Maharashtra Board Class 5 Maths Chapter 5 Fractions Set 22 Solutions

Question 1. Add the following:
(1) \( \frac{1}{8} + \frac{3}{4} \)
Answer: Solution:
The smallest common multiple of 4 and 8 is 8. So making 8 is the common denominator of the given fractions.
\( \frac{1}{8} + \frac{3 \times 2}{4 \times 2} = \frac{1}{8} + \frac{6}{8} \)

\( = \frac{1+6}{8} = \frac{7}{8} \)
Answer: \( \frac{7}{8} \)
In simple words: To add fractions, find a common denominator, then add the numerators. In this case, 8 is the common denominator, so \( \frac{1}{8} + \frac{6}{8} = \frac{7}{8} \).

🎯 Exam Tip: Always find the least common multiple (LCM) of the denominators to simplify addition/subtraction of fractions, ensuring the final answer is in its simplest form.

(2) \( \frac{2}{21} + \frac{3}{7} \)
Answer: Solution:
21 is the multiple of 7. So making 21 as denominator of both the fractions.
\( \frac{2}{21} + \frac{3 \times 3}{7 \times 3} = \frac{2}{21} + \frac{9}{21} \)

\( = \frac{2+9}{21} = \frac{11}{21} \)
Answer: \( \frac{11}{21} \)
In simple words: Since 21 is a multiple of 7, we convert \( \frac{3}{7} \) to have a denominator of 21, then add the numerators to get \( \frac{11}{21} \).

🎯 Exam Tip: When one denominator is a multiple of the other, use the larger denominator as the common denominator to efficiently add or subtract fractions.

(3) \( \frac{2}{5} + \frac{1}{3} \)
Answer: Solution:
Least common multiple of 5 and 3 is 15. So making common denominator of both the fractions 15.
\( \frac{2}{5} + \frac{1}{3} = \frac{2 \times 3}{5 \times 3} + \frac{1 \times 5}{3 \times 5} \)

\( = \frac{6}{15} + \frac{5}{15} \)

\( = \frac{6+5}{15} = \frac{11}{15} \)
Answer: \( \frac{11}{15} \)
In simple words: Find the LCM of 5 and 3 which is 15. Convert both fractions to have 15 as the denominator, then add their numerators to get \( \frac{11}{15} \).

🎯 Exam Tip: For denominators that are prime to each other, their product is the least common multiple, which simplifies finding a common denominator.

(4) \( \frac{2}{7} + \frac{1}{2} \)
Answer: Solution:
Smallest common multiple of 2 and 7 is 14. So, making denominator of both the fractions 14.
\( \frac{2}{7} + \frac{1}{2} = \frac{2 \times 2}{7 \times 2} + \frac{1 \times 7}{2 \times 7} \)

\( = \frac{4}{14} + \frac{7}{14} \)

\( = \frac{4+7}{14} = \frac{11}{14} \)
Answer: \( \frac{11}{14} \)
In simple words: The LCM of 7 and 2 is 14. Convert both fractions to have 14 as the denominator, then add the numerators to find the sum \( \frac{11}{14} \).

🎯 Exam Tip: Understanding how to find common multiples is crucial for accurately adding fractions, especially when denominators are different.

(5) \( \frac{3}{9} + \frac{3}{5} \)
Answer: Solution:
Smallest common multiple of 9 and 5 is 45.
\( \frac{3}{9} + \frac{3}{5} = \frac{3 \times 5}{9 \times 5} + \frac{3 \times 9}{5 \times 9} \)

\( = \frac{15}{45} + \frac{27}{45} \)

\( = \frac{15+27}{45} = \frac{42}{45} \)
Answer: \( \frac{42}{45} \)
In simple words: Find the LCM of 9 and 5 which is 45. Convert both fractions to have 45 as the denominator, then add the numerators to get \( \frac{42}{45} \).

🎯 Exam Tip: Always simplify the resulting fraction if possible. While \( \frac{42}{45} \) is correct, it can be further simplified to \( \frac{14}{15} \) by dividing both numerator and denominator by 3.

Question 2. Subtract the following:
(1) \( \frac{3}{10} - \frac{1}{20} \)
Answer: Solution:
20 is the multiples of 10. So,
\( \frac{3}{10} - \frac{1}{20} = \frac{3 \times 2}{10 \times 2} - \frac{1}{20} \)

\( = \frac{6}{20} - \frac{1}{20} \)

\( = \frac{6-1}{20} = \frac{5}{20} \)
Answer: \( \frac{5}{20} \)
In simple words: Since 20 is a multiple of 10, convert \( \frac{3}{10} \) to have a denominator of 20, then subtract the numerators to get \( \frac{5}{20} \).

🎯 Exam Tip: Just like addition, subtraction of fractions requires a common denominator. The same principles of finding LCM apply.

