Maharashtra Board Class 5 Maths Chapter 5 Fractions Set 21 Solutions

Std 5 Maths Chapter 5 Fractions

Question 1. Subtract the following.
(1) \( \frac{5}{7} - \frac{1}{7} \)
Answer: \( \frac{5}{7} - \frac{1}{7} = \frac{5-1}{7} = \frac{4}{7} \)
In simple words: To subtract fractions with the same denominator, subtract the numerators and keep the denominator the same. Here, 5 minus 1 equals 4, so the answer is 4/7.

🎯 Exam Tip: Ensure that the denominators are identical before proceeding with the subtraction of numerators to get full marks.

Question 1. Subtract the following.
(2) \( \frac{5}{8} - \frac{3}{8} \)
Answer: \( \frac{5}{8} - \frac{3}{8} = \frac{5-3}{8} = \frac{2}{8} \)
In simple words: When denominators are the same, simply subtract the numerators. In this case, 5 minus 3 is 2, resulting in the fraction 2/8.

🎯 Exam Tip: Remember to always simplify the resulting fraction to its lowest terms if possible, though not explicitly asked here.

Question 1. Subtract the following.
(3) \( \frac{7}{9} - \frac{2}{9} \)
Answer: \( \frac{7}{9} - \frac{2}{9} = \frac{7-2}{9} = \frac{5}{9} \)
In simple words: Since the denominators are both 9, subtract the numerators: 7 minus 2 equals 5. The final fraction is 5/9.

🎯 Exam Tip: Accuracy in subtracting the numerators is key when the denominators are already equal.

Question 1. Subtract the following.
(4) \( \frac{8}{11} - \frac{5}{11} \)
Answer: \( \frac{8}{11} - \frac{5}{11} = \frac{8-5}{11} = \frac{3}{11} \)
In simple words: With a common denominator of 11, subtract 5 from 8 to get 3. The result is 3/11.

🎯 Exam Tip: Always double-check your subtraction calculation for the numerators.

Question 1. Subtract the following.
(5) \( \frac{9}{13} - \frac{4}{13} \)
Answer: \( \frac{9}{13} - \frac{4}{13} = \frac{9-4}{13} = \frac{5}{13} \)
In simple words: Subtracting 4 from 9, with both fractions having 13 as the denominator, gives 5. So, the answer is 5/13.

🎯 Exam Tip: Maintain the common denominator throughout the subtraction process.

Question 1. Subtract the following.
(6) \( \frac{7}{10} - \frac{3}{10} \)
Answer: \( \frac{7}{10} - \frac{3}{10} = \frac{7-3}{10} = \frac{4}{10} \)
In simple words: Subtract 3 from 7, keeping the denominator 10. This gives 4/10.

🎯 Exam Tip: Remember that fractions like 4/10 can often be simplified (to 2/5), which is good practice for exams.

Question 1. Subtract the following.
(7) \( \frac{9}{12} - \frac{2}{12} \)
Answer: \( \frac{9}{12} - \frac{2}{12} = \frac{9-2}{12} = \frac{7}{12} \)
In simple words: With 12 as the common denominator, subtract 2 from 9, resulting in 7. The fraction is 7/12.

🎯 Exam Tip: Focus on accurate subtraction of the numerators while retaining the common denominator.

Question 1. Subtract the following.
(8) \( \frac{10}{15} - \frac{3}{15} \)
Answer: \( \frac{10}{15} - \frac{3}{15} = \frac{10-3}{15} = \frac{7}{15} \)
In simple words: Subtract 3 from 10, keeping 15 as the denominator, which results in 7/15.

🎯 Exam Tip: Ensure that the final fraction is written clearly and correctly after performing the subtraction.

Question 2. \( \frac{7}{10} \) of a wall is to be painted. Ramu has painted \( \frac{4}{10} \) of it. How much more needs to be painted?
Answer: Solution:
To be painted - painted
\( \frac{7}{10} - \frac{4}{10} = \frac{7-4}{10} = \frac{3}{10} \)
Answer:
\( \frac{3}{10} \) more needs to be painted.
In simple words: To find out how much more needs painting, subtract the portion already painted from the total portion to be painted. Here, 7/10 minus 4/10 leaves 3/10 of the wall still to be painted.

🎯 Exam Tip: For word problems involving fractions, identify the total and the part, then use subtraction for "how much more" or "remaining" questions.

