Foundation June 2019 Paper 1 Q9
9
(a) Write these fractions in order of size.
Start with the smallest fraction.
\(\dfrac{7}{10} \qquad \dfrac{4}{5} \qquad \dfrac{1}{2} \qquad \dfrac{29}{40}\) (2)
Start with the smallest fraction.
\(\dfrac{7}{10} \qquad \dfrac{4}{5} \qquad \dfrac{1}{2} \qquad \dfrac{29}{40}\) (2)
(b) Show that \(\quad \dfrac{8}{15} + \dfrac{3}{10} = \dfrac{5}{6}\) (2)
(c) Show that \(\quad 4\dfrac{2}{3} \div 1\dfrac{1}{9} = 4\dfrac{1}{5}\) (3)
| Scheme | Marks |
|---|---|
eg 0.7, 0.8, 0.5, 0.725 eg \(\dfrac{28}{40}, \dfrac{32}{40}, \dfrac{20}{40}, \dfrac{29}{40}\) | M1 |
| \(\dfrac{1}{2}, \dfrac{7}{10}, \dfrac{29}{40}, \dfrac{4}{5}\) | A1 |
| (2) |
Notes
M1: for converting all four fractions to a common form e.g. common denominators or decimals or 3 fractions in the correct order or correct reverse order
A1: Any correct form
| Scheme | Marks | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
eg \(\dfrac{16}{30} + \dfrac{9}{30}\) or
| M1 | |||||||||
eg \(\dfrac{16}{30} + \dfrac{9}{30} = \dfrac{25}{30} = \dfrac{5}{6}\) Answer: shown | A1 | |||||||||
| (2) |
Notes
M1: for \(\dfrac{16}{30}\) and \(\dfrac{9}{30}\) or
both fractions expressed as equivalent fractions with denominators that are a common multiple of 10 and 15 eg. \(\dfrac{80}{150}\) and \(\dfrac{45}{150}\)
A1: conclusion to given answer coming from correct working which shows all steps
| Scheme | Marks |
|---|---|
| e.g. \(\dfrac{14}{3}\) and \(\dfrac{10}{9}\) | M1 |
| e.g. \(\dfrac{14}{3} \times \dfrac{9}{10}\) | M1 |
e.g. \(\dfrac{14}{3} \times \dfrac{9}{10} = \dfrac{126}{30} = \dfrac{21}{5} = 4\dfrac{1}{5}\) or \(\dfrac{14}{3} \times \dfrac{9}{10} = \dfrac{126}{30} = 4\dfrac{6}{30} = 4\dfrac{1}{5}\) or \(\dfrac{\cancel{14}^{\,7}}{\cancel{3}^{\,1}} \times \dfrac{\cancel{9}^{\,3}}{\cancel{10}^{\,5}} = \dfrac{21}{5} = 4\dfrac{1}{5}\) or \(\dfrac{126}{27}, \;\dfrac{30}{27} = \dfrac{126}{30} = \dfrac{21}{5} = 4\dfrac{1}{5}\) Answer: Shown | A1 |
| (3) | |
| (7 marks) |
Notes
M1: Both fractions expressed as improper fractions
M1: or for both fractions expressed as equivalent fractions with denominators that are a common multiple of 3 and 9 eg. \(\dfrac{42}{9} \div \dfrac{10}{9}\) or \(\dfrac{126}{27}, \dfrac{30}{27}\)
A1: Dep on M2 for conclusion to \(4\dfrac{1}{5}\) from correct working – either sight of the result of the multiplication e.g. \(\dfrac{126}{30}\) must be seen or correct cancelling prior to the multiplication to \(\dfrac{21}{5}\)
NB: use of decimals scores no marks