Pearson Edexcel GCSE (9-1) Mathematics revision notes
Fractions, decimals and percentages Revision Notes
Review revision notes for Fractions, decimals and percentages in Edexcel Mathematics.
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Fractions, decimals and percentages
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Fractions and percentages as operators Revision Notes
Using fractions as operators
To find a fraction of an amount, multiply the amount by the fraction. You can divide by the denominator first and then multiply by the numerator when this makes the calculation easier. For example, 5/8 of 64 is 64 ÷ 8 × 5 = 40.
Using percentages as operators
To find a percentage of an amount, multiply by its decimal equivalent. For example, 35% is 0.35, so 35% of 80 is 0.35 × 80 = 28. A percentage decrease can be found by calculating the percentage amount and subtracting it.
Success checks
Read the wording carefully: ‘of’ usually means multiply. Check that a proper fraction of a positive quantity gives a smaller result, and that a percentage below 100% also gives a smaller result. Show intermediate steps for multi-stage calculations.
Fractions in ratio problems Revision Notes
Finding amounts from a total
For a ratio a:b, the whole contains a+b equal parts. Divide the total quantity by a+b to find one part, then multiply by the relevant ratio term. For example, in the ratio 3:5 with total 32, one part is 4 and the amounts are 12 and 20.
Using a difference or finding a fraction
If two quantities have ratio a:b, their difference represents a-b parts. Divide the known difference by a-b to find one part. To express one quantity as a fraction of the whole, use its ratio term over a+b and simplify; for example, the second share in 2:6 is 6/8 = 3/4.
Checking ratio calculations
Check that calculated amounts have the required ratio, add to the stated total, or have the stated difference. Keep units consistent, and convert an improper or unsimplified fraction when the question requests a simplified fraction.
Recurring decimals and fractions Revision Notes
Recurring decimal to fraction
Use x for the recurring decimal. Multiply by 10, 100 or another suitable power so that identical recurring parts appear after the decimal point. Subtract the original equation from the multiplied equation, solve for x, and reduce the resulting fraction fully.
Fraction to recurring decimal
Simplify the fraction before deciding whether its decimal terminates or recurs. Use written division to produce the decimal digits. If a remainder repeats, the corresponding block of digits repeats. For example, 5/12 = 0.41(6), because the digit 6 repeats indefinitely.
Checking the result
A converted fraction can be checked by dividing its numerator by its denominator or by multiplying the fraction by the denominator. Make sure the recurring block starts in the correct place, especially when there are non-recurring digits before the repeated block.
Terminating decimals and fractions Revision Notes
Decimal to fraction
Count the decimal places. Use the place-value denominator: tenths use 10, hundredths use 100, and thousandths use 1000. Remove the decimal point from the numerator, then simplify by dividing the numerator and denominator by a common factor.
Fraction to decimal
Divide the numerator by the denominator. Alternatively, convert the fraction to an equivalent fraction whose denominator is 10, 100 or 1000, then write the numerator as a decimal. Check that the decimal terminates.
Useful checks
The value must stay the same after conversion. A fraction less than 1 should give a decimal between 0 and 1, while an improper fraction greater than 1 should give a decimal greater than 1. Simplify fraction answers fully.
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