Arithmetic and Algebra

Overview

Arithmetic describes relationships among quantities. Fractions tell us about parts of a whole, ratios compare quantities in a stated order, and averages summarise a total spread across a number of observations. Algebra adds symbols so that the same relationships can be written even when one quantity is not yet known.

Begin by naming the quantities. In a price increase, the original price is the reference amount. In a ratio split, the sum of the ratio parts determines how the total is divided. In an average, the observation count tells you how much weight each group contributes. A correct calculation can still answer the wrong question if the reference or unit was chosen incorrectly.

Practise translating a sentence into a relationship before calculating. For example, “a fixed fee plus an amount per item” becomes a constant plus a multiple of the item count. After solving an equation, substitute your answer into that original relationship. Estimation, unit checks and substitution are complementary ways to find errors.

Continue learning

• Foundations of Algebra

  Write a clear equation for an unknown quantity and preserve equality while solving it step by step.

• Everyday Arithmetic Relationships

  Choose the correct base, total and unit when working with percentages, ratios, weighted averages and simple interest.