Percentages for OCR GCSE Maths
This page covers the following topics:
3. Reverse percentages
A percentage is the number of parts of a quantity per 100 and is denoted by the symbol %. A percentage can be written as a fraction by putting it over a denominator of 100. This in turn can be made into a decimal. To calculate the percentage of a quantity, the value should be multiplied by the percentage. To find the percentage change, divide the change in value by the initial value and then multiply it by 100%.
Simple interest is calculated by multiplying the initial amount by the product of the interest and the number of time periods that have passed added to 1. This formula is given by X = A(1 + rt), where A is the initial amount, r is the interest rate and t is the number of time periods that have passed.
With compound interest, not only does the initial value receive interest, but also the additional interest for each time period. Compound interest is an example of exponential growth and decay that arise when there is an increase or decrease by the same factor over each time period.
When a certain amount is equivalent to a certain percentage, divide both values by the value of the percentage to get the quantity equivalent to 1%. Multiplying both values by 100 will give the original value of the quantity.
Write down 4/25 as a percentage.
4/25 = 16/100, therefore 16%.
A shop has an ongoing sale of 40% off. Given that the reduction to a T-shirt is £12, calculate the full value of the T-shirt.
12 ÷ 40 = £0.30 is equivalent to 1%.
Multiplying by 100 gives £30 to be equivalent to 100% of the value.
Express 2% as a fraction.
2/100 = 1/50
Given that 60% of a quantity is 75, calculate what the value equivalent to 38% is.
75 ÷ 60% = 1.25 is equivalent to 1%.
Multiplying by 38 gives that 47.5 is equivalent to 38%.
Given that 27% of a quantity is 54, calculate what the value equivalent to 72% is.
54 ÷ 27 = 2 is equivalent to 1%.
Multiplying by 72 gives that 144 is equivalent to 72%.
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