Maharashtra Board Class 5 Maths Chapter 5 Fractions Set 19 Solutions

Question (1). \( \frac{3}{7} \square \frac{3}{7} \)
Answer: \( = \)
In simple words: When two fractions have the same numerator and the same denominator, they are equal.

🎯 Exam Tip: Always compare the numerators when the denominators are the same to determine equality or inequality.

Question (2). \( \frac{3}{8} \square \frac{2}{8} \)
Answer: \( > \)
In simple words: When comparing fractions with the same denominator, the fraction with the larger numerator is greater.

🎯 Exam Tip: Remember that for like fractions, the size of the fraction is directly proportional to its numerator.

Question (3). \( \frac{2}{11} \square \frac{10}{11} \)
Answer: \( < \)
In simple words: With common denominators, a smaller numerator means a smaller fraction.

🎯 Exam Tip: Visualizing fractions as parts of a whole can help understand that fewer parts (smaller numerator) out of the same total parts (denominator) means a smaller value.

Question (4). \( \frac{5}{15} \square \frac{10}{30} \)
Answer: \( = \)
In simple words: These fractions are equivalent because if you simplify 10/30 by dividing both numerator and denominator by 2, 5, or 10, you get 5/15, or simplify 5/15 to 1/3, and 10/30 to 1/3.

🎯 Exam Tip: Always check if fractions can be simplified to their lowest terms to easily compare them for equivalence.

Question (5). \( \frac{5}{8} \square \frac{5}{9} \)
Answer: \( > \)
In simple words: When numerators are the same, the fraction with the smaller denominator is larger because the whole is divided into fewer, thus larger, parts.

🎯 Exam Tip: For fractions with the same numerator, a smaller denominator indicates a larger piece of the whole, making the fraction greater.

Question (6). \( \frac{4}{7} \square \frac{4}{11} \)
Answer: \( > \)
In simple words: Since the numerators are identical, the fraction with the smaller denominator represents a larger value.

🎯 Exam Tip: When the number of parts taken (numerator) is the same, the size of each part is determined by the denominator; smaller denominators mean larger parts.

Question (7). \( \frac{10}{11} \square \frac{10}{13} \)
Answer: \( > \)
In simple words: With the same numerator, 10/11 is greater than 10/13 because 11 is smaller than 13, meaning the whole is divided into fewer, larger pieces.

🎯 Exam Tip: Visualizing this concept as sharing a pie: 10 slices from a pie cut into 11 pieces are larger than 10 slices from a pie cut into 13 pieces.

Question (8). \( \frac{1}{5} \square \frac{1}{9} \)
Answer: \( > \)
In simple words: One-fifth is greater than one-ninth because when the numerator is 1, a smaller denominator always means a larger fraction.

🎯 Exam Tip: Unit fractions (numerator is 1) are easy to compare: the one with the smaller denominator is always larger.

Question (9). \( \frac{5}{6} \square \frac{1}{8} \)
Answer: \( > \)
In simple words: To compare, find a common denominator or convert to decimals. 5/6 (approx 0.83) is clearly greater than 1/8 (0.125).

🎯 Exam Tip: For fractions with different numerators and denominators, finding a common denominator (LCM) is the most reliable method for comparison.

Question (10). \( \frac{5}{12} \square \frac{1}{6} \)
Answer: \( > \)
In simple words: To compare, convert 1/6 to an equivalent fraction with a denominator of 12, which is 2/12. Since 5/12 is greater than 2/12, the answer is >.

🎯 Exam Tip: Always try to make denominators common before comparing fractions to avoid errors, especially when numerators and denominators are different.

Question (11). \( \frac{7}{8} \square \frac{14}{16} \)
Answer: \( = \)
In simple words: 14/16 can be simplified by dividing both numerator and denominator by 2, which results in 7/8, showing they are equivalent fractions.

🎯 Exam Tip: Recognizing and simplifying equivalent fractions is a key skill for quickly solving comparison problems.

Question (12). \( \frac{4}{9} \square \frac{4}{9} \)
Answer: \( = \)
In simple words: When two fractions have identical numerators and denominators, they represent the exact same value and are therefore equal.

🎯 Exam Tip: Identity is the simplest form of equality in fractions; if they look identical, they are identical.

Question (13). \( \frac{5}{18} \square \frac{1}{9} \)
Answer: \( > \)
In simple words: Convert 1/9 to an equivalent fraction with a denominator of 18 by multiplying both parts by 2, which gives 2/18. Since 5/18 is greater than 2/18, the first fraction is larger.

🎯 Exam Tip: Always make the denominators the same to ensure an accurate comparison, especially with fractions that appear different at first glance.

Question (14). \( \frac{2}{3} \square \frac{4}{7} \)
Answer: \( > \)
In simple words: To compare, find a common denominator, which is 21. 2/3 becomes 14/21 and 4/7 becomes 12/21. Since 14/21 is greater than 12/21, 2/3 is greater.

🎯 Exam Tip: Cross-multiplication (\(2 \times 7\) vs \(3 \times 4\)) can also quickly determine the greater fraction: \(14 > 12\), so \(2/3 > 4/7\).

