CBSE Class 6 Mathematics Fractions Worksheet Set 06

Question 1. Simplify: (i) \(4\frac{2}{3} - 3\frac{1}{4} + 2\frac{3}{6}\)
Answer: Convert mixed fractions to improper fractions:
\(4\frac{2}{3} = \frac{14}{3}\)
\(3\frac{1}{4} = \frac{13}{4}\)
\(2\frac{3}{6} = \frac{15}{6} = \frac{5}{2}\)
Find the LCM of denominators 3, 4, and 2, which is 12.
Convert each fraction to have the denominator 12:
\(\frac{14}{3} = \frac{14 \times 4}{3 \times 4} = \frac{56}{12}\)
\(\frac{13}{4} = \frac{13 \times 3}{4 \times 3} = \frac{39}{12}\)
\(\frac{5}{2} = \frac{5 \times 6}{2 \times 6} = \frac{30}{12}\)
Combine the terms:
\(\frac{56}{12} - \frac{39}{12} + \frac{30}{12} = \frac{56 - 39 + 30}{12} = \frac{47}{12} = 3\frac{11}{12}\)
In simple words: Convert mixed fractions into improper fractions, make the denominators the same, and then add or subtract the numerators.

Exam Tip: Always simplify fractions to their lowest terms before finding the LCM, and double-check your arithmetic when combining numerators.

Question 1. (ii) \(6 - 2\frac{3}{5}\)
Answer: Convert the whole number 6 into a fraction with denominator 5:
\(6 = \frac{30}{5}\)
Convert the mixed fraction \(2\frac{3}{5}\) into an improper fraction:
\(2\frac{3}{5} = \frac{13}{5}\)
Subtract the two fractions:
\(\frac{30}{5} - \frac{13}{5} = \frac{30 - 13}{5} = \frac{17}{5} = 3\frac{2}{5}\)
In simple words: Write the whole number as a fraction with the same denominator as the mixed fraction, then subtract.

Exam Tip: When subtracting a mixed fraction from a whole number, converting the whole number to a fraction with a common denominator is the quickest method.

Question 2. The teacher taught \(\frac{3}{5}\) of a book. Vivek revised \(\frac{1}{5}\) more on his own. How much does he still have to revise ?
Answer: Fraction of the book taught by the teacher = \(\frac{3}{5}\)
Fraction of the book revised by Vivek on his own = \(\frac{1}{5}\)
Total fraction of the book revised so far = \(\frac{3}{5} + \frac{1}{5} = \frac{3 + 1}{5} = \frac{4}{5}\)
Assuming the entire book represents 1 whole, the fraction of the book still left to revise is:
\(1 - \frac{4}{5} = \frac{5}{5} - \frac{4}{5} = \frac{1}{5}\)
In simple words: Add what was taught and what was revised to find the total completed portion, then subtract that from 1 to find the remaining part.

Exam Tip: Read word problems carefully to identify whether parts should be combined with addition or taken away with subtraction from a whole.

Question 3. Rama, Rati, Rupa and Radha each bought a pizza. Rama had \(\frac{7}{8}\) of her pizza, Rati had \(\frac{6}{7}\) of her pizza, Rupa had \(\frac{5}{6}\) of hers and Radha had \(\frac{4}{5}\) of hers. Who ate the maximum part of their pizzas?
Answer: Fractions eaten by each person:
Rama = \(\frac{7}{8} = 1 - \frac{1}{8}\)
Rati = \(\frac{6}{7} = 1 - \frac{1}{7}\)
Rupa = \(\frac{5}{6} = 1 - \frac{1}{6}\)
Radha = \(\frac{4}{5} = 1 - \frac{1}{5}\)
When comparing fractions that are less than 1 by a unit fraction (numerator 1), the fraction with the largest remaining part (the largest denominator) is actually the smallest, and the fraction with the smallest remaining part (the smallest denominator) is the largest.
Comparing the leftover fractions: \(\frac{1}{8} < \frac{1}{7} < \frac{1}{6} < \frac{1}{5}\)
Therefore, the eaten fractions in ascending order are:
\(\frac{4}{5} < \frac{5}{6} < \frac{6}{7} < \frac{7}{8}\)
Rama ate the maximum part (\(\frac{7}{8}\)).
In simple words: Look at how much of each pizza is missing. The one who left the smallest piece uneaten ate the most pizza.

Exam Tip: For fractions where the numerator is less than the denominator by 1, the fraction with the larger numbers is always greater in value.

Question 4. Fill in the missing number:
(i) \(\frac{8}{10} - \Box = \frac{3}{4}\)
Answer: Let the missing number be \(x\).
\(\frac{8}{10} - x = \frac{3}{4}\)
Simplify \(\frac{8}{10}\) to lowest terms:
\(\frac{8}{10} = \frac{4}{5}\)
Rearranging the equation to solve for \(x\):
\(x = \frac{4}{5} - \frac{3}{4}\)
Find the LCM of 5 and 4, which is 20:
\(x = \frac{4 \times 4}{5 \times 4} - \frac{3 \times 5}{4 \times 5}\)
\(x = \frac{16}{20} - \frac{15}{20} = \frac{1}{20}\)
Missing box value = \(\frac{1}{20}\)
In simple words: Rearrange the equation so the unknown box is by itself, then subtract the fractions using a common denominator.

Exam Tip: Always reduce fractions to their simplest form before performing addition or subtraction to make calculations easier.

Question 4. (ii) \(\frac{\Box}{27} - \frac{5}{27} = \frac{12}{27}\)
Answer: Let the missing number in the box be \(x\).
Since all denominators are equal to 27, we can write the equation using numerators only:
\(\frac{x - 5}{27} = \frac{12}{27}\)
\(x - 5 = 12\)
\(x = 12 + 5\)
\(x = 17\)
Missing box value = 17
In simple words: Since the denominators are already the same, just set up a simple equation with the numerators and solve for the missing number.

Exam Tip: When fractions have identical denominators, you can ignore the denominators and perform operations directly on the numerators.