Answers: Introduction to numerical fractions
These are the answers to Questions: Introduction to numerical fractions.
Please attempt the questions before reading these answers!
Q1
1.1. \(\displaystyle \quad \dfrac{2}{5}\)
1.2. \(\displaystyle \quad \dfrac{7}{8}\)
1.3. \(\displaystyle \quad \dfrac{3}{4}\)
1.4. \(\displaystyle \quad \dfrac{1}{6}\)
1.5. \(\displaystyle \quad 1\dfrac{1}{4} \textsf{ or } \dfrac{5}{4}\)
1.6. \(\displaystyle \quad \dfrac{6}{10} \textsf{ or } \dfrac{3}{5}\)
1.7. \(\displaystyle \quad 1\dfrac{1}{3} \textsf{ or } \dfrac{4}{3}\)
1.8. \(\displaystyle \quad \dfrac{9}{16}\)
1.9. \(\displaystyle \quad 2\dfrac{3}{4} \textsf{ or } \dfrac{11}{4}\)
1.10. \(\displaystyle \quad \dfrac{11}{20}\)
Q2
2.1. \(\displaystyle \quad \dfrac{3}{2}\)
2.2. \(\displaystyle \quad -\dfrac{8}{3}\)
2.3. \(\displaystyle \quad \dfrac{13}{4}\)
2.4. \(\displaystyle \quad -\dfrac{27}{5}\)
2.5. \(\displaystyle \quad \dfrac{31}{7}\)
2.6. \(\displaystyle \quad \dfrac{37}{6}\)
2.7. \(\displaystyle \quad -\dfrac{43}{5}\)
2.8. \(\displaystyle \quad \dfrac{92}{9}\)
2.9. \(\displaystyle \quad -\dfrac{82}{11}\)
2.10. \(\displaystyle \quad \dfrac{51}{4}\)
Q3
3.1. \(\displaystyle \quad 2\dfrac{1}{2}\)
3.2. \(\displaystyle \quad -1\dfrac{3}{4}\)
3.3. \(\displaystyle \quad 3\dfrac{1}{3}\)
3.4. \(\displaystyle \quad -1\dfrac{4}{7}\)
3.5. \(\displaystyle \quad 2\)
3.6. \(\displaystyle \quad -4\dfrac{1}{6}\)
3.7. \(\displaystyle \quad 3\dfrac{4}{9}\)
3.8. \(\displaystyle \quad 4\dfrac{6}{11}\)
3.9. \(\displaystyle \quad -8\)
3.10. \(\displaystyle \quad -7\dfrac{9}{13}\)
Q4
4.1. \(\displaystyle \quad 3\)
4.2. \(\displaystyle \quad 9\)
4.3. \(\displaystyle \quad 15\)
4.4. \(\displaystyle \quad 10\)
4.5. \(\displaystyle \quad -15\)
4.6. \(\displaystyle \quad -4\)
4.7. \(\displaystyle \quad 32\)
4.8. \(\displaystyle \quad 24\)
4.9. \(\displaystyle \quad -9\)
4.10. \(\displaystyle \quad 100\)
4.11. \(\displaystyle \quad -24\)
4.12. \(\displaystyle \quad 55\)
4.13. \(\displaystyle \quad -9\)
4.14. \(\displaystyle \quad 36\)
4.15. \(\displaystyle \quad 42\)
Q5
5.1. \(\displaystyle \quad \dfrac{1}{2}\)
5.2. \(\displaystyle \quad \dfrac{1}{3}\)
5.3. \(\displaystyle \quad \dfrac{3}{5}\)
5.4. \(\displaystyle \quad \dfrac{3}{4}\)
5.5. \(\displaystyle \quad \dfrac{3}{5}\)
5.6. \(\displaystyle \quad \dfrac{1}{3}\)
5.7. \(\displaystyle \quad \dfrac{2}{3}\)
5.8. \(\displaystyle \quad \dfrac{5}{7}\)
5.9. \(\displaystyle \quad \dfrac{2}{3}\)
5.10. \(\displaystyle \quad \dfrac{5}{6}\)
Q6
6.1. \(\displaystyle \quad \dfrac{6}{4} = 1\dfrac{2}{4} = 1\dfrac{1}{2}\)
6.2. \(\displaystyle \quad 2\dfrac{2}{8} = \dfrac{18}{8} = \dfrac{9}{4}\)
6.3. \(\displaystyle \quad \dfrac{12}{10} = 1\dfrac{2}{10} = 1\dfrac{1}{5}\)
6.4. \(\displaystyle \quad -\dfrac{15}{9} = -1\dfrac{6}{9} = -1\dfrac{2}{3}\)
6.5. \(\displaystyle \quad 3\dfrac{4}{6} = \dfrac{22}{6} = \dfrac{11}{3}\)
6.6. \(\displaystyle \quad -1\dfrac{6}{8} = -\dfrac{14}{8} = -\dfrac{7}{4}\)
6.7. \(\displaystyle \quad \dfrac{20}{12} = 1\dfrac{8}{12} = 1\dfrac{2}{3}\)
6.8. \(\displaystyle \quad \dfrac{30}{25} = 1\dfrac{5}{25} = 1\dfrac{1}{5}\)
6.9. \(\displaystyle \quad 5\dfrac{10}{15} = \dfrac{85}{15} = \dfrac{17}{3}\)
6.10. \(\displaystyle \quad -\dfrac{45}{20} = -2\dfrac{5}{20} = -2\dfrac{1}{4}\)
6.11. \(\displaystyle \quad 4\dfrac{8}{10} = \dfrac{48}{10} = \dfrac{24}{5}\)
6.12. \(\displaystyle \quad \dfrac{50}{30} = 1\dfrac{20}{30} = 1\dfrac{2}{3}\)
6.13. \(\displaystyle \quad \dfrac{75}{-50} = -\dfrac{75}{50} = -1\dfrac{25}{50} = -1\dfrac{1}{2}\)
6.14. \(\displaystyle \quad 6\dfrac{12}{16} = \dfrac{108}{16} = \dfrac{27}{4}\)
6.15. \(\displaystyle \quad -2\dfrac{14}{21} = -\dfrac{56}{21} = -\dfrac{8}{3}\)
Version history and licensing
v1.0: initial version created 12/25 by Donald Campbell as part of a University of St Andrews VIP project.