Mathematics - 9260 OxfordAQA

Fractions, Decimal And Percentages

Visão Geral

A shop advertises 20 per cent off. A bank offers 4 per cent a year. A report says prices rose by 130 per cent. Three sentences, three completely different pieces of arithmetic, and the marks in this topic go to the candidate who can tell instantly which one is in front of them. Fractions, decimals and percentages are three notations for the same idea, and the fastest route through almost every question here is to convert to whichever of the three makes the calculation shortest.

You will convert freely between the three forms, use each of them as an operator that acts on a quantity, express one quantity as a fraction or a percentage of another even when the answer is greater than 1 or greater than 100 per cent, and handle percentage increase and decrease, simple interest and compound interest. On the Extension Tier you will also convert a recurring decimal into an exact fraction, solve reverse percentage problems where the figure you are given is the answer rather than the start, and use the compound interest formula the specification prints in full.

Objetivos

  1. [Core] understand and use equivalent fractions, understand and use percentages, convert between fractions, terminating decimals and percentages
  2. [Extension] convert between fractions and recurring decimals
  3. [Core] interpret fractions, decimals and percentages as operators
  4. [Core] express one quantity as a fraction/percentage of another, where the fraction is less than 1 or greater than 1 or the percentage is less than 100 or greater than 100
  5. [Core] solve problems involving percentage change, including increase/decrease, simple interest and compound interest
  6. [Extension] reverse percentage problems
  7. [Extension] knowledge and use of the compound interest formula value of investment = P(1 + r/100)ⁿ where P is the amount invested, r is the percentage rate of interest and n is the number of years of compound interest

Mapa mental

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Nota de Aula

A specimen Core paper opens with a one mark question that asks you to circle the percentage that is more than \( \tfrac14 \) and less than \( \tfrac12 \), from the list 15, 20, 35, 55 and 60 per cent. It is a trivial question if you convert first: \( \tfrac14 = 25\% \) and \( \tfrac12 = 50\% \), so the only candidate strictly between them is 35 per cent. It is an awkward one if you try to compare a fraction with a percentage directly. That is the entire message of this topic. Comparing, ordering and calculating all get easier the moment everything is written in the same form.

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  1. Circle the percentage that is more than one quarter and less than one half. A. 15% B. 20% C. 35% D. 55% Answer: C
  2. Which multiplier increases a quantity by 130 per cent? A. 0.30 B. 1.30 C. 2.30 D. 130 Answer: C
  3. Which of these fractions gives a terminating decimal? A. 4/15 B. 5/11 C. 2/7 D. 9/16 Answer: D
  4. A price is reduced by 10 per cent and then increased by 10 per cent. Compared with the original price, the final price is A. the same B. 1 per cent lower C. 1 per cent higher D. 10 per cent lower Answer: B
  5. A price including 20 per cent sales tax is $54. What was the price before tax? A. $43.20 B. $45.00 C. $45.90 D. $64.80 Answer: B

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