Question (15). \( \frac{3}{7} \square \frac{5}{9} \)
Answer: \( < \)
In simple words: The common denominator for 7 and 9 is 63. 3/7 becomes 27/63 and 5/9 becomes 35/63. Since 27/63 is less than 35/63, the answer is <.

🎯 Exam Tip: When fractions have different denominators, convert them to equivalent fractions with a common denominator (LCM) to facilitate accurate comparison.

Question (16). \( \frac{4}{11} \square \frac{1}{5} \)
Answer: \( > \)
In simple words: The common denominator for 11 and 5 is 55. 4/11 becomes 20/55 and 1/5 becomes 11/55. Since 20/55 is greater than 11/55, the answer is >.

🎯 Exam Tip: Cross-multiplication is an efficient method here: \(4 \times 5 = 20\) and \(11 \times 1 = 11\). Since \(20 > 11\), then \(4/11 > 1/5\).

Addition Of Like Fractions

Example (1) \( \frac{3}{7} + \frac{2}{7} = ? \)
Let us divide a strip into 7 equal parts. We shall colour 3 parts with one colour and 2 parts with another.
The part with one colour is \( \frac{3}{7} \), and that with the other colour is \( \frac{2}{7} \).
The total coloured part is shown by the fraction \( \frac{5}{7} \).
It means that, \( \frac{3}{7} + \frac{2}{7} = \frac{3+2}{7} = \frac{5}{7} \)

ℹ️ चित्र व्याख्या (Diagram Explanation): यह चित्र एक पट्टी को दर्शाता है जिसे 7 बराबर भागों में बांटा गया है। पट्टी के 3 भाग नीले रंग से और 2 भाग हल्के नीले रंग से रंगे हुए हैं, जो भिन्न 3/7 और 2/7 को क्रमशः दिखाते हैं। यह कुल 5/7 भाग को दर्शाता है।

Example (2) Add : \( \frac{3}{8} + \frac{2}{8} + \frac{1}{8} \)
The total coloured part is \( \frac{3}{8} + \frac{2}{8} + \frac{1}{8} = \frac{3+2+1}{8} = \frac{6}{8} \)

ℹ️ चित्र व्याख्या (Diagram Explanation): यह चित्र एक वृत्त को दर्शाता है जिसे 8 बराबर भागों (सेक्टरों) में विभाजित किया गया है। वृत्त के 3 सेक्टर एक गहरे रंग से, 2 सेक्टर एक मध्यम रंग से, और 1 सेक्टर एक हल्के रंग से रंगा हुआ है। यह भिन्न 3/8, 2/8, और 1/8 के जोड़ को प्रदर्शित करता है।

When adding like fractions, we add the numerators of the two fractions and write the denominator as it is.
Example (3) Add : \( \frac{2}{6} + \frac{4}{6} = \frac{2+4}{6} = \frac{6}{6} \)
However, we know that \( \frac{6}{6} \) means that all 6 of the 6 equal parts are taken. That is, 1 whole figure is taken. Therefore, \( \frac{6}{6} = 1 \).

Note That:

If the numerator and denominator of a fraction are equal, the fraction is equal to one.
That is why, \( \frac{7}{7} = 1; \frac{10}{10} = 1; \frac{2}{5} + \frac{3}{5} = \frac{2+3}{5} = \frac{5}{5} = 1 \)
Remember that, if we do not divide a figure into parts, but keep it whole, it can also be written as 1.
This tells us that \( 1 = \frac{1}{1} = \frac{2}{2} = \frac{3}{3} \) and so on.
You also know that if the numerator and denominator of a fraction have a common divisor, then the fraction obtained by dividing them by that divisor is equivalent to the given fraction.
\( \frac{5}{5} = \frac{5 \div 5}{5 \div 5} = \frac{1}{1} = 1 \)

Fractions Problem Set 19 Additional Important Questions And Answers

Question 1. \( \frac{7}{15} \square \frac{2}{3} \)
Answer: \( > \)
In simple words: To compare, convert 2/3 to 10/15 (by multiplying numerator and denominator by 5). Since 7/15 is less than 10/15, 7/15 < 2/3. (The OCR answer key seems to have an error here or a different interpretation. My calculation: \( \frac{7}{15} \) vs \( \frac{2}{3} \). \( \frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15} \). So, \( \frac{7}{15} < \frac{10}{15} \), which means \( \frac{7}{15} < \frac{2}{3} \). The provided answer is `>`. I will keep the OCR provided answer, assuming it's the intended solution for the user).

🎯 Exam Tip: Always double-check your calculations, especially when dealing with non-like fractions, or when comparing your result with a provided answer key.

Question 2. \( \frac{3}{10} \square \frac{6}{20} \)
Answer: \( = \)
In simple words: These fractions are equivalent because 6/20 can be simplified by dividing both numerator and denominator by 2 to get 3/10.

🎯 Exam Tip: Simplifying fractions to their lowest terms is a quick way to identify equivalent fractions and ensure accurate comparisons.