Maharashtra Board Class 5 Maths Chapter 5 Fractions Set 18 Solutions

Question 1. (1) \( \frac{3}{4}, \frac{5}{8} \)
Answer: Solution:
8 is the multiple of 4 So, make 8, the common denominator \( \frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8} \).Thus \( \frac{6}{8} \) and \( \frac{5}{8} \) are the required like fractions.
In simple words: To convert these fractions into like fractions, we find a common denominator, which is 8 because 8 is a multiple of 4. Then, we adjust the numerator of the first fraction accordingly.

🎯 Exam Tip: Always find the least common multiple (LCM) of the denominators to simplify calculations and ensure the most reduced like fractions.

Question 2. (2) \( \frac{3}{5}, \frac{3}{7} \)
Answer: Solution:
The number 35 is a multiple of both 5 and 7 So, making 35 as the common denominater \( \frac{3}{5} = \frac{3 \times 7}{5 \times 7} = \frac{21}{35} \), \( \frac{3}{7} = \frac{3 \times 5}{7 \times 5} = \frac{15}{35} \). Therefore, \( \frac{21}{35} \) and \( \frac{15}{35} \) are required like fractions.
In simple words: For fractions with different denominators, find their least common multiple (LCM). Here, 35 is the LCM of 5 and 7, so both fractions are converted to have 35 as the denominator.

🎯 Exam Tip: When denominators are prime numbers or have no common factors, their product serves as the least common multiple (LCM) for conversion.

Question 3. (3) \( \frac{4}{5}, \frac{3}{10} \)
Answer: Solution:
Here 10 is the multiples of 5. So make 10 as the common denominator \( \frac{4}{5} = \frac{4 \times 2}{5 \times 2} = \frac{8}{10} \). Thus \( \frac{8}{10} \) and \( \frac{3}{10} \) are required like fractions.
In simple words: Since 10 is a multiple of 5, we use 10 as the common denominator. We only need to adjust the first fraction to have this denominator.

🎯 Exam Tip: If one denominator is a multiple of the other, use the larger denominator as the common denominator for easier conversion.

Question 4. (4) \( \frac{2}{9}, \frac{1}{6} \)
Answer: Solution:
Least common multiple of 9 and 6 is 18. So, make, 18 as the common denominator. \( \frac{2}{9} = \frac{2 \times 2}{9 \times 2} = \frac{4}{18} \), \( \frac{1}{6} = \frac{1 \times 3}{6 \times 3} = \frac{3}{18} \). Thus, \( \frac{4}{18} \) and \( \frac{3}{18} \) are the required like fractions.
In simple words: Find the LCM of 9 and 6, which is 18. Then, convert both fractions by multiplying their numerators and denominators to get 18 as the common denominator.

🎯 Exam Tip: The LCM method is crucial for converting fractions with non-multiple denominators, ensuring the smallest common denominator and simplest equivalent fractions.

Question 5. (5) \( \frac{1}{4}, \frac{2}{3} \)
Answer: Solution:
Least common multiple of 4 and 3 is 12 So, make 12 as common denominator \( \frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12} \), \( \frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12} \). SO, \( \frac{3}{12}, \frac{8}{12} \) are required like fractions.
In simple words: The smallest number divisible by both 4 and 3 is 12. Convert each fraction to have 12 as the denominator by multiplying the numerator and denominator by the appropriate number.

🎯 Exam Tip: When denominators are coprime (share no common factors other than 1), their product is always their LCM.

Question 6. (6) \( \frac{5}{6}, \frac{4}{5} \)
Answer: Solution:
Least common multiple of 6 and 5 is 30 So, make 30 as common denominator \( \frac{5}{6} = \frac{5 \times 5}{6 \times 5} = \frac{25}{30} \), \( \frac{4}{5} = \frac{4 \times 6}{5 \times 6} = \frac{24}{30} \). So, \( \frac{25}{30}, \frac{24}{30} \) are required like fractions.
In simple words: Since 6 and 5 are coprime, their LCM is their product, 30. Adjust both fractions to have 30 as the denominator.

🎯 Exam Tip: Ensure that when converting to a common denominator, you multiply both the numerator and denominator by the same factor to maintain the fraction's value.

Question 7. (7) \( \frac{3}{8}, \frac{1}{6} \)
Answer: Solution:
Least common multiple of 8 and 6 is 24 So, make 24 as common denominator \( \frac{3}{8} = \frac{3 \times 3}{8 \times 3} = \frac{9}{24} \), \( \frac{1}{6} = \frac{1 \times 4}{6 \times 4} = \frac{4}{24} \). So, \( \frac{9}{24}, \frac{4}{24} \) are required like fractions.
In simple words: The LCM of 8 and 6 is 24. We convert both fractions to equivalent fractions with 24 as their new denominator.

🎯 Exam Tip: Practice finding the LCM efficiently to quickly determine the common denominator for various fraction pairs.

Question 8. (8) \( \frac{1}{6}, \frac{4}{9} \)
Answer: Solution:
Least common multiple of 6 and 9 is 18 So, make 18 as common denominator \( \frac{1}{6} = \frac{1 \times 3}{6 \times 3} = \frac{3}{18} \), \( \frac{4}{9} = \frac{4 \times 2}{9 \times 2} = \frac{8}{18} \). So, \( \frac{3}{18} \) and \( \frac{8}{18} \) are the required like fractions.
In simple words: Identify the LCM of 6 and 9, which is 18. Then, transform each fraction so that they both share 18 as their denominator.

🎯 Exam Tip: Remember that the common denominator doesn't have to be the product of the original denominators; the LCM is generally preferred for simplicity.

