Instructions:
Solve each problem. Show your work and simplify answers to lowest terms.
Part 1: Addition/Subtraction (Unlike Denominators)
1. \( \frac{2}{3} + \frac{1}{4} = \)
LCM of 3 and 4 = 12
\( \frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12} \)
\( \frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12} \)
\( \frac{8}{12} + \frac{3}{12} = \frac{11}{12} \)
2. \( 1\frac{1}{2} - \frac{3}{5} = \)
\( 1\frac{1}{2} = \frac{3}{2} \)
LCM of 2 and 5 = 10
\( \frac{3}{2} = \frac{3 \times 5}{2 \times 5} = \frac{15}{10} \)
\( \frac{3}{5} = \frac{3 \times 2}{5 \times 2} = \frac{6}{10} \)
\( \frac{15}{10} - \frac{6}{10} = \frac{9}{10} \)
3. \( \frac{5}{6} + 2\frac{2}{3} = \)
\( 2\frac{2}{3} = \frac{8}{3} \)
LCM of 6 and 3 = 6
\( \frac{5}{6} = \frac{5}{6} \)
\( \frac{8}{3} = \frac{8 \times 2}{3 \times 2} = \frac{16}{6} \)
\( \frac{5}{6} + \frac{16}{6} = \frac{21}{6} = \frac{7}{2} = 3\frac{1}{2} \)
4. \( 3\frac{1}{4} - 1\frac{1}{3} = \)
\( 3\frac{1}{4} = \frac{13}{4} \), \( 1\frac{1}{3} = \frac{4}{3} \)
LCM of 4 and 3 = 12
\( \frac{13}{4} = \frac{13 \times 3}{4 \times 3} = \frac{39}{12} \)
\( \frac{4}{3} = \frac{4 \times 4}{3 \times 4} = \frac{16}{12} \)
\( \frac{39}{12} - \frac{16}{12} = \frac{23}{12} = 1\frac{11}{12} \)
5. \( \frac{7}{8} - \frac{1}{6} + \frac{1}{3} = \)
LCM of 8, 6, 3 = 24
\( \frac{7}{8} = \frac{7 \times 3}{8 \times 3} = \frac{21}{24} \)
\( \frac{1}{6} = \frac{1 \times 4}{6 \times 4} = \frac{4}{24} \)
\( \frac{1}{3} = \frac{1 \times 8}{3 \times 8} = \frac{8}{24} \)
\( \frac{21}{24} - \frac{4}{24} + \frac{8}{24} = \frac{25}{24} = 1\frac{1}{24} \)
Part 2: Multiplication
6. \( \frac{2}{5} \times \frac{3}{4} = \)
\( \frac{2}{5} \times \frac{3}{4} = \frac{2 \times 3}{5 \times 4} = \frac{6}{20} = \frac{3}{10} \)
7. \( 1\frac{1}{3} \times \frac{2}{7} = \)
\( 1\frac{1}{3} = \frac{4}{3} \)
\( \frac{4}{3} \times \frac{2}{7} = \frac{4 \times 2}{3 \times 7} = \frac{8}{21} \)
8. \( 2\frac{1}{2} \times 1\frac{3}{5} = \)
\( 2\frac{1}{2} = \frac{5}{2} \), \( 1\frac{3}{5} = \frac{8}{5} \)
\( \frac{5}{2} \times \frac{8}{5} = \frac{5 \times 8}{2 \times 5} = \frac{40}{10} = 4 \)
9. \( \frac{5}{6} \times 3 = \)
\( \frac{5}{6} \times \frac{3}{1} = \frac{5 \times 3}{6 \times 1} = \frac{15}{6} = \frac{5}{2} = 2\frac{1}{2} \)
10. \( \frac{3}{8} \times \frac{4}{9} \times \frac{6}{7} = \)
\( \frac{3}{8} \times \frac{4}{9} \times \frac{6}{7} = \frac{3 \times 4 \times 6}{8 \times 9 \times 7} = \frac{72}{504} \)
Simplify: \( \frac{72 ÷ 72}{504 ÷ 72} = \frac{1}{7} \)
Answer Key
1. \( \frac{11}{12} \)
2. \( \frac{9}{10} \)
3. \( 3\frac{1}{2} \)
4. \( 1\frac{11}{12} \)
5. \( 1\frac{1}{24} \)
6. \( \frac{3}{10} \)
7. \( \frac{8}{21} \)
8. \( 4 \)
9. \( 2\frac{1}{2} \)
10. \( \frac{1}{7} \)
Tip: Always convert mixed numbers to improper fractions before calculating! 🧮✨
