CBSE Class 7 Mathematics Fractions and Decimals Assignment Set 09

VII - Mathematics Assignment No-02 - Fractions and Decimals

Q1. Add \(\frac{5}{7} + \frac{7}{14} + \frac{5}{21}\)
Answer: Find the LCM of the denominators \(7\), \(14\), and \(21\).
LCM of \(7\), \(14\), and \(21\) = \(42\)
Convert each fraction to an equivalent fraction with denominator \(42\):
\(\frac{5}{7} = \frac{5 \times 6}{7 \times 6} = \frac{30}{42}\)
\(\frac{7}{14} = \frac{7 \times 3}{14 \times 3} = \frac{21}{42}\)
\(\frac{5}{21} = \frac{5 \times 2}{21 \times 2} = \frac{10}{42}\)
Add the numerators:
\(\frac{30 + 21 + 10}{42} = \frac{61}{42} = 1 \frac{19}{42}\)
In simple words: Find a common denominator to add fractions together.

Exam Tip: Always reduce fractions to their simplest form or convert improper fractions to mixed fractions if required.

Q2. Add \(4 \frac{2}{3} + 5 \frac{1}{4} + 7 \frac{5}{6}\)
Answer: Convert mixed fractions into improper fractions first:
\(4 \frac{2}{3} = \frac{14}{3}\)
\(5 \frac{1}{4} = \frac{21}{4}\)
\(7 \frac{5}{6} = \frac{47}{6}\)
Find the LCM of the denominators \(3\), \(4\), and \(6\), which is \(12\).
Convert each fraction:
\(\frac{14}{3} = \frac{14 \times 4}{3 \times 4} = \frac{56}{12}\)
\(\frac{21}{4} = \frac{21 \times 3}{4 \times 3} = \frac{63}{12}\)
\(\frac{47}{6} = \frac{47 \times 2}{6 \times 2} = \frac{94}{12}\)
Add the converted numerators:
\(\frac{56 + 63 + 94}{12} = \frac{213}{12} = \frac{71}{4} = 17 \frac{3}{4}\)
In simple words: Convert mixed numbers to improper fractions before finding a common denominator to add.

Exam Tip: You can also add whole numbers and fractions separately, but converting to improper fractions reduces calculation errors.

Q3. Subtract \(\frac{7}{24}\) from \(\frac{1}{2}\)
Answer: Set up the subtraction expression:
\(\frac{1}{2} - \frac{7}{24}\)
Find the LCM of \(2\) and \(24\), which is \(24\).
Convert \(\frac{1}{2}\) to a denominator of \(24\):
\(\frac{1}{2} = \frac{1 \times 12}{2 \times 12} = \frac{12}{24}\)
Subtract the fractions:
\(\frac{12}{24} - \frac{7}{24} = \frac{12 - 7}{24} = \frac{5}{24}\)
In simple words: 'Subtract A from B' means calculate B - A.

Exam Tip: Pay close attention to the order of numbers in subtraction statements containing the word 'from'.

Q4. Subtract \(\frac{1}{4}\) from the sum of \(\frac{5}{12}\) and \(\frac{1}{6}\)
Answer: First, find the sum of \(\frac{5}{12}\) and \(\frac{1}{6}\):
LCM of \(12\) and \(6\) is \(12\).
\(\frac{1}{6} = \frac{1 \times 2}{6 \times 2} = \frac{2}{12}\)
Sum = \(\frac{5}{12} + \frac{2}{12} = \frac{7}{12}\)
Now, subtract \(\frac{1}{4}\) from this sum:
\(\frac{7}{12} - \frac{1}{4}\)
Convert \(\frac{1}{4}\) to have a denominator of \(12\):
\(\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}\)
Perform the subtraction:
\(\frac{7}{12} - \frac{3}{12} = \frac{4}{12} = \frac{1}{3}\)
In simple words: Add the first two numbers together, then subtract the last number from that total result.

Exam Tip: Break multi-step word problems into sequential arithmetic expressions to avoid mistakes.

Q5. Simplify \(\frac{3}{5} - \frac{7}{10} - \frac{3}{15} + \frac{7}{9}\)
Answer: First, simplify the individual fraction \(\frac{3}{15}\) to \(\frac{1}{5}\):
\(\frac{3}{5} - \frac{7}{10} - \frac{1}{5} + \frac{7}{9}\)
Group the denominators with common factors or find the LCM of \(5\), \(10\), and \(9\).
LCM of \(5\), \(10\), and \(9\) is \(90\).
Convert each fraction to have a denominator of \(90\):
\(\frac{3}{5} = \frac{3 \times 18}{5 \times 18} = \frac{54}{90}\)
\(-\frac{7}{10} = -\frac{7 \times 9}{10 \times 9} = -\frac{63}{90}\)
\(-\frac{1}{5} = -\frac{1 \times 18}{5 \times 18} = -\frac{18}{90}\)
\(\frac{7}{9} = \frac{7 \times 10}{9 \times 10} = \frac{70}{90}\)
Combine all the numerators over the common denominator \(90\):
\(\frac{54 - 63 - 18 + 70}{90} = \frac{43}{90}\)
In simple words: Reduce fractions where possible, find a common denominator, and combine numerators carefully respecting signs.

