4MA0 Foundation June 2015 Paper 1R Q10
10
(a) Write these fractions in order of size.
Start with the smallest fraction.
Start with the smallest fraction.
\(\dfrac{7}{8}\) \(\dfrac{3}{4}\) \(\dfrac{11}{12}\) \(\dfrac{13}{16}\)
(2)(b) Show that \(\dfrac{2}{5} \div \dfrac{6}{7} = \dfrac{7}{15}\) (2)
(c) Show that \(\dfrac{2}{5} - \dfrac{1}{6} = \dfrac{7}{30}\) (2)
| Scheme | Marks |
|---|---|
| \(\dfrac{3}{4}\;\;\dfrac{13}{16}\;\;\dfrac{7}{8}\;\;\dfrac{11}{12}\) | B2 |
| (2) |
Notes
B2: If not B2 then B1 for:
• 3 fractions in correct order or
• 2 fractions correctly converted to decimals (rounded or truncated) or
• 2 fractions expressed as equivalent fractions with denominator of 48 or
• \(\dfrac{11}{12}\;\;\dfrac{7}{8}\;\;\dfrac{13}{16}\;\;\dfrac{3}{4}\) (ie in reverse order)
| Scheme | Marks |
|---|---|
| \(\dfrac{2}{5} \times \dfrac{7}{6}\) or \(\dfrac{1}{5} \times \dfrac{7}{3}\) | M1 |
| show | A1 |
| (2) |
Notes
M1: or \(\dfrac{14a}{35a} \div \dfrac{30a}{35a}\) (\(a \geqslant 1\); denominators the same and a multiple of 35)
A1: (dep on M1) for a fraction equivalent to \(\dfrac{7}{15}\) coming directly from M1 or \(\dfrac{7}{15}\) from a correctly cancelled fraction division
| Scheme | Marks |
|---|---|
| eg \(\dfrac{2 \times 6}{5 \times 6} - \dfrac{1 \times 5}{6 \times 5}\) | M1 |
| show | A1 |
| (2) | |
| Total 6 marks |
Notes
M1: for both fractions correct with a common denominator (a multiple of 30)
A1: for \(\dfrac{7}{30}\) from \(\dfrac{12}{30} - \dfrac{5}{30}\) or any fraction equivalent to \(\dfrac{7}{30}\) from a correct method