CBSE Class 7 Mathematics Fractions Assignment Set 09

ASSIGNMENT NO. 1
FRACTIONS

Q1. Reduce the following to the lowest form
(a) \(\dfrac{144}{180}\)
(b) \(\dfrac{192}{224}\)
(c) \(\dfrac{165}{198}\)
(d) \(\dfrac{36}{48}\)
(e) \(\dfrac{616}{728}\)
Answer:
(a) Find the greatest common divisor (GCD) of 144 and 180, which is 36.
Divide numerator and denominator by 36:
\(\dfrac{144 \div 36}{180 \div 36} = \frac{4}{5}\)
(b) Find the GCD of 192 and 224, which is 32.
Divide numerator and denominator by 32:
\(\dfrac{192 \div 32}{224 \div 32} = \frac{6}{7}\)
(c) Find the GCD of 165 and 198, which is 33.
Divide numerator and denominator by 33:
\(\dfrac{165 \div 33}{198 \div 33} = \frac{5}{6}\)
(d) Find the GCD of 36 and 48, which is 12.
Divide numerator and denominator by 12:
\(\dfrac{36 \div 12}{48 \div 12} = \frac{3}{4}\)
(e) Find the GCD of 616 and 728, which is 56.
Divide numerator and denominator by 56:
\(\dfrac{616 \div 56}{728 \div 56} = \frac{11}{13}\)
In simple words: To reduce a fraction to its lowest form, divide both the numerator and the denominator by their highest common factor.

Exam Tip: Always check if the numerator and denominator share any common factors other than 1 to ensure the fraction is fully simplified.

Q2. Arrange the following in ascending order
(a) \(\dfrac{5}{8}, \dfrac{5}{6}, \dfrac{7}{4}\)
(b) \(\dfrac{7}{6}, \dfrac{5}{9}, \dfrac{5}{12}\)
Answer:
(a) To compare fractions, convert them to have a common denominator. The denominators are 8, 6, and 4. The LCM is 24.
\(\dfrac{5}{8} = \dfrac{5 \times 3}{8 \times 3} = \dfrac{15}{24}\)
\(\dfrac{5}{6} = \dfrac{5 \times 4}{6 \times 4} = \dfrac{20}{24}\)
\(\dfrac{7}{4} = \dfrac{7 \times 6}{4 \times 6} = \dfrac{42}{24}\)
Comparing the numerators: \(15 < 20 < 42\)
So, ascending order is: \(\dfrac{5}{8} < \dfrac{5}{6} < \dfrac{7}{4}\)
(b) The denominators are 6, 9, and 12. The LCM is 36.
\(\dfrac{7}{6} = \dfrac{7 \times 6}{6 \times 6} = \dfrac{42}{36}\)
\(\dfrac{5}{9} = \dfrac{5 \times 4}{9 \times 4} = \dfrac{20}{36}\)
\(\dfrac{5}{12} = \dfrac{5 \times 3}{12 \times 3} = \dfrac{15}{36}\)
Comparing the numerators: \(15 < 20 < 42\)
So, ascending order is: \(\dfrac{5}{12} < \dfrac{5}{9} < \dfrac{7}{6}\)
In simple words: Make the denominators the same by finding their LCM, then compare the numerators from smallest to largest.

Exam Tip: Finding the Least Common Multiple (LCM) of the denominators makes comparing and ordering fractions straightforward and accurate.

Q3. Write the Equivalent fraction (any 3)
(a) \(\dfrac{3}{5}\)
(b) \(\dfrac{2}{3}\)
(c) \(\dfrac{6}{11}\)
Answer:
(a) Multiply the numerator and denominator by 2, 3, and 4 respectively:
\(\dfrac{3 \times 2}{5 \times 2} = \dfrac{6}{10}, \quad \dfrac{3 \times 3}{5 \times 3} = \dfrac{9}{15}, \quad \dfrac{3 \times 4}{5 \times 4} = \dfrac{12}{20}\)
(b) Multiply the numerator and denominator by 2, 3, and 4 respectively:
\(\dfrac{2 \times 2}{3 \times 2} = \dfrac{4}{6}, \quad \dfrac{2 \times 3}{3 \times 3} = \dfrac{6}{9}, \quad \dfrac{2 \times 4}{3 \times 4} = \dfrac{8}{12}\)
(c) Multiply the numerator and denominator by 2, 3, and 4 respectively:
\(\dfrac{6 \times 2}{11 \times 2} = \dfrac{12}{22}, \quad \dfrac{6 \times 3}{11 \times 3} = \dfrac{18}{33}, \quad \dfrac{6 \times 4}{11 \times 4} = \dfrac{24}{44}\)
In simple words: Multiply both the top and bottom numbers of a fraction by the same nonzero number to find an equivalent fraction.

Exam Tip: You can generate infinite equivalent fractions by multiplying or dividing both terms by the same integer.

Q4. The Reciprocal of the following fraction is :-
(a) \(9\dfrac{2}{3}\)
(b) \(7\dfrac{1}{4}\)
(c) \(\dfrac{1}{11}\)
(d) \(\dfrac{5}{18}\)
Answer:
(a) First convert mixed fraction to improper fraction: \(9\dfrac{2}{3} = \dfrac{9 \times 3 + 2}{3} = \dfrac{29}{3}\)
Reciprocal of \(\dfrac{29}{3}\) is \(\dfrac{3}{29}\)
(b) Convert mixed fraction to improper fraction: \(7\dfrac{1}{4} = \dfrac{7 \times 4 + 1}{4} = \dfrac{29}{4}\)
Reciprocal of \(\dfrac{29}{4}\) is \(\dfrac{4}{29}\)
(c) Reciprocal of \(\dfrac{1}{11}\) is \(\dfrac{11}{1} = 11\)
(d) Reciprocal of \(\dfrac{5}{18}\) is \(\dfrac{18}{5}\)
In simple words: Flip the fraction upside down to find its reciprocal. For mixed numbers, always convert to an improper fraction first.

Exam Tip: Never forget to convert mixed numbers into improper fractions before attempting to find their reciprocals.