Hint
Use the stated units and precision. Convert the mixed number with ac+b, simplify using the HCF, and use the correct decimal/percentage scale.
Worked solution
(a)
The unsimplified numerator is \(1(5)+2=7\). Divide numerator and denominator by their HCF to obtain \(\displaystyle \frac{7}{5}\).
Answer: \(\displaystyle \frac{7}{5}\)
(b)
Dividing 2 by 5 gives 0.4. Multiplying that value by 100 gives the numerical percentage \(40\).
Answer: 0.4; \(40\)%.
(c)
Convert the mixed number with ac+b, simplify using the HCF, and use the correct decimal/percentage scale.
\(40\)
Answer: \(40\)
Maths4U indicative marking guidance
Maths4U indicative marking guidance, not an official mark scheme. Credit complete valid alternative methods and consequential reasoning. An unexplained result does not earn a method mark.
(a) · 3 marks
- 1 mark: Convert the whole-number part to the same denominator and combine the numerator.
- 1 mark: Reduce the resulting fraction completely.
- 1 mark: Give the complete requested result, using the required units, precision and boundary inclusion.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Keep intermediate values exact until the final step.
(b) · 2 marks
- 1 mark: Convert the fraction to its terminating decimal, then apply the factor of 100 for percent.
- 1 mark: Give the complete requested result, using the required units, precision and boundary inclusion.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Check the answer against the original conditions.
(c) · 2 marks
- 1 mark: Convert the mixed number with ac+b, simplify using the HCF, and use the correct decimal/percentage scale.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Keep intermediate values exact until the final step.
Total: 7 marks.