M1: for correct improper fractions or fractional part of numbers written correctly over a common denominator
M1: for correct fractions with a common denominator with minus sign or mixed numbers to the stage shown
\(\dfrac{154}{21} - \dfrac{75}{21}\) or \(\dfrac{22 \times 7}{21} - \dfrac{25 \times 3}{21}\) implies the first M1
A1: Dep on M2 for a correct answer from fully correct working
If a student shows that \(3\dfrac{16}{21} = \dfrac{79}{21}\) then they must show correct working to \(\dfrac{79}{21}\) and can gain full marks for this
or correct working to \(\dfrac{27}{7}\) and writing \(3\dfrac{6}{7} = \dfrac{27}{7}\)
Working required
Answer: shown
A1
(3)
(3 marks)
Notes
M1: for \(2\dfrac{1}{4}\) and \(1\dfrac{5}{7}\) expressed as improper fractions
M1: correct cancelling or multiplication of numerators and denominators without cancelling
A1: dep on M2, for conclusion to \(3\dfrac{6}{7}\) from correct working – either sight of the result of the multiplication e.g. \(\dfrac{108}{28}\) oe must be seen
or correct cancelling prior to the multiplication to \(\dfrac{27}{7}\)
NB: use of decimals scores no marks unless as a check
M1: for both fractions written as improper fractions
M1: for multiplying the numerators and multiplying the denominators or cancelling the fractions fully or cancelling fractions partially and multiplying across
A1: completion to given result. dep on M2
If a student shows clearly in their working that \(3\dfrac{3}{4} = \dfrac{15}{4}\) they only need to show that the LHS comes to \(\dfrac{15}{4}\)
