Maharashtra Board Class 5 Maths Chapter 5 Fractions Set 17 Solutions

Question 1. Write the proper number in the box.
\((1) \frac{1}{2} = \frac{\square}{20}\)
Answer: Here \(20 = 2 \times 10\)
\(\therefore \frac{1}{2} = \frac{1 \times 10}{2 \times 10} = \frac{10}{20}\)
In simple words: To find the equivalent fraction, determine the multiplication factor for the denominator, and then apply the same factor to the numerator to fill the box.

🎯 Exam Tip: When finding equivalent fractions, always multiply or divide both the numerator and denominator by the exact same non-zero number.

\((2) \frac{3}{4} = \frac{15}{\square}\)
Answer: Here \(15 = 3 \times 5\)
\(\therefore \frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20}\)
In simple words: Identify how the given numerator was scaled to get the new numerator, then apply that same scaling (multiplication) to the denominator to complete the fraction.

🎯 Exam Tip: Focus on the relationship between the given numerators (or denominators) to find the scaling factor for the missing part of the equivalent fraction.

\((3) \frac{9}{11} = \frac{18}{\square}\)
Answer: Here \(18 = 9 \times 2\)
hence, \(\frac{4}{20} = \frac{4 \div 4}{20 \div 4} = \frac{1}{5}\)
In simple words: The problem asks to find the missing denominator for \(9/11 = 18/ \square\), which would be \(11 \times 2 = 22\). The provided solution shows an unrelated simplification of \(4/20\).

🎯 Exam Tip: Pay close attention to the specific fraction and its missing part in the question; ensure your calculations directly address that particular equivalence.

\((4) \frac{10}{40} = \frac{\square}{8}\)
Answer: Here \(40 \div 5 = 8\),
hence, \(\frac{4}{6} = \frac{4 \div 2}{6 \div 2} = \frac{2}{3}\)
In simple words: The problem asks for the missing numerator in \(10/40 = \square/8\), which should be \(10 \div 5 = 2\). The provided solution shows an unrelated simplification of \(4/6\).

🎯 Exam Tip: For equivalent fractions, if the denominator is divided by a factor, the numerator must also be divided by the same factor to find the missing value.

\((5) \frac{14}{26} = \frac{\square}{13}\)
Answer: Here \(26 \div 2 = 13\),
hence, \(\frac{14}{26} = \frac{14 \div 2}{26 \div 2} = \frac{7}{13}\)
In simple words: To find the missing numerator, determine by what number the denominator was divided, then divide the original numerator by the same number.

🎯 Exam Tip: Simplification of fractions involves dividing both parts by their greatest common divisor to get an equivalent, simpler form.

\((6) \frac{\square}{3} = \frac{4}{6}\)
Answer: Here \(6 \div 2 = 3\),
hence, \(\frac{10}{40} = \frac{10 \div 5}{40 \div 5} = \frac{2}{8}\)
In simple words: The problem asks to find the missing numerator in \(\square/3 = 4/6\), which should be \(4 \div 2 = 2\). The provided solution shows an unrelated simplification of \(10/40\).

🎯 Exam Tip: Always analyze the given equivalent fraction to deduce the relationship (multiplication or division) needed to find the missing part of the target fraction.

\((7) \frac{1}{\square} = \frac{4}{20}\)
Answer: Here \(4 \div 4 = 1\),
hence, \(\frac{9}{11} = \frac{9 \times 2}{11 \times 2} = \frac{18}{22}\)
In simple words: The problem asks for the missing denominator in \(1/\square = 4/20\), which should be \(20 \div 4 = 5\). The provided solution shows an unrelated equivalent fraction for \(9/11\).

🎯 Exam Tip: When the numerator is simplified, the denominator must be simplified by the exact same factor to maintain the fraction's value.

\((8) \frac{\square}{5} = \frac{10}{25}\)
Answer: Here \(25 \div 5 = 5\),
hence, \(\frac{10}{25} = \frac{10 \div 5}{25 \div 5} = \frac{2}{5}\)
In simple words: To find the missing numerator, determine the division factor applied to the denominator, and then divide the original numerator by that same factor.

🎯 Exam Tip: Always verify that the operation (multiplication or division) used to change one part of the fraction is consistently applied to the other part.

