an improper fraction to a mixed number, divide the numerator by the denominator. The quotient becomes the whole number, the remainder becomes the new numerator, and the denominator stays the same.

🎯 Exam Tip: Always simplify the fractional part of a mixed number if possible. This demonstrates a complete understanding of fractions and can prevent loss of marks.

Question 3. Write the following examples using fraction:
(i) If 9 kg rice is shared among 5 people, how many kilograms of rice does each person get?
(ii) To make 5 shirts of the same size, 11 meters of cloth is needed. How much cloth is needed for one shirt?
Answer:
(i) Total quantity of rice = 9 kg
Number of people = 5
Therefore, kilograms of rice received by each person = \( \frac{9}{5} \)
Therefore, each person will get \( \frac{9}{5} \) kg of rice.
(ii) Total meters of cloth = 11 meters
Number of shirts to be made = 5
Meters of cloth needed to make 1 shirt = \( \frac{11}{5} \)
Therefore, cloth needed to make 1 shirt is \( \frac{11}{5} \) meters.
In simple words: When a total quantity is divided equally among a certain number of parts or individuals, the share for each part is represented as a fraction, where the total quantity is the numerator and the number of parts is the denominator.

🎯 Exam Tip: Clearly identify the total quantity and the number of divisions. The question asks for a fractional representation, so ensure your final answer is in the correct fraction format with appropriate units.