Exam Tip: Always simplify fractions before finding the LCM to keep numbers smaller and easier to manage.

Q6. Subtract the sum of \(\frac{7}{12}\) and \(\frac{3}{4}\) from the sum of \(\frac{9}{12}\) and \(\frac{7}{10}\)
Answer: Calculate the first sum (Sum 1):
\(\frac{7}{12} + \frac{3}{4}\)
LCM of \(12\) and \(4\) is \(12\).
\(\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}\)
Sum 1 = \(\frac{7}{12} + \frac{9}{12} = \frac{16}{12} = \frac{4}{3}\)
Calculate the second sum (Sum 2):
\(\frac{9}{12} + \frac{7}{10}\)
Note that \(\frac{9}{12} = \frac{3}{4}\).
LCM of \(4\) and \(10\) is \(20\).
\(\frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20}\)
\(\frac{7}{10} = \frac{7 \times 2}{10 \times 2} = \frac{14}{20}\)
Sum 2 = \(\frac{15}{20} + \frac{14}{20} = \frac{29}{20}\)
Now, subtract Sum 1 from Sum 2:
\(\frac{29}{20} - \frac{4}{3}\)
LCM of \(20\) and \(3\) is \(60\).
\(\frac{29}{20} = \frac{29 \times 3}{20 \times 3} = \frac{87}{60}\)
\(\frac{4}{3} = \frac{4 \times 20}{3 \times 20} = \frac{80}{60}\)
Subtract the fractions:
\(\frac{87}{60} - \frac{80}{60} = \frac{7}{60}\)
In simple words: Find both sums independently, then subtract the first sum value from the second sum value.

Exam Tip: Simplifying fractions at intermediate steps keeps numbers manageable.

Q7. Simplify \(26 - 18 \frac{1}{3} - 5 \frac{1}{4} + 7\)
Answer: Group the whole numbers and fractional parts together:
\((26 + 7) - 18 \frac{1}{3} - 5 \frac{1}{4}\)
\(= 33 - 18 \frac{1}{3} - 5 \frac{1}{4}\)
Convert mixed fractions to improper fractions:
\(18 \frac{1}{3} = \frac{55}{3}\)
\(5 \frac{1}{4} = \frac{21}{4}\)
Express the whole number as a fraction with denominator \(12\) (LCM of \(3\) and \(4\)):
\(33 = \frac{33 \times 12}{12} = \frac{396}{12}\)
Convert the improper fractions to have a denominator of \(12\):
\(\frac{55}{3} = \frac{55 \times 4}{3 \times 4} = \frac{220}{12}\)
\(\frac{21}{4} = \frac{21 \times 3}{4 \times 3} = \frac{63}{12}\)
Combine all terms over the common denominator:
\(\frac{396 - 220 - 63}{12} = \frac{396 - 283}{12} = \frac{113}{12} = 9 \frac{5}{12}\)
In simple words: Combine whole numbers first, then convert everything into fractions with a common denominator to subtract.

Exam Tip: Converting mixed numbers entirely to improper fractions is often less prone to sign errors when multiple subtractions are involved.

Q8. Add \(7 \frac{1}{4} + 2 \frac{1}{3} + 5 \frac{1}{4} + 3 \frac{1}{5}\)
Answer: Group the whole numbers and the fractional parts:
Whole numbers part = \(7 + 2 + 5 + 3 = 17\)
Fractional parts = \(\frac{1}{4} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5}\)
Combine like fractions first:
\(\frac{1}{4} + \frac{1}{4} = \frac{2}{4} = \frac{1}{2}\)
Now add the remaining fractions:
\(\frac{1}{2} + \frac{1}{3} + \frac{1}{5}\)
Find the LCM of \(2\), \(3\), and \(5\), which is \(30\).
Convert each fraction:
\(\frac{1}{2} = \frac{15}{30}\)
\(\frac{1}{3} = \frac{10}{30}\)
\(\frac{1}{5} = \frac{6}{30}\)
Sum of fractions = \(\frac{15 + 10 + 6}{30} = \frac{31}{30} = 1 \frac{1}{30}\)
Add this result to the whole numbers sum:
\(17 + 1 \frac{1}{30} = 18 \frac{1}{30}\)
In simple words: Add whole numbers and fractions separately, then combine the final whole number and mixed fraction.

Exam Tip: Look for identical denominators (like \(\frac{1}{4}\) and \(\frac{1}{4}\)) to simplify your work before finding a common LCM.