CBSE Class 7 Mathematics Fractions Assignment Set 08

Find the Sum of the following fractions

Question (a). \(\frac{7}{10} + \frac{2}{15}\)
Answer: Find the least common multiple (LCM) of the denominators 10 and 15, which is 30.
Convert each fraction to an equivalent fraction with a denominator of 30:
\(\frac{7}{10} = \frac{7 \times 3}{10 \times 3} = \frac{21}{30}\)
\(\frac{2}{15} = \frac{2 \times 2}{15 \times 2} = \frac{4}{30}\)
Add the numerators while keeping the common denominator:
\(\frac{21}{30} + \frac{4}{30} = \frac{21 + 4}{30} = \frac{25}{30}\)
Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, 5:
\(\frac{25 \div 5}{30 \div 5} = \frac{5}{6}\)
In simple words: Make the bottom numbers the same, add the top numbers, and simplify your answer.

Exam Tip: Always find the LCM of denominators rather than just multiplying them to keep numbers small and manageable.

Question (b). \(\frac{5}{7} + \frac{2}{7}\)
Answer: Since the denominators are already the same, combine the numerators directly over the common denominator:
\(\frac{5 + 2}{7} = \frac{7}{7}\)
Simplify the fraction:
\(\frac{7}{7} = 1\)
In simple words: When the bottom numbers match, just add the top numbers together.

Exam Tip: Check if denominators are identical first before doing any LCM work to save time.

Question (c). \(\frac{9}{11} - \frac{4}{5}\)
Answer: Find the LCM of the denominators 11 and 5, which is 55.
Convert each fraction to an equivalent fraction with a denominator of 55:
\(\frac{9}{11} = \frac{9 \times 5}{11 \times 5} = \frac{45}{55}\)
\(\frac{4}{5} = \frac{4 \times 11}{5 \times 11} = \frac{44}{55}\)
Subtract the numerators:
\(\frac{45}{55} - \frac{44}{55} = \frac{45 - 44}{55} = \frac{1}{55}\)
In simple words: Convert both fractions to have 55 as the denominator, then subtract the top numbers.

Exam Tip: For prime denominators like 11 and 5, their LCM is simply their product (55).

Question (d). \(4 + \frac{7}{8}\)
Answer: Write the whole number 4 as a fraction with denominator 8:
\(4 = \frac{4 \times 8}{8} = \frac{32}{8}\)
Add the fractions:
\(\frac{32}{8} + \frac{7}{8} = \frac{32 + 7}{8} = \frac{39}{8}\)
Convert the improper fraction into a mixed number:
\(\frac{39}{8} = 4\frac{7}{8}\)
In simple words: Combine a whole number and a fraction by turning the whole number into a fraction with the same bottom number.

Exam Tip: Adding a fraction to a whole number simply results in a mixed number where the whole part and fraction part are combined.

Question (e). \(2 - \frac{3}{5}\)
Answer: Convert the whole number 2 into a fraction with a denominator of 5:
\(2 = \frac{2 \times 5}{5} = \frac{10}{5}\)
Subtract the fractions:
\(\frac{10}{5} - \frac{3}{5} = \frac{10 - 3}{5} = \frac{7}{5}\)
In simple words: Change the whole number 2 into \(\frac{10}{5}\) so you can subtract \(\frac{3}{5}\).

Exam Tip: To subtract a fraction from a whole number, borrow 1 from the whole number and write it as a fraction equal to 1 (e.g., \(2 = 1 + \frac{5}{5} = 1\frac{5}{5}\)).

Question (f). \(8\frac{1}{2} - 3\frac{3}{5}\)
Answer: Convert both mixed numbers into improper fractions:
\(8\frac{1}{2} = \frac{8 \times 2 + 1}{2} = \frac{17}{2}\)
\(3\frac{3}{5} = \frac{3 \times 5 + 3}{5} = \frac{18}{5}\)
Find the LCM of 2 and 5, which is 10.
Convert both fractions to have a denominator of 10:
\(\frac{17}{2} = \frac{17 \times 5}{2 \times 5} = \frac{85}{10}\)
\(\frac{18}{5} = \frac{18 \times 2}{5 \times 2} = \frac{36}{10}\)
Subtract the fractions:
\(\frac{85}{10} - \frac{36}{10} = \frac{85 - 36}{10} = \frac{49}{10}\)
Convert back to a mixed number:
\(\frac{49}{10} = 4\frac{9}{10}\)
In simple words: Convert mixed numbers to improper fractions, make the bottom numbers equal, and subtract.

