Word Problems and Practical Reasoning
Word problems translate everyday situations into arithmetic. The core skill is translation: converting sentences into operations. Look for cue words - 'total', 'altogether', and 'combined' suggest addition; 'difference', 'how many more', and 'remaining' suggest subtraction; 'per', 'each', and 'rate' suggest multiplication or division. Underline the quantities and their units before writing anything.
Many problems are multi-step: a purchase with a discount then tax, a journey split into stages, or a work-rate task. Break these into numbered steps and solve one at a time. For work-rate problems, think in rates per unit time (if A finishes in 4 hours, A does 1/4 per hour; combined rates add). For 'meet in the middle' distance problems, add the speeds.
Traps: a question that supplies a number you never need (a deliberate distractor); mixing units such as minutes and hours; and answering an intermediate value instead of the final question. Always re-read the last sentence to confirm what is actually requested.
Worked example: A tap fills a tank in 6 hours, another in 3 hours. Combined rate = 1/6 + 1/3 = 1/2 per hour, so the tank fills in 2 hours. Rule of thumb: state the final question in your own words before solving.