Question 2. Find an equivalent fraction with denominator 18, for each of the following fractions.
\(\frac{1}{2}, \frac{2}{3}, \frac{4}{6}, \frac{2}{9}, \frac{7}{9}, \frac{5}{3}\)
Answer:
Solution:
(1) \(\frac{1}{2} = \frac{1 \times 9}{2 \times 9} = \frac{9}{18}\)
(2) \(\frac{2}{3} = \frac{2 \times 6}{3 \times 6} = \frac{12}{18}\)
(3) \(\frac{4}{6} = \frac{4 \times 3}{6 \times 3} = \frac{12}{18}\)
(4) \(\frac{2}{9} = \frac{2 \times 2}{9 \times 2} = \frac{4}{18}\)
(5) \(\frac{7}{9} = \frac{7 \times 2}{9 \times 2} = \frac{14}{18}\)
(6) \(\frac{5}{3} = \frac{5 \times 6}{3 \times 6} = \frac{30}{18}\)
In simple words: To make the denominator 18, multiply both the numerator and denominator of each fraction by the factor that transforms its original denominator into 18.

🎯 Exam Tip: When converting fractions to a common denominator, ensure all calculations are accurate to avoid errors in the equivalent fractions.

Question 3. Find an equivalent fraction with denominator 5, for each of the following fractions.
\(\frac{6}{15}, \frac{10}{25}, \frac{12}{30}, \frac{6}{10}, \frac{21}{35}\)
Answer:
Solution:
\(\frac{6}{15} = \frac{\square}{5}\)
Here \(15 \div 3 = 5\), hence, \(\frac{6}{15} = \frac{6 \div 3}{15 \div 3} = \frac{2}{5}\)
\(\frac{10}{25} = \frac{\square}{5}\)
Here \(25 \div 5 = 5\), hence, \(\frac{10}{25} = \frac{10 \div 5}{25 \div 5} = \frac{2}{5}\)
\(\frac{12}{30} = \frac{\square}{5}\)
Here \(30 \div 6 = 5\), hence, \(\frac{12}{30} = \frac{12 \div 6}{30 \div 6} = \frac{2}{5}\)
\(\frac{6}{10} = \frac{\square}{5}\)
Here \(10 \div 2 = 5\), hence, \(\frac{6}{10} = \frac{6 \div 2}{10 \div 2} = \frac{3}{5}\)
\(\frac{21}{35} = \frac{\square}{5}\)
Here \(35 \div 7 = 5\), hence, \(\frac{21}{35} = \frac{21 \div 7}{35 \div 7} = \frac{3}{5}\)
In simple words: To convert a fraction to an equivalent fraction with a smaller denominator (like 5), divide both the numerator and denominator by the factor that reduces the original denominator to the target denominator.

🎯 Exam Tip: Division is key when simplifying fractions or reducing them to a common smaller denominator. Ensure you use the correct common divisor.

Question 4. From the fractions given below, pair off the equivalent fractions.
\(\frac{2}{3}, \frac{5}{7}, \frac{5}{11}, \frac{7}{9}, \frac{14}{18}, \frac{15}{33}, \frac{18}{27}, \frac{10}{14}\)
Answer:
Solution:
\(\frac{2}{3} = \frac{18}{27}\) ;
\(\frac{5}{7} = \frac{10}{14}\) ;
\(\frac{5}{11} = \frac{15}{33}\) ;
\(\frac{7}{9} = \frac{14}{18}\)
In simple words: To find equivalent pairs, simplify each fraction to its lowest terms or compare them by cross-multiplication or finding common denominators.

🎯 Exam Tip: Simplifying all fractions to their simplest form first makes pairing equivalent fractions much easier and reduces computational errors.

Question 5. Find two equivalent fractions for each of the following fractions.
\(\frac{7}{9}, \frac{4}{5}, \frac{3}{11}\)
Answer:
Solution:
(1) \(\frac{2}{5} = \frac{12}{\square}\), \(2 \times 6 = 12\). Hence, \(\frac{2}{5} = \frac{2 \times 6}{5 \times 6} = \frac{12}{30}\)
(2) \(\frac{3}{4} = \frac{12}{\square}\), \(3 \times 4 = 12\). Hence, \(\frac{3}{4} = \frac{3 \times 4}{4 \times 4} = \frac{12}{16}\)
(3) \(\frac{4}{7} = \frac{12}{\square}\), \(4 \times 3 = 12\). Hence, \(\frac{4}{7} = \frac{4 \times 3}{7 \times 3} = \frac{12}{21}\)
(4) \(\frac{6}{11} = \frac{12}{\square}\), \(6 \times 2 = 12\). Hence, \(\frac{6}{11} = \frac{6 \times 2}{11 \times 2} = \frac{12}{22}\)
In simple words: Although the question asks for equivalent fractions of \(7/9, 4/5, 3/11\), the provided solution gives examples of finding one equivalent fraction for \(2/5, 3/4, 4/7, 6/11\). These examples demonstrate multiplying both numerator and denominator by the same number to create an equivalent fraction.

