Page 1: Essential Mathematical Operations and Concepts

This detailed page covers fundamental mathematical operations essential for maths foundation paper 1 questions, including integer operations, ratio simplification, factorising, and percentage calculations.

Definition: Integer operations involve working with positive and negative whole numbers, following specific rules for addition and subtraction.

Example: When adding integers with the same signs, add the absolute values and keep the common sign. For 12 + (-7), the result is 5 because we subtract the absolute values since signs differ.

Highlight: For adding and subtracting negative numbers, remember that subtracting a negative is the same as adding a positive.

Vocabulary: HCF (Highest Common Factor) is crucial for simplifying ratios. For example, in 4:12, the HCF is 4, resulting in the simplified ratio 1:3.

Example: For reverse percentages, when an item costs £72 after a 20% reduction, calculate the original price by dividing 72 by 80% (0.8) and multiplying by 100, giving £90.

Definition: Factorising involves finding the HCF of terms and expressing the expression as a product of this factor and remaining terms.

Example: For decimal multiplication, such as 10.72 × 0.4, first remove decimals, multiply the numbers, then place decimals in the final answer based on the total decimal places in the original numbers.