CBSE Class 7 Mathematics Fractions and Decimals Assignment Set 10

VII - Mathematics Assignment No-01 - Fractions and Decimals

Q1. Reduce \(\frac{20}{25}\) in its lowest term
Answer: Find the Highest Common Factor (HCF) of 20 and 25, which is 5.
Divide both numerator and denominator by 5:
\(\frac{20 \div 5}{25 \div 5} = \frac{4}{5}\)
In simple words: Divide the top and bottom numbers by their common divisor to simplify the fraction.

Exam Tip: Always check if the numerator and denominator have any common factors other than 1 to ensure the fraction is in its simplest form.

Q2. Reduce \(\frac{125}{1000}\) in its lowest term.
Answer: Find the Highest Common Factor (HCF) of 125 and 1000, which is 125.
Divide both numerator and denominator by 125:
\(\frac{125 \div 125}{1000 \div 125} = \frac{1}{8}\)
In simple words: Simplify the fraction by canceling out common factors until no more division is possible.

Exam Tip: Recognizing powers of 5 and 10 can help simplify fractions quickly.

Q3. Which is greater \(\frac{1}{4}\) or \(\frac{1}{8}\)
Answer: To compare fractions with the same numerator, the fraction with the smaller denominator is greater.
Alternatively, convert to a common denominator (8):
\(\frac{1}{4} = \frac{1 \times 2}{4 \times 2} = \frac{2}{8}\)
Comparing \(\frac{2}{8}\) and \(\frac{1}{8}\):
\(\frac{2}{8} > \frac{1}{8}\), so \(\frac{1}{4} > \frac{1}{8}\)
In simple words: When a whole is divided into fewer parts, each part is larger.

Exam Tip: For unit fractions (numerator 1), the smaller the denominator, the larger the overall fraction.

Q4. Which is smaller \(\frac{3}{7}\) or \(\frac{1}{2}\)
Answer: Convert both fractions to a common denominator. The Least Common Multiple (LCM) of 7 and 2 is 14.
\(\frac{3}{7} = \frac{3 \times 2}{7 \times 2} = \frac{6}{14}\)
\(\frac{1}{2} = \frac{1 \times 7}{2 \times 7} = \frac{7}{14}\)
Comparing \(\frac{6}{14}\) and \(\frac{7}{14}\):
\(\frac{6}{14} < \frac{7}{14}\), so \(\frac{3}{7} < \frac{1}{2}\)
In simple words: Make the denominators equal by finding their LCM, then compare the numerators.

Q5. Arrange in ascending order \(\frac{3}{4}, \frac{5}{6}, \frac{7}{8}, \frac{5}{12}\)
Answer: Find the LCM of the denominators (4, 6, 8, 12), which is 24.
Convert each fraction to an equivalent fraction with denominator 24:
\(\frac{3}{4} = \frac{3 \times 6}{4 \times 6} = \frac{18}{24}\)
\(\frac{5}{6} = \frac{5 \times 4}{6 \times 4} = \frac{20}{24}\)
\(\frac{7}{8} = \frac{7 \times 3}{8 \times 3} = \frac{21}{24}\)
\(\frac{5}{12} = \frac{5 \times 2}{12 \times 2} = \frac{10}{24}\)
Compare the numerators (10, 18, 20, 21):
\(\frac{10}{24} < \frac{18}{24} < \frac{20}{24} < \frac{21}{24}\)
Ascending order: \(\frac{5}{12}, \frac{3}{4}, \frac{5}{6}, \frac{7}{8}\)
In simple words: Convert all fractions to have the same bottom number (denominator), then order them from smallest to largest top number.

Exam Tip: Ascending order means arranging numbers from smallest to largest.

