4MA0 Foundation January 2018 Paper 2 Q14
14
(a) Write these fractions in order of size.
Start with the smallest fraction.
\[\dfrac{5}{12} \qquad \dfrac{7}{8} \qquad \dfrac{3}{4} \qquad \dfrac{1}{2} \qquad \dfrac{9}{24}\] (2)
Start with the smallest fraction.
\[\dfrac{5}{12} \qquad \dfrac{7}{8} \qquad \dfrac{3}{4} \qquad \dfrac{1}{2} \qquad \dfrac{9}{24}\] (2)
(b) Show that \(\dfrac{2}{7} \div \dfrac{4}{5} = \dfrac{5}{14}\) (2)
(c) Show that \(3\dfrac{1}{6} - 1\dfrac{2}{3} = 1\dfrac{1}{2}\) (3)
| Scheme | Marks |
|---|---|
eg. \(\dfrac{10}{24},\ \dfrac{21}{24},\ \dfrac{18}{24},\ \dfrac{12}{24},\ \dfrac{9}{24}\) or 0.416…, 0.875, 0.75, 0.5, 0.375 | M1 |
| \(\dfrac{9}{24},\ \dfrac{5}{12},\ \dfrac{1}{2},\ \dfrac{3}{4},\ \dfrac{7}{8}\) | A1 |
| (2) |
Notes
M1: correct conversion of at least 3 fractions into the same form (common denominators or decimals) or at least 4 fractions in correct order in answer
| Scheme | Marks |
|---|---|
| \(\dfrac{2}{7} \times \dfrac{5}{4}\) | M1 |
\(\dfrac{2}{7} \times \dfrac{5}{4} = \dfrac{10}{28} = \dfrac{5}{14}\) or show cancelling giving \(\dfrac{1}{7} \times \dfrac{5}{2} = \dfrac{5}{14}\) Answer: \(\dfrac{5}{14}\) | A1 |
| (2) |
Notes
A1: answer from correct working with \(\dfrac{10}{28}\) oe seen
or \(\dfrac{5}{14}\) from correct cancelling
Alternative method
| Scheme | Marks |
|---|---|
\(\dfrac{10}{35} \div \dfrac{28}{35}\) oe or \(\dfrac{2}{4} = 0.5\;\; \dfrac{7}{5} = 1.4\) | M1 |
\(\dfrac{10}{28} = \dfrac{5}{14}\) oe or \(\dfrac{0.5}{1.4} = \dfrac{5}{14}\) Answer: \(\dfrac{5}{14}\) | A1 |
Notes
A1: answer from correct working with \(\dfrac{10}{28}\) oe seen or from use of decimals with \(\dfrac{0.5}{1.4}\) seen.
| Scheme | Marks |
|---|---|
eg \(\dfrac{19}{6} - \dfrac{5}{3}\) eg \(\dfrac{19}{6} - \dfrac{10}{6}\) or \((2)\dfrac{1}{6} - \dfrac{4}{6}\) \(2 - \dfrac{3}{6}\) or \(3\dfrac{1}{6} - 1\dfrac{4}{6}\) \(2 - \dfrac{3}{6}\) or \(\dfrac{7}{6} - \dfrac{4}{6}\) \(1\dfrac{7}{6} - \dfrac{4}{6}\) | M1 |
| M1 | |
eg \(\dfrac{9}{6} = 1\dfrac{3}{6} = 1\dfrac{1}{2}\) or \(1\dfrac{3}{6} = 1\dfrac{1}{2}\) or \(1\dfrac{3}{6} = 1\dfrac{1}{2}\) or \(1\dfrac{3}{6} = 1\dfrac{1}{2}\) Answer: \(1\dfrac{1}{2}\) | A1 |
| (3) |
Notes
M1: common denominator used for subtraction or improper fractions
M1: Method which would lead to \(\dfrac{9}{6}\) oe or \(1\dfrac{3}{6}\) oe
dep on first M1
A1: answer from correct working with all steps seen