Consumer arithmetic

