Exercise: 2-C
Q1: \(1\frac{2}{3}+\frac{5}{6}\ of\ \frac{24}{25}\)
Step 1: Convert the mixed number to an improper fraction:
\(1\frac{2}{3} = \frac{5}{3}\)
Step 2: Calculate \( \frac{5}{6} \ of \ \frac{24}{25} \):
\(\frac{5}{6} \times \frac{24}{25} = \frac{120}{150} = \frac{4}{5}\)
Step 3: Add \( \frac{5}{3} \) and \( \frac{4}{5} \):
To add, find a common denominator (LCM of 3 and 5 is 15):
\(\frac{5}{3} = \frac{25}{15}, \quad \frac{4}{5} = \frac{12}{15}\)
Add the fractions:
\(\frac{25}{15} + \frac{12}{15} = \frac{37}{15}\)
Step 4: Convert the improper fraction back to a mixed number:
\(\frac{37}{15} = 2\frac{7}{15}\)
Answer: \( 2\frac{7}{15} \)
Q2: \(\frac{1}{3}\ of\ 4\frac{2}{3}\div2\frac{1}{3}\times1\frac{1}{2}\)
Step 1: Convert the mixed numbers to improper fractions:
\(4\frac{2}{3} = \frac{14}{3}, \quad 2\frac{1}{3} = \frac{7}{3}, \quad 1\frac{1}{2} = \frac{3}{2}\)
Step 2: Calculate \( \frac{1}{3} \ of \ 4\frac{2}{3} \):
\(\frac{1}{3} \times \frac{14}{3} = \frac{14}{9}\)
Step 3: Perform the division:
\(\frac{14}{9} \div \frac{7}{3} = \frac{14}{9} \times \frac{3}{7} = \frac{42}{63} = \frac{2}{3}\)
Step 4: Multiply by \( 1\frac{1}{2} \):
\(\frac{2}{3} \times \frac{3}{2} = 1\)
Answer: \( 1 \)
Q3: \(2\frac{1}{4}+1\frac{1}{6}-1\frac{2}{3}\div2\frac{2}{3}\ of\ 3\frac{3}{4}\)
Step 1: Convert mixed numbers to improper fractions
\(\frac{9}{4} + \frac{7}{6} – \frac{5}{3} \div \left(\frac{8}{3} \times \frac{15}{4}\right)\)
Step 2: Calculate \( 2\frac{2}{3} \ of \ 3\frac{3}{4} \):
\(\frac{8}{3} \times \frac{15}{4} = \frac{120}{12} = 10\)
Step 3: Now divide \(1\frac{2}{3}\) by 10
\(\frac{5}{3} \div 10 = \frac{5}{3} \times \frac{1}{10} = \frac{5}{30} = \frac{1}{6}\)
Step 4: Addition and subtraction
\(\frac{9}{4} + \frac{7}{6} – \frac{1}{6} = 3\frac{1}{4}\)
Answer: \(3\frac{1}{4}\)
Q4: \(1\frac{1}{2}\times2\frac{3}{4}\div1\frac{4}{7}\ of\ 2\frac{5}{8}\)
Step 1: Convert mixed numbers to improper fractions
\(\frac{3}{2} \times \frac{11}{4} \div \left(\frac{11}{7} \times \frac{21}{8}\right)\)
Step 2: Step 2: Calculate \( 1\frac{4}{7} \ of \ 2\frac{5}{8} \):
\(\frac{11}{7} \times \frac{21}{8} = \frac{231}{56} = \frac{4}{7}\)
Step 3: Now divide \(2\frac{3}{4}\) by the result from Step 2
\(\frac{11}{4} \div \frac{4}{7} = \frac{11}{4} \times \frac{7}{4} = \frac{77}{16}\)
Step 4: Multiply by \(1\frac{1}{2}\)
\(\frac{3}{2} \times \frac{4}{7} = \frac{6}{7}\)
Answer: \( \frac{6}{7}\)
Q5: \(\left(2\frac{3}{4}+1\frac{5}{6}\right)\div2\frac{1}{5}\ of\ 3\frac{1}{3}\)
Step 1: Convert mixed numbers to improper fractions
