Maharashtra Board Class 6 Maths Chapter 4 Operations on Fractions Set 12 Solutions

Question 1. Multiply:
(i) \( \frac{7}{5} \times \frac{1}{4} \)
(ii) \( \frac{6}{7} \times \frac{2}{5} \)
(iii) \( \frac{5}{9} \times \frac{4}{9} \)
(iv) \( \frac{4}{11} \times \frac{2}{7} \)
(v) \( \frac{1}{5} \times \frac{7}{2} \)
(vi) \( \frac{9}{7} \times \frac{7}{8} \)
(vii) \( \frac{5}{6} \times \frac{6}{5} \)
(viii) \( \frac{6}{17} \times \frac{3}{2} \)
Answer:
(i) Solution:
\( \frac{7}{5} \times \frac{1}{4} = \frac{7 \times 1}{5 \times 4} = \frac{7}{20} \)
(ii) Solution:
\( \frac{6}{7} \times \frac{2}{5} = \frac{6 \times 2}{7 \times 5} = \frac{12}{35} \)
(iii) Solution:
\( \frac{5}{9} \times \frac{4}{9} = \frac{5 \times 4}{9 \times 9} = \frac{20}{81} \)
(iv) Solution:
\( \frac{4}{11} \times \frac{2}{7} = \frac{4 \times 2}{11 \times 7} = \frac{8}{77} \)
(v) Solution:
\( \frac{1}{5} \times \frac{7}{2} = \frac{1 \times 7}{5 \times 2} = \frac{7}{10} \)
(vi) Solution:
\( \frac{9}{7} \times \frac{7}{8} = \frac{9 \times 7}{7 \times 8} = \frac{9}{8} \)
(vii) Solution:
\( \frac{5}{6} \times \frac{6}{5} = \frac{5 \times 6}{6 \times 5} = 1 \)
(viii) Solution:
\( \frac{6}{17} \times \frac{3}{2} = \frac{6 \times 3}{17 \times 2} = \frac{3 \times 6}{17 \times 2} = \frac{3 \times 3}{17 \times 1} = \frac{9}{17} \)
In simple words: To multiply fractions, multiply the numerators together and the denominators together. Simplify the resulting fraction if possible by cancelling common factors before or after multiplication.

🎯 Exam Tip: Remember to simplify fractions to their lowest terms for full marks. Cross-cancellation can make multiplication easier.

Question 2. Ashokrao planted bananas on \( \frac{2}{7} \) of his field of 21 acres. What is the area of the banana plantation?
Answer:
Solution:
Area of banana plantation is \( \frac{2}{7} \) of 21
\( \therefore \) Area of banana plantation
\( = \frac{2}{7} \times 21 = \frac{2}{7} \times \frac{21}{1} = \frac{2 \times 21}{7 \times 1} = \frac{42}{7} = 6 \) acres
\( \therefore \) Area of banana plantation is 6 acres
In simple words: To find the area of the banana plantation, multiply the total field area by the fraction representing the portion used for bananas.

🎯 Exam Tip: Clearly show all multiplication and simplification steps. State the final answer with appropriate units (acres in this case).

Question 3. Of the total number of soldiers in our army, \( \frac{1}{2} \) are posted on the northern border and one-third of them on the north-eastern border. If the number of soldiers in the north is 5,40,000, how many are posted in the north-east?
Answer:
Solution:
Number of soldiers posted on northern border = 5,40,000
Since, number of soldiers in north-east = one third of the soldiers on northern border
\( \therefore \) Number of soldiers in the north-east
\( = \frac{1}{3} \times 5,40,000 = \frac{1 \times 5,40,000}{3 \times 1} = 1,80,000 \)
\( \therefore \) The number of soldiers in the north-east is 1,80,000.
In simple words: Calculate the number of soldiers in the north-east by taking one-third of the given number of soldiers posted on the northern border.

🎯 Exam Tip: Read the question carefully to identify which fraction applies to which quantity. Show the multiplication clearly and state the final count of soldiers.