Questions: Arithmetic on numerical fractions
Before attempting these questions, it is highly recommended that you read Guide: Arithmetic on numerical fractions. You may also find Calculator: Highest common factor, lowest common multiple useful.
Q1
Calculate the following additions and subtractions by first finding a common denominator. Write your answer in its simplest form.
1.1. \(\displaystyle \quad \dfrac{3}{8} + \dfrac{1}{8}\)
1.2. \(\displaystyle \quad -\dfrac{2}{7} + \dfrac{5}{7}\)
1.3. \(\displaystyle \quad \dfrac{13}{20} - \dfrac{17}{20}\)
1.4. \(\displaystyle \quad \dfrac{1}{3} + \dfrac{1}{6}\)
1.5. \(\displaystyle \quad \dfrac{3}{4} - \dfrac{1}{2}\)
1.6. \(\displaystyle \quad \dfrac{2}{5} + \dfrac{1}{10}\)
1.7. \(\displaystyle \quad \dfrac{5}{6} - \dfrac{1}{3}\)
1.8. \(\displaystyle \quad \dfrac{1}{2} + \dfrac{3}{10}\)
1.9. \(\displaystyle \quad \dfrac{7}{10} + \dfrac{2}{15}\)
1.10. \(\displaystyle \quad \dfrac{3}{8} + \dfrac{5}{10}\)
1.11. \(\displaystyle \quad \dfrac{3}{4} - \dfrac{2}{5}\)
1.12. \(\displaystyle \quad -\dfrac{2}{3} + \dfrac{3}{4}\)
1.13. \(\displaystyle \quad \dfrac{9}{10} - \dfrac{1}{15}\)
1.14. \(\displaystyle \quad -\dfrac{7}{12} - \dfrac{1}{15}\)
1.15. \(\displaystyle \quad \dfrac{11}{14} + 1\)
Q2
Calculate the following multiplications. Write your answer in its simplest form.
2.1. \(\displaystyle \quad \dfrac{1}{4} \cdot \dfrac{1}{3}\)
2.2. \(\displaystyle \quad \dfrac{2}{5} \cdot \dfrac{3}{7}\)
2.3. \(\displaystyle \quad \dfrac{3}{5} \cdot 10\)
2.4. \(\displaystyle \quad \dfrac{5}{8} \cdot \dfrac{4}{15}\)
2.5. \(\displaystyle \quad \dfrac{2}{3} \cdot \dfrac{9}{10}\)
2.6. \(\displaystyle \quad -\dfrac{1}{7} \cdot \dfrac{3}{4}\)
2.7. \(\displaystyle \quad \dfrac{6}{11} \cdot \dfrac{22}{3}\)
2.8. \(\displaystyle \quad 8 \cdot \dfrac{5}{12}\)
2.9. \(\displaystyle \quad -\dfrac{7}{9} \cdot \dfrac{6}{5}\)
2.10. \(\displaystyle \quad \dfrac{4}{5} \cdot \left(-\dfrac{15}{16}\right)\)
2.11. \(\displaystyle \quad \dfrac{12}{13} \cdot \dfrac{1}{6}\)
2.12. \(\displaystyle \quad \left(-\dfrac{9}{10}\right) \cdot \left(-\dfrac{5}{12}\right)\)
Q3
Calculate the following divisions. Write your answer in its simplest form.
3.1. \(\displaystyle \quad \dfrac{1}{3} \div \dfrac{1}{6}\)
3.2. \(\displaystyle \quad \dfrac{2}{5} \div \dfrac{3}{4}\)
3.3. \(\displaystyle \quad \dfrac{3}{8} \div 2\)
3.4. \(\displaystyle \quad \dfrac{4}{9} \div \dfrac{8}{3}\)
3.5. \(\displaystyle \quad 5 \div \dfrac{1}{4}\)
3.6. \(\displaystyle \quad \dfrac{5}{7} \div \dfrac{10}{21}\)
3.7. \(\displaystyle \quad -\dfrac{1}{2} \div \dfrac{3}{5}\)
3.8. \(\displaystyle \quad \dfrac{6}{11} \div 3\)
3.9. \(\displaystyle \quad \dfrac{7}{10} \div \left(-\dfrac{14}{15}\right)\)
3.10. \(\displaystyle \quad -\dfrac{8}{9} \div \dfrac{2}{3}\)
3.11. \(\displaystyle \quad \dfrac{11}{12} \div \dfrac{22}{9}\)
3.12. \(\displaystyle \quad \left(-\dfrac{4}{7}\right) \div (-8)\)
Q4
Calculate the following by first converting the mixed numbers into improper fractions. Write your answer in its simplest form.
4.1. \(\displaystyle \quad 1\dfrac{1}{3} + 2\dfrac{1}{6}\)
4.2. \(\displaystyle \quad 3\dfrac{1}{2} - 1\dfrac{1}{4}\)
4.3. \(\displaystyle \quad 1\dfrac{1}{5} \cdot 2\dfrac{1}{2}\)
4.4. \(\displaystyle \quad 4\dfrac{1}{2} \div 1\dfrac{1}{8}\)
4.5. \(\displaystyle \quad 2\dfrac{3}{4} + 1\dfrac{1}{3}\)
4.6. \(\displaystyle \quad 5\dfrac{1}{8} - 2\dfrac{3}{4}\)
4.7. \(\displaystyle \quad -1\dfrac{2}{5} \cdot \dfrac{3}{7}\)
4.8. \(\displaystyle \quad 3\dfrac{1}{4} \div -1\dfrac{5}{8}\)
4.9. \(\displaystyle \quad -2\dfrac{1}{3} - 1\dfrac{3}{5}\)
4.10. \(\displaystyle \quad 1\dfrac{5}{6} \cdot 2\dfrac{2}{11}\)
4.11. \(\displaystyle \quad -4\dfrac{1}{5} \div -2\dfrac{1}{10}\)
4.12. \(\displaystyle \quad 3\dfrac{1}{9} + 1\dfrac{5}{6}\)
After attempting the questions above, please click this link to find the answers.
Version history and licensing
v1.0: initial version created 12/25 by Donald Campbell as part of a University of St Andrews VIP project.