Q6. Arrange in descending order \(\frac{3}{8}, \frac{5}{7}, \frac{3}{10}, \frac{2}{5}\)
Answer: Find the LCM of the denominators (8, 7, 10, 5), which is 280.
Convert each fraction to have the denominator 280:
\(\frac{3}{8} = \frac{3 \times 35}{8 \times 35} = \frac{105}{280}\)
\(\frac{5}{7} = \frac{5 \times 40}{7 \times 40} = \frac{200}{280}\)
\(\frac{3}{10} = \frac{3 \times 28}{10 \times 28} = \frac{84}{280}\)
\(\frac{2}{5} = \frac{2 \times 56}{5 \times 56} = \frac{112}{280}\)
Compare the numerators (200, 112, 105, 84):
\(\frac{200}{280} > \frac{112}{280} > \frac{105}{280} > \frac{84}{280}\)
Descending order: \(\frac{5}{7}, \frac{2}{5}, \frac{3}{8}, \frac{3}{10}\)
In simple words: Make denominators equal using LCM and arrange fractions from largest to smallest.

Exam Tip: Descending order means arranging numbers from largest to smallest.

Q7. Convert into improper fractions:
(i) \(34 \frac{3}{4}\)
Answer: Multiply the whole number by the denominator and add the numerator:
\(\frac{(34 \times 4) + 3}{4} = \frac{136 + 3}{4} = \frac{139}{4}\)

(ii) \(275 \frac{1}{5}\)
Answer: Multiply the whole number by the denominator and add the numerator:
\(\frac{(275 \times 5) + 1}{5} = \frac{1375 + 1}{5} = \frac{1376}{5}\)
In simple words: To convert a mixed fraction, do (Whole \times Denominator + Numerator) over the same denominator.

Exam Tip: Keep the denominator exactly the same in the resulting improper fraction.

Q8. Convert into mixed numbers:
(i) \(\frac{375}{7}\)
Answer: Divide 375 by 7:
\(375 \div 7 = 53\) with a remainder of 4.
Mixed number = \(53 \frac{4}{7}\)

(ii) \(\frac{121}{4}\)
Answer: Divide 121 by 4:
\(121 \div 4 = 30\) with a remainder of 1.
Mixed number = \(30 \frac{1}{4}\)
In simple words: Divide the top number by the bottom number. The quotient is the whole number, the remainder is the new top number, and the divisor stays at the bottom.

Exam Tip: Always verify your mixed number by converting it back into an improper fraction.

Q9. Write 3 equivalent fractions of:
(i) \(\frac{3}{7}\)
Answer: Multiply the numerator and denominator by 2, 3, and 4 respectively:
\(\frac{3 \times 2}{7 \times 2} = \frac{6}{14}\)
\(\frac{3 \times 3}{7 \times 3} = \frac{9}{21}\)
\(\frac{3 \times 4}{7 \times 4} = \frac{12}{28}\)
Equivalent fractions: \(\frac{6}{14}, \frac{9}{21}, \frac{12}{28}\)

(ii) \(\frac{5}{8}\)
Answer: Multiply the numerator and denominator by 2, 3, and 4 respectively:
\(\frac{5 \times 2}{8 \times 2} = \frac{10}{16}\)
\(\frac{5 \times 3}{8 \times 3} = \frac{15}{24}\)
\(\frac{5 \times 4}{8 \times 4} = \frac{20}{32}\)
Equivalent fractions: \(\frac{10}{16}, \frac{15}{24}, \frac{20}{32}\)
In simple words: Multiply both the top and bottom numbers by the same counting numbers (2, 3, 4) to find equivalent fractions.

Exam Tip: Equivalent fractions represent the same value even though their numbers look different.

Q10. Fill the gap:
(i) \(\frac{7}{5} = \frac{\square}{10}\)
Answer: The denominator 5 is multiplied by 2 to get 10. Therefore, multiply the numerator by 2:
\(\square = 7 \times 2 = 14\)
Missing value = 14

(ii) \(\frac{32}{49} = \frac{160}{\square}\)
Answer: The numerator 32 is multiplied by 5 to get 160 (\(160 \div 32 = 5\)). Therefore, multiply the denominator by 5:
\(\square = 49 \times 5 = 245\)
Missing value = 245
In simple words: Find what number the given part was multiplied or divided by, and apply the exact same operation to find the missing part.

Exam Tip: Cross-multiplication can also be used to find unknown gaps in proportional fractions.