🎯 Exam Tip: To find two equivalent fractions, simply multiply both the numerator and the denominator by two different non-zero whole numbers (e.g., multiply by 2, then multiply by 3).

Like Fractions And Unlike Fractions

Fractions such as \(\frac{1}{6}, \frac{2}{6}, \frac{5}{6}\), whose denominators are equal, are called 'like fractions'. Fractions such as \(\frac{1}{3}, \frac{4}{7}, \frac{9}{11}\) which have different denominators are called unlike fractions'.

Converting Unlike Fractions Into Like Fractions

Example (1) Convert \(\frac{5}{6}\) and \(\frac{7}{9}\) into like fractions.
Here, we must find a common multiple for the numbers 6 and 9.
Multiples of 6 : 6, 12, 18, 24, 30, 36, ........
Multiples of 9 : 9, 18, 27, 36, 45 ........
Here, the number 18 is a multiple of both 6 and 9. So, let us make 18 the denominator of both fractions.
\(\frac{5}{6} = \frac{5 \times 3}{6 \times 3} = \frac{15}{18}\)
\(\frac{7}{9} = \frac{7 \times 2}{9 \times 2} = \frac{14}{18}\)
Thus, \(\frac{15}{18}\) and \(\frac{14}{18}\) are like fractions, respectively equivalent to \(\frac{5}{6}\) and \(\frac{7}{9}\). Here, 18 is a multiple of both 6 and 9. We could also choose numbers like 36 and 54 as the common denominators.

Example (2) Convert \(\frac{4}{8}\) and \(\frac{5}{16}\) into like fractions.
As 16 is twice 8, it is easy to make 16 the common denominator.
\(\frac{4}{8} = \frac{4 \times 2}{8 \times 2} = \frac{8}{16}\)
Thus, \(\frac{8}{16}\) and \(\frac{5}{16}\) are the required like fractions.

Example (3) Find a common denominator for \(\frac{4}{7}\) and \(\frac{3}{4}\).
The number 28 is a multiple of both 7 and 4. So, make 28 the common
denominator. \(\frac{4}{7} = \frac{4 \times 4}{7 \times 4} = \frac{16}{28}\), \(\frac{3}{4} = \frac{3 \times 7}{4 \times 7} = \frac{21}{28}\). Therefore, \(\frac{16}{28}\) and \(\frac{21}{28}\) are the required like fractions.

Fractions Problem Set 17 Additional Important Questions And Answers

Question 1. Find two equivalent fractions for each of the following fraction:
\((1) \frac{7}{9} (2) \frac{4}{5} (3) \frac{3}{11} (4) \frac{12}{13} (5) \frac{15}{17}\)
Answer:
Solution:
(1) \(\frac{7}{9} = \frac{7 \times 2}{9 \times 2} = \frac{14}{18}\); \(\frac{7}{9} = \frac{7 \times 4}{9 \times 4} = \frac{28}{36}\)
(2) \(\frac{4}{5} = \frac{4 \times 3}{5 \times 3} = \frac{12}{15}\); \(\frac{4}{5} = \frac{4 \times 5}{5 \times 5} = \frac{20}{25}\)
(3) \(\frac{3}{11} = \frac{3 \times 8}{11 \times 8} = \frac{24}{88}\); \(\frac{3}{11} = \frac{3 \times 3}{11 \times 3} = \frac{9}{33}\)
(4) \(\frac{12}{13} = \frac{12 \times 5}{13 \times 5} = \frac{60}{65}\); \(\frac{12}{13} = \frac{12 \times 7}{13 \times 7} = \frac{84}{91}\)
(5) \(\frac{15}{17} = \frac{15 \times 2}{17 \times 2} = \frac{30}{34}\); \(\frac{15}{17} = \frac{15 \times 5}{17 \times 5} = \frac{75}{85}\)
In simple words: To find equivalent fractions, multiply both the numerator and denominator by the same non-zero whole number. This generates a new fraction that has the same value.

🎯 Exam Tip: Remember that there are infinitely many equivalent fractions for any given fraction; choose simple multipliers like 2, 3, or 5 for easy calculation in exams.