(2) \( \frac{3}{4} - \frac{1}{2} \)
Answer: Solution:
4 is the multiple of 2. So,
\( \frac{3}{4} - \frac{1}{2} = \frac{3}{4} - \frac{1 \times 2}{2 \times 2} \)

\( = \frac{3}{4} - \frac{2}{4} \)

\( = \frac{3-2}{4} = \frac{1}{4} \)
Answer: \( \frac{1}{4} \)
In simple words: Convert \( \frac{1}{2} \) to have a denominator of 4, making it \( \frac{2}{4} \), then subtract it from \( \frac{3}{4} \) to get \( \frac{1}{4} \).

🎯 Exam Tip: Always look for the simplest common denominator to make calculations easier and reduce chances of error.

(3) \( \frac{6}{14} - \frac{2}{7} \)
Answer: Solution:
14 is the multiples of 7. So,
\( \frac{6}{14} - \frac{2}{7} = \frac{6}{14} - \frac{2 \times 2}{7 \times 2} \)

\( = \frac{6}{14} - \frac{4}{14} \)

\( = \frac{6-4}{14} = \frac{2}{14} \)
Answer: \( \frac{2}{14} \)
In simple words: Since 14 is a multiple of 7, convert \( \frac{2}{7} \) to \( \frac{4}{14} \), then subtract it from \( \frac{6}{14} \) to get \( \frac{2}{14} \).

🎯 Exam Tip: Remember to simplify the final answer. \( \frac{2}{14} \) simplifies to \( \frac{1}{7} \), which is a better representation.

(4) \( \frac{4}{6} - \frac{3}{5} \)
Answer: Solution:
Smallest common multiple of 6 and 5 is 30. So,
\( \frac{4}{6} - \frac{3}{5} = \frac{4 \times 5}{6 \times 5} - \frac{3 \times 6}{5 \times 6} \)

\( = \frac{20}{30} - \frac{18}{30} \)

\( = \frac{20-18}{30} = \frac{2}{30} \)
Answer: \( \frac{2}{30} \)
In simple words: Find the LCM of 6 and 5 which is 30. Convert both fractions to have 30 as the denominator, then subtract the numerators to get \( \frac{2}{30} \).

🎯 Exam Tip: Always reduce the final fraction to its simplest form. \( \frac{2}{30} \) can be simplified to \( \frac{1}{15} \).

(5) \( \frac{2}{7} - \frac{1}{4} \)
Answer: Solution:
Smallest common multiple of 7 and 4 is 28.
\( \frac{2}{7} - \frac{1}{4} = \frac{2 \times 4}{7 \times 4} - \frac{1 \times 7}{4 \times 7} \)

\( = \frac{8}{28} - \frac{7}{28} \)

\( = \frac{8-7}{28} = \frac{1}{28} \)
Answer: \( \frac{1}{28} \)
In simple words: The LCM of 7 and 4 is 28. Convert both fractions to have 28 as the denominator, then subtract the numerators to find the difference \( \frac{1}{28} \).

🎯 Exam Tip: Practice finding the LCM quickly to save time in exams. For numbers with no common factors, their product is the LCM.

A Fraction Of A Collection And A Multiple Of A Fraction

ℹ️ चित्र व्याख्या (Diagram Explanation): यह चित्र 20 बिंदुओं के संग्रह के एक-चौथाई (1/4) और आधे (1/2) को दर्शाता है। बाईं ओर, 20 बिंदुओं को चार समूहों में बांटा गया है, प्रत्येक में 5 बिंदु हैं, यह दिखाता है कि 20 का 1/4 हिस्सा 5 होता है। दाईं ओर, 20 बिंदुओं को दो समूहों में बांटा गया है, प्रत्येक में 10 बिंदु हैं, यह दर्शाता है कि 20 का 1/2 हिस्सा 10 होता है।
ℹ️ चित्र व्याख्या (Diagram Explanation): यह चित्र 20 बिंदुओं के संग्रह के तीन-चौथाई (3/4) हिस्से को दर्शाता है। 20 बिंदुओं को चार बराबर समूहों में बांटा गया है, प्रत्येक समूह में 5 बिंदु हैं। चित्र यह दिखाता है कि 20 का एक-चौथाई 5 होता है, और इसलिए तीन-चौथाई (3 x 1/4) 5 का तीन गुना यानी 15 बिंदु होते हैं (5 x 3 = 15)।
ℹ️ चित्र व्याख्या (Diagram Explanation): यह चित्र दर्शाता है कि "5 का दुगुना 10 होता है" और "10 का आधा 5 होता है।" बाईं ओर, 5 गेंदों की 2 पंक्तियाँ हैं जो 5 x 2 = 10 दर्शाती हैं। दाईं ओर, 10 गेंदों को दो बराबर समूहों में बांटा गया है, यह दर्शाता है कि 10 का आधा 5 होता है।
ℹ️ चित्र व्याख्या (Diagram Explanation): यह चित्र दर्शाता है कि "5 का तिगुना 15 होता है" और "15 का एक-तिहाई 5 होता है।" बाईं ओर, 5 गेंदों की 3 पंक्तियाँ हैं जो 5 x 3 = 15 दर्शाती हैं। दाईं ओर, 15 गेंदों को तीन बराबर समूहों में बांटा गया है, यह दर्शाता है कि 15 का एक-तिहाई 5 होता है। To get \( \frac{2}{3} \) times 15 is to find \( \frac{1}{3} \) times 15 and take it twice.
ℹ️ चित्र व्याख्या (Diagram Explanation): यह चित्र दर्शाता है कि 15 का \( \frac{1}{3} \) हिस्सा 5 होता है, और फिर 15 का \( \frac{2}{3} \) हिस्सा प्राप्त करने के लिए इसे दुगुना किया जाता है, जो कि 10 होता है। बाईं ओर 15 गोले तीन बराबर समूहों में बँटे हैं, प्रत्येक में 5 गोले हैं, यह दर्शाता है कि \( \frac{1}{3} \) of 15 is 5. यह उदाहरण भिन्न के गुणनफल को दर्शाता है। Meena has 5 rupees. Tina has twice as many rupees. That is, Tina has \( 5 \times 2 = 10 \) rupees. Meena has half as many rupees as Tina, that is, \( \frac{1}{2} \) of 10, or, 5 rupees.

Question. Ramu has to travel a distance of 20 km. If he has travelled \( \frac{4}{5} \) of the distance by car, how many kilometres did he travel by car?
Answer: Solution:
\( \frac{4}{5} \) of 20 km is \( 20 \times \frac{4}{5} \). So, we take \( \frac{1}{5} \) of 20, 4 times.
\( \frac{1}{5} \) of 20 = 4. 4 times 4 is \( 4 \times 4 = 16 \).
It means that \( 20 \times \frac{4}{5} = 16 \).
Ramu travelled a distance of 16 kilometres by car.
In simple words: To find \( \frac{4}{5} \) of 20 km, first find \( \frac{1}{5} \) of 20 (which is 4), and then multiply that by 4 to get 16 km.

🎯 Exam Tip: When calculating a fraction of a quantity, divide the quantity by the denominator and then multiply by the numerator.

Addition And Subtraction Problem Set 13 Additional Important Questions And Answers

(1) \( \frac{5}{6} + \frac{1}{12} \)
Answer: Solution:
12 is the multiple of 6
\( \frac{5}{6} + \frac{1}{12} = \frac{5 \times 2}{6 \times 2} + \frac{1}{12} \)

\( = \frac{10}{12} + \frac{1}{12} \)

\( = \frac{10+1}{12} = \frac{11}{12} \)
Answer: \( \frac{11}{12} \)
In simple words: Convert \( \frac{5}{6} \) to \( \frac{10}{12} \) to match the denominator, then add the numerators to get \( \frac{11}{12} \).

🎯 Exam Tip: For additional questions, apply the same fundamental rules of fractions consistently to ensure accurate solutions.

(2) \( \frac{1}{9} + \frac{2}{3} \)
Answer: Solution:
Here 9 is the multiples of 3. So, making like fractions of denominator 9, we get
\( \frac{1}{9} + \frac{2 \times 3}{3 \times 3} = \frac{1}{9} + \frac{6}{9} \)

\( = \frac{1+6}{9} = \frac{7}{9} \)
Answer: \( \frac{7}{9} \)
In simple words: Convert \( \frac{2}{3} \) to \( \frac{6}{9} \) as 9 is a multiple of 3, then add the numerators to find the sum \( \frac{7}{9} \).

🎯 Exam Tip: Always check if the denominators are multiples of each other before calculating a general LCM to simplify steps.

Subtract the following:

(1) \( \frac{4}{9} - \frac{2}{5} \)
Answer: Solution:
Common multiple of 9 and 5 is 45
\( \frac{4}{9} - \frac{2}{5} = \frac{4 \times 5}{9 \times 5} - \frac{2 \times 9}{5 \times 9} \)

\( = \frac{20}{45} - \frac{18}{45} \)

\( = \frac{20-18}{45} = \frac{2}{45} \)
Answer: \( \frac{2}{45} \)
In simple words: Find the LCM of 9 and 5 which is 45. Convert both fractions to have 45 as the denominator, then subtract the numerators to get \( \frac{2}{45} \).

🎯 Exam Tip: When dealing with subtraction, precision in common denominator conversion is key to avoid sign errors in the numerator.

(2) \( \frac{1}{2} + \frac{3}{4} - \frac{7}{8} \)
Answer: Solution:
\( \frac{1}{2} + \frac{3}{4} - \frac{7}{8} = \frac{1 \times 4}{2 \times 4} + \frac{3 \times 2}{4 \times 2} - \frac{7}{8} \)

\( = \frac{4}{8} + \frac{6}{8} - \frac{7}{8} \)

\( = \frac{4+6-7}{8} = \frac{3}{8} \)
Answer: \( \frac{3}{8} \)
In simple words: Find the common denominator for 2, 4, and 8 (which is 8). Convert all fractions to have 8 as the denominator, then perform the addition and subtraction of the numerators to get \( \frac{3}{8} \).

🎯 Exam Tip: When multiple operations are present, ensure all fractions share a common denominator before combining their numerators.