GCSE Maths Numeracy WJEC

Addition, subtraction, multiplication and division

Addition and Subtraction

• Addition and subtraction are inverse operations, used to combine or separate numbers respectively.

• Becoming proficient with mental arithmetic is beneficial for quick addition and subtraction.

• For larger numbers, or numbers with decimals, using column method addition or subtraction can be helpful.

• Remember, in subtraction, the order of the numbers matters. This is called the commutative property.

Multiplication and Division

• Multiplication, like addition, is a commutative operation - changing the order of the numbers does not alter the result.

• Division, by contrast, is non-commutative, so remember the position of numbers is vital.

• Know your times tables up to 12x12 off by heart - this is a fundamental skill.

• You can use long multiplication and division algorithms for larger numbers, or when dealing with decimals.

• Recall that division by zero is undefined, so always check your sums to avoid a division by zero error.

• Furthermore, remember multiplication and division are higher order operations and should be done first according to BIDMAS (Brackets, Indices, Division, Multiplication, Addition, Subtraction) order of operations.

Fractions

• Be comfortable with converting between mixed numbers and improper fractions as this skill often comes up in exams.

• When adding or subtracting fractions, they must have the same denominator.

• Multiplying fractions is straightforward: multiply the numerators together for the new numerator, and the denominators for the new denominator.

• Dividing fractions requires 'flipping' the second fraction (reciprocal) and then multiply.

• Keep in mind that fractions, decimals, and percentages are different ways of representing the same thing, and be confident in converting between them.

Decimals

• Understand that decimals, fractions and percentages interrelate.

• Be adept at adding, subtracting, multiplying, and dividing decimals by moving the decimal point.

• Appreciate the relationship between decimal places, significant figures and rounding.

Percentages

• Percentages are another way of expressing fractions and decimals. Know the percentage equivalents of common fractions.

• Be comfortable calculating a percentage of a quantity, and increasing or decreasing a number by a certain percentage.

• It's often helpful to convert percentages to decimals or fractions to perform more complex calculations. Remember that the word 'per cent' literally means 'out of 100'.

Measures

• Mastery of basic conversion principles will allow you to solve a range of problems involving weights, lengths, and capacities.

• Recognise and use common units of measurement, in both the metric and the imperial system.

• Know that area is measured in square units, and volume in cubic units.

• Understand how to calculate the perimeter and area of simple shapes, as well as the volume of cuboids and cylinders.

Remember, practice with a mix of "easy" and more challenging problems to build confidence and solidify knowledge. Regular revision and practice under exam conditions are the most effective ways to prepare.