Number - Fractions, decimals and percentages: interpret fractions and percentages as operators

The idea

Used as an operator, a fraction or a percentage acts on a number, and the word 'of' means multiply. So 3/4 of 20 is 3/4 × 20, which is 15, and 35% of 80 is 0.35 × 80, which is 28. Wherever you can, work with one multiplier instead of two steps: 15% more than an amount is that amount × 1.15, and 15% less is the amount × 0.85, because a fall of 15% keeps 85% of the value. Multiplying a positive number by a multiplier between 0 and 1 makes it smaller, and a multiplier greater than 1 makes it larger. The idea reverses as well, so if a price after a 20% rise is £54, the original is 54 ÷ 1.2, which is £45. Expect questions that chain two operators, a rise then a fall, where you multiply the multipliers together rather than adding the percentages.

What earns the marks

• Turning the percentage into a decimal multiplier, such as 1.15 for a rise of 15%.
• A correct method seen, such as finding 10% and 5% and adding them, even if the arithmetic slips.
• Dividing rather than multiplying when the question gives the value after the change and asks for the original.
• The final value written with its units or its pound sign, rounded as the question directs.

Common mistakes and how to put them right

• Taking a 10% rise followed by a 10% fall back to the starting value, when the multipliers give 1.1 × 0.9 = 0.99.

• Multiplying by 0.15 for a 15% increase instead of by 1.15.

• Finding the percentage of the wrong amount in a two stage question, using the original where the new value is needed.

• Multiplying by 1.2 to reverse a 20% rise instead of dividing by it.

Exam tips

• Write the multiplier down before you touch the calculator; most method marks here are for the multiplier.
• Ask whether the answer should be bigger or smaller than the starting number, and check your result against that.
• For money, give two decimal places, so an answer of 45.5 is written as £45.50.