Numerical Computation and Arithmetic Reasoning
What to master
Arithmetic reasoning mixes computation with word problems. Know the four operations with whole numbers, fractions, decimals, and percentages; order of operations (brackets, powers, multiplication and division left to right, addition and subtraction left to right); averages; ratios and proportions; and simple unit conversions (hours to minutes, dollars to cents). Estimation is a tool, not a substitute: it catches answers that are wildly off.
Traps
- Percent questions: 15% of 240 differs from 240 increased by 15%.
- Dividing by a fraction: 3/4 ÷ 1/2 = 3/4 × 2/1 = 3/2, not 3/8.
- Averages: total ÷ number of items, and add the new item when one is added.
- Mixing units: 2 hours 30 minutes is 150 minutes, not 2.30 hours.
- Order of operations: 8 + 2 × 5 = 18, not 50.
- Careless borrowing in subtraction and decimal point placement.
Worked example
A clerk earns $12.50 per hour and works 38 hours. Overtime is paid at 1.5 times the rate for 3 extra hours. Total = 38 × 12.50 = $475.00; overtime = 3 × 18.75 = $56.25; total $531.25.
Rule of thumb
Write the units beside each number, estimate the answer first, then compute exactly and compare. If the exact answer is far from the estimate, recheck the setup.