Exam Tip: Converting mixed numbers to improper fractions first reduces errors when borrowing is required during subtraction.

Question (g). \(\frac{11}{15} - \frac{7}{20}\)
Answer: Find the LCM of the denominators 15 and 20. Prime factorizations: \(15 = 3 \times 5\), \(20 = 2^2 \times 5\). LCM = \(2^2 \times 3 \times 5 = 60\).
Convert each fraction to have a denominator of 60:
\(\frac{11}{15} = \frac{11 \times 4}{15 \times 4} = \frac{44}{60}\)
\(\frac{7}{20} = \frac{7 \times 3}{20 \times 3} = \frac{21}{60}\)
Subtract the numerators:
\(\frac{44}{60} - \frac{21}{60} = \frac{44 - 21}{60} = \frac{23}{60}\)
In simple words: Find the common denominator 60, adjust the top numbers, and subtract.

Exam Tip: Use prime factorization to quickly find the LCM when denominators are larger numbers.

Question (h). \(4\frac{2}{3} - 3\frac{1}{4} + 2\frac{1}{6}\)
Answer: Convert all mixed numbers to improper fractions:
\(4\frac{2}{3} = \frac{14}{3}\)
\(3\frac{1}{4} = \frac{13}{4}\)
\(2\frac{1}{6} = \frac{13}{6}\)
Find the LCM of denominators 3, 4, and 6, which is 12.
Convert each fraction to have a denominator of 12:
\(\frac{14}{3} = \frac{14 \times 4}{3 \times 4} = \frac{56}{12}\)
\(\frac{13}{4} = \frac{13 \times 3}{4 \times 3} = \frac{39}{12}\)
\(\frac{13}{6} = \frac{13 \times 2}{6 \times 2} = \frac{26}{12}\)
Perform addition and subtraction from left to right:
\(\frac{56}{12} - \frac{39}{12} + \frac{26}{12} = \frac{56 - 39 + 26}{12} = \frac{17 + 26}{12} = \frac{43}{12}\)
In simple words: Convert to improper fractions, use 12 as the common bottom number, then combine the top numbers.

Exam Tip: Handle multiple additions and subtractions by converting everything into improper fractions first to avoid sign errors.

Question (i). \(4\frac{3}{4} + 9\frac{2}{5}\)
Answer: Convert both mixed numbers to improper fractions:
\(4\frac{3}{4} = \frac{19}{4}\)
\(9\frac{2}{5} = \frac{47}{5}\)
Find the LCM of 4 and 5, which is 20.
Convert each fraction to have a denominator of 20:
\(\frac{19}{4} = \frac{19 \times 5}{4 \times 5} = \frac{95}{20}\)
\(\frac{47}{5} = \frac{47 \times 4}{5 \times 4} = \frac{188}{20}\)
Add the numerators:
\(\frac{95}{20} + \frac{188}{20} = \frac{95 + 188}{20} = \frac{283}{20}\)
In simple words: Change mixed fractions into improper fractions, make the bottom numbers 20, and add the top numbers.

Exam Tip: Alternatively, you can add whole numbers \((4 + 9 = 13)\) and fractions \((\frac{3}{4} + \frac{2}{5})\) separately, then combine them.

Question (j). \(\frac{5}{6} + 3 + 3\frac{3}{4}\)
Answer: Convert all terms into improper fractions:
\(\frac{5}{6} = \frac{5}{6}\)
\(3 = \frac{3}{1}\)
\(3\frac{3}{4} = \frac{15}{4}\)
Find the LCM of denominators 6, 1, and 4, which is 12.
Convert each fraction to have a denominator of 12:
\(\frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12}\)
\(\frac{3}{1} = \frac{3 \times 12}{1 \times 12} = \frac{36}{12}\)
\(\frac{15}{4} = \frac{15 \times 3}{4 \times 3} = \frac{45}{12}\)
Add all the numerators together:
\(\frac{10}{12} + \frac{36}{12} + \frac{45}{12} = \frac{10 + 36 + 45}{12} = \frac{91}{12}\)
In simple words: Turn every term into a fraction, find the common bottom number 12, and add all top numbers together.

Exam Tip: Never leave whole numbers out of the common denominator step; treat them as fractions with a denominator of 1.