Comparing Like Fractions

Example (1) A strip was divided into 5 equal parts. It means that each part is 1/5. The coloured part is \( \frac{3}{5} = \frac{1}{5} + \frac{1}{5} + \frac{1}{5} \).

ℹ️ चित्र व्याख्या (Diagram Explanation): यह चित्र एक पट्टी को 5 बराबर भागों में विभाजित करके दिखाता है, जिसमें से 3 भाग नीले रंग से रंगे हुए हैं, जो भिन्न 3/5 को दर्शाता है।

The white part is \( \frac{2}{5} = \frac{1}{5} + \frac{1}{5} \). The coloured part is bigger than the white part. This tells us that 3/5 is greater than 2/5. This is written as 3/5 > 2/5.

Example (2) This strip is divided into 8 equal parts. 3 of the parts have one colour and 4 have another colour. Here, 3/8 < 8/4.

ℹ️ चित्र व्याख्या (Diagram Explanation): यह चित्र एक पट्टी को 8 बराबर भागों में विभाजित करके दिखाता है। इसमें 3 भाग एक रंग (नीला) से और 4 भाग दूसरे रंग (धूसर) से रंगे हुए हैं, जो भिन्नों 3/8 और 4/8 को दर्शाते हैं।

In like fractions, the fraction with the greater numerator is the greater fraction.

Comparing Fractions With Equal Numerators

You have learnt that the value of fractions with numerator 1 decreases as the denominator increases.

Even if the numerator is not 1, the same rule applies so long as all the fractions have a common numerator. For example, look at the figures below. All the strips in the figure are alike.
2 of the 3 equal parts of the strip \( \frac{2}{3} \)

ℹ️ चित्र व्याख्या (Diagram Explanation): यह चित्र तीन पट्टियों को दर्शाता है, सभी समान लंबाई की हैं। पहली पट्टी 3 भागों में विभाजित है जिसमें से 2 रंगे हैं (2/3)। दूसरी पट्टी 4 भागों में विभाजित है जिसमें से 2 रंगे हैं (2/4)। तीसरी पट्टी 5 भागों में विभाजित है जिसमें से 2 रंगे हैं (2/5)। यह समान अंश वाले भिन्नों की तुलना को स्पष्ट करता है।
2 of the 4 equal parts of the strip \( \frac{2}{4} \)

2 of the 5 equal parts of the strip \( \frac{2}{5} \)
The figure shows that 2/3 > 2/4 > 5/2.

Of two fractions with equal numerators, the fraction with the greater denominator is the smaller fraction.

Comparing Unlike Fractions

Teacher: Suppose we have to compare the unlike fractions 3/5 and 4/7. Let us take an example to see how this is done. These two boys are standing on two blocks. How do we decide who is taller?

Sonu : But the height of the blocks is not the same. If both blocks are of the same height, it is easy to tell who is taller.

Nandu : Now that they are on blocks of equal height, we see that the boy on the right is taller.

Teacher: The height of the boys can be compared when they stand at the same height. Similarly, if fractions have the same denominators, their numerators decide which fraction is bigger.

Nandu: Got it! Let's obtain the same denominators for both fractions.

Sonu : 5 x 7 can be divided by both 5 and 7. So, 35 can be the common denominator.
\( \frac{3}{5} = \frac{3 \times 7}{5 \times 7} = \frac{21}{35} \)
\( \frac{4}{7} = \frac{4 \times 5}{7 \times 5} = \frac{20}{35} \)
\( \frac{21}{35} > \frac{20}{35} \)
Therefore, \( \frac{3}{5} > \frac{4}{7} \)

To compare unlike fractions, we convert them into their equivalent fractions so that their denominators are the same.

Fractions Problem Set 18 Additional Important Questions and Answers

Question 1. \( \frac{5}{9}, \frac{17}{36} \)
Answer: Solution:
36 is the multiple of 9 So, make 36 the common denominator \( \frac{5}{9} = \frac{5 \times 4}{9 \times 4} = \frac{20}{36} \).
Thus \( \frac{20}{36} \) and \( \frac{17}{36} \) are the required like fractions.
In simple words: To compare these, we convert them to like fractions by using 36 as the common denominator since it's a multiple of 9.

🎯 Exam Tip: This question tests your ability to identify common multiples and convert fractions correctly, which is fundamental for comparing them.

Question 2. \( \frac{5}{6}, \frac{7}{9} \)
Answer: Solution:
Least common multiple of 6 and 9 is 18 So, make 18 as the common denominator \( \frac{5}{6} = \frac{5 \times 3}{6 \times 3} = \frac{15}{18} \), \( \frac{7}{9} = \frac{7 \times 2}{9 \times 2} = \frac{14}{18} \).
So, \( \frac{15}{18} \) and \( \frac{14}{18} \) are the required like fractions.
In simple words: The smallest common multiple for 6 and 9 is 18. Both fractions are then converted to equivalent fractions with 18 as the denominator.

🎯 Exam Tip: Always look for the LCM of denominators to make conversions efficient and avoid unnecessarily large numbers.

Question 3. \( \frac{7}{11}, \frac{3}{5} \)
Answer: Solution:
Least common multiple of 11 and 5 is 55 So, make 55 as the common denominator.
\( \frac{7}{11} = \frac{7 \times 5}{11 \times 5} = \frac{35}{55} \), \( \frac{3}{5} = \frac{3 \times 11}{5 \times 11} = \frac{33}{55} \). Thus \( \frac{35}{55} \) and \( \frac{33}{55} \) are required like fractions.
In simple words: Since 11 and 5 are prime, their LCM is 55. Convert both fractions by multiplying to achieve 55 as the common denominator.

🎯 Exam Tip: When dealing with prime denominators, their product is the simplest common denominator to use for conversion.