Addition, subtraction, multiplication and division
Addition and Subtraction
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Addition and subtraction are inverse operations, used to combine or separate numbers respectively.
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Becoming proficient with mental arithmetic is beneficial for quick addition and subtraction.
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For larger numbers, or numbers with decimals, using column method addition or subtraction can be helpful.
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Remember, in subtraction, the order of the numbers matters. This is called the commutative property.
Multiplication and Division
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Multiplication, like addition, is a commutative operation - changing the order of the numbers does not alter the result.
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Division, by contrast, is non-commutative, so remember the position of numbers is vital.
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Know your times tables up to 12x12 off by heart - this is a fundamental skill.
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You can use long multiplication and division algorithms for larger numbers, or when dealing with decimals.
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Recall that division by zero is undefined, so always check your sums to avoid a division by zero error.
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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
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Be comfortable with converting between mixed numbers and improper fractions as this skill often comes up in exams.
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When adding or subtracting fractions, they must have the same denominator.
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Multiplying fractions is straightforward: multiply the numerators together for the new numerator, and the denominators for the new denominator.
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Dividing fractions requires 'flipping' the second fraction (reciprocal) and then multiply.
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Keep in mind that fractions, decimals, and percentages are different ways of representing the same thing, and be confident in converting between them.
Decimals
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Understand that decimals, fractions and percentages interrelate.
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Be adept at adding, subtracting, multiplying, and dividing decimals by moving the decimal point.
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Appreciate the relationship between decimal places, significant figures and rounding.
Percentages
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Percentages are another way of expressing fractions and decimals. Know the percentage equivalents of common fractions.
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Be comfortable calculating a percentage of a quantity, and increasing or decreasing a number by a certain percentage.
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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
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Mastery of basic conversion principles will allow you to solve a range of problems involving weights, lengths, and capacities.
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Recognise and use common units of measurement, in both the metric and the imperial system.
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Know that area is measured in square units, and volume in cubic units.
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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.