\(\frac{11}{4} + \frac{11}{6} \div \left(\frac{11}{5} \times \frac{10}{3}\right)\)
Step 2: First add \(2\frac{3}{4}\) and \(1\frac{5}{6}\)
\(\frac{11}{4} + \frac{11}{6} = \frac{33}{12} + \frac{22}{12} = \frac{55}{12}\)
Step 3: Step 3: Calculate \( 2\frac{1}{5} \ of \ 3\frac{1}{3} \):
\(\frac{11}{5} \times \frac{10}{3} = \frac{110}{15} = \frac{22}{3}\)
Step 4: Now divide \(\frac{55}{12}\) by \(\frac{22}{3}\)
\(\frac{55}{12} \div \frac{22}{3} = \frac{55}{12} \times \frac{3}{22} = \frac{5}{8}\)
Answer: \( \frac{5}{8} \)
Q6: \(\frac{7}{15}\ of\ \left(\frac{2}{3}+\frac{7}{12}\right)\div\left(\frac{5}{6}-\frac{3}{5}\right)\)
Step 1: Add inside the brackets
\(\frac{2}{3} + \frac{7}{12} = \frac{8}{12} + \frac{7}{12} = \frac{15}{12} = \frac{5}{4}\)
Step 2: Step 2: Calculate \( \frac{7}{15} \ of \ \frac{5}{4} \):
\(\frac{7}{15} \times \frac{5}{4} = \frac{35}{60} = \frac{7}{12}\)
Step 3: Subtract inside the second bracket
\(\frac{5}{6} – \frac{3}{5} = \frac{25}{30} – \frac{18}{30} = \frac{7}{30}\)
Step 4: Now divide \(\frac{7}{12}\) by \(\frac{7}{30}\)
\(\frac{7}{12} \div \frac{7}{30} = \frac{7}{12} \times \frac{30}{7} = \frac{5}{2}\)
Answer: \( \frac{5}{2} \)
Q7: \(\left(22\div5\frac{1}{2}\right)\div2\frac{1}{5}\ of\ 3\frac{1}{3}+1\frac{5}{11}\)
Step 1: Convert mixed numbers to improper fractions
\(22 \div \frac{11}{2} \div \left(\frac{11}{5} \times \frac{10}{3}\right) + \frac{16}{11}\)
Step 2:Solve Bracket
\(22 \div \frac{11}{2} = 22 \times \frac{2}{11} = \frac{44}{11} = 4\)
Step 3: Step 3: Calculate \( 2\frac{1}{5} \ of \ 3\frac{1}{3} \):
\(\frac{11}{5} \times \frac{10}{3} = \frac{110}{15} = \frac{22}{3}\)
Step 4: Now divide 4 by \(\frac{22}{3}\)
\(4 \div \frac{22}{3} = 4 \times \frac{3}{22} = \frac{12}{22} = \frac{6}{11}\)
Step 5: Add \(1\frac{5}{11}\)
\(\frac{6}{11} + \frac{16}{11} = \frac{22}{11} = 2\)
Answer: \( 2 \)
Q8: \(6\frac{1}{3}\div\left(2\frac{1}{5}+3\frac{1}{2}\right)\ of\ 3\frac{1}{3}\)
Step 1: Convert mixed numbers to improper fractions
\(6\frac{1}{3} = \frac{19}{3}, 2\frac{1}{5} = \frac{11}{5}, 3\frac{1}{2} = \frac{7}{2}, 3\frac{1}{3} = \frac{10}{3}\)
Step 2: Add \(2\frac{1}{5} + 3\frac{1}{2}\)
\(\frac{11}{5} + \frac{7}{2} = \frac{22}{10} + \frac{35}{10} = \frac{57}{10}\)
Step 3: Step 3: Calculate \( \frac{57}{10} \ of \ 3\frac{1}{3} \):
\(\frac{57}{10} \times \frac{10}{3} = \frac{570}{30} = \frac{19}{1}\)
Step 4: Now divide \(\frac{19}{3}\) by 19
\(\frac{19}{3} \div 19 = \frac{19}{3} \times \frac{1}{19} = \frac{1}{3}\)
Answer: \( \frac{1}{3} \)