Addition And Subtraction Of Unlike Fractions

Example (1) Add: \( \frac{2}{3} + \frac{1}{6} \)

ℹ️ चित्र व्याख्या (Diagram Explanation): यह चित्र भिन्न योग का प्रदर्शन करता है। पहली पट्टी में, तीन में से दो भाग रंगे हुए हैं, जो \( \frac{2}{3} \) दर्शाते हैं। दूसरी पट्टी को छह समान भागों में विभाजित किया गया है, जिसमें चार भाग रंगे हुए हैं, जो \( \frac{4}{6} \) के बराबर है। तीसरी पट्टी में, छह में से एक भाग रंगा हुआ है, जो \( \frac{1}{6} \) दर्शाता है। चौथी पट्टी में, छह में से पाँच भाग रंगे हुए हैं, जो \( \frac{5}{6} \) के कुल योग को प्रदर्शित करता है।
First let us show the fraction \( \frac{2}{3} \) by coloring two of the three equal parts on a strip.
You have learnt to add and to subtract fractions with common denominators. Here, we have to add the fraction \( \frac{2}{3} \) to the fraction \( \frac{1}{6} \).
So let us divide each part on this strip into two equal parts.
\( \frac{4}{6} \) is a fraction equivalent to \( \frac{2}{3} \). Now, as \( \frac{1}{6} \) is to be added to \( \frac{4}{6} \) i.e. to \( \frac{2}{3} \), we shall colour one more of the six parts on the strip. Now, the total coloured part is \( \frac{5}{6} \).
Therefore, \( \frac{4}{6} + \frac{1}{6} = \frac{4+1}{6} = \frac{5}{6} \)
That is, \( \frac{2}{3} + \frac{1}{6} = \frac{5}{6} \)
In simple words: To add fractions with different denominators, first find equivalent fractions with a common denominator. Here, \( \frac{2}{3} \) is converted to \( \frac{4}{6} \), then added to \( \frac{1}{6} \) by adding the numerators over the common denominator.

🎯 Exam Tip: Always find the least common multiple (LCM) of the denominators to make them common, then adjust the numerators accordingly before adding or subtracting.

Example (2) Add: \( \frac{1}{2} + \frac{2}{5} \)
Here, the smallest common multiple of the two denominators is 10. So, we shall change the denominator of both fractions to 10.
\( \frac{1}{2} + \frac{2}{5} \)
\( = \frac{1 \times 5}{2 \times 5} + \frac{2 \times 2}{5 \times 2} \)
\( = \frac{5}{10} + \frac{4}{10} \)
\( = \frac{5+4}{10} \)
\( = \frac{9}{10} \)
In simple words: To add unlike fractions, find a common denominator, convert both fractions to equivalent forms with that common denominator, and then add their numerators. Here, the common denominator for 2 and 5 is 10, leading to \( \frac{5}{10} + \frac{4}{10} = \frac{9}{10} \).

🎯 Exam Tip: The ability to find the LCM quickly is crucial for efficiently adding or subtracting unlike fractions.

Example (3) Add : \( \frac{3}{8} + \frac{1}{16} \)
Here, 16 is twice 8. So, we shall change the denominator of both fractions to 16.
\( \frac{3}{8} + \frac{1}{16} \)
\( = \frac{3 \times 2}{8 \times 2} + \frac{1}{16} \)
\( = \frac{6}{16} + \frac{1}{16} \)
\( = \frac{6+1}{16} \)
\( = \frac{7}{16} \)
In simple words: When one denominator is a multiple of the other, convert only the fraction with the smaller denominator to match the larger one. Then add the numerators.

🎯 Exam Tip: Recognizing when one denominator is a multiple of another can simplify the process of finding a common denominator, saving time and reducing error.

Example (4) Subtract : \( \frac{3}{4} - \frac{5}{8} \)
Let us make 8 the common denominator of the given fractions.
\( \frac{3}{4} - \frac{5}{8} \)
\( = \frac{3 \times 2}{4 \times 2} - \frac{5}{8} \)
\( = \frac{6}{8} - \frac{5}{8} \)
\( = \frac{6-5}{8} \)
\( = \frac{1}{8} \)
In simple words: To subtract fractions with different denominators, first make the denominators common. Then subtract the numerators and keep the common denominator. Here, \( \frac{3}{4} \) becomes \( \frac{6}{8} \), so \( \frac{6}{8} - \frac{5}{8} = \frac{1}{8} \).

🎯 Exam Tip: Always convert to equivalent fractions with a common denominator *before* performing subtraction.

Example (5) Subtract: \( \frac{4}{5} - \frac{2}{3} \)
The smallest common multiple of the denominators is 15. So, we shall change the denominator of both fractions to 15.
\( \frac{4}{5} - \frac{2}{3} \)
\( = \frac{4 \times 3}{5 \times 3} - \frac{2 \times 5}{3 \times 5} \)
\( = \frac{12}{15} - \frac{10}{15} \)
\( = \frac{12-10}{15} \)
\( = \frac{2}{15} \)
In simple words: When denominators are different, find their least common multiple (LCM) and convert both fractions to equivalent forms using this LCM as the new denominator. Then, subtract the numerators.

🎯 Exam Tip: Miscalculating the equivalent numerators after finding a common denominator is a common mistake; double-check these calculations.

Addition And Subtraction Problem Set 13 Additional Important Questions And Answers

Question. (1) \( \frac{9}{14} - \frac{3}{14} \)
Answer: \( \frac{9}{14} - \frac{3}{14} = \frac{9-3}{14} = \frac{6}{14} \)
In simple words: Subtract the numerators directly since the denominators are the same. Here, 9 minus 3 is 6, giving 6/14.

🎯 Exam Tip: Always ensure the denominators are common before subtracting. Remember to simplify fractions if possible.

Question. (2) \( \frac{5}{6} - \frac{3}{6} \)
Answer: \( \frac{5}{6} - \frac{3}{6} = \frac{5-3}{6} = \frac{2}{6} \)
In simple words: Subtracting 3 from 5 while keeping the denominator 6 gives 2/6.

🎯 Exam Tip: Simplifying 2/6 to 1/3 demonstrates a deeper understanding of fractions and is often required in exams.

Question. (3) \( \frac{9}{16} - \frac{5}{16} \)
Answer: \( \frac{9}{16} - \frac{5}{16} = \frac{9-5}{16} = \frac{4}{16} \)
In simple words: When the denominators are identical, subtract the numerators. In this case, 9 minus 5 is 4, so the result is 4/16.

🎯 Exam Tip: Simplifying the fraction 4/16 to 1/4 would be the complete answer in many exam scenarios.

Question. (4) \( \frac{7}{8} - \frac{3}{8} - \frac{1}{8} \)
Answer: \( \frac{7}{8} - \frac{3}{8} - \frac{1}{8} = \frac{7-3-1}{8} = \frac{3}{8} \)
In simple words: For multiple subtractions with the same denominator, subtract all numerators in sequence and keep the common denominator. Here, 7 minus 3 minus 1 equals 3, resulting in 3/8.

🎯 Exam Tip: When performing multiple operations on fractions with common denominators, combine all numerators into a single operation over the shared denominator.

Question. (5) \( \frac{7}{9} \) part of the work done by Neha and Supriya together. \( \frac{5}{9} \) part of this work was done by Neha. How much work done by Supriya?
Answer: Solution:
Total work done - work done by Neha = work done by Supriya
\( \frac{7}{9} - \frac{5}{9} = \frac{7-5}{9} = \frac{2}{9} \)
Answer:
\( \frac{2}{9} \) work done by Supriya
In simple words: To find Supriya's work, subtract Neha's work from the total work they did together. Since they share a common denominator (9), simply subtract the numerators (7-5=2), resulting in 2/9.

🎯 Exam Tip: Carefully read word problems to identify the "total" and "parts" to correctly set up the fraction operations. Ensure to provide the answer with appropriate units or context.

Question. (6) Mr. Sharma is \( \frac{14}{9} \) m tall. Mrs. Sharma is \( \frac{4}{9} \) shorter than him. What is Mrs. Sharma's height?
Answer: Solution:
Mrs. Sharma's height
\( \frac{14}{9} - \frac{4}{9} = \frac{14-4}{9} = \frac{10}{9} \)
Answer:
Mrs. Sharma's height = \( \frac{10}{9} \)
In simple words: To find Mrs. Sharma's height, subtract the height difference from Mr. Sharma's height. Since the denominators are the same, subtract the numerators (14 minus 4 equals 10), giving 10/9 meters.

🎯 Exam Tip: In real-world problems involving measurements, always include the units (e.g., meters, cm) in your final answer for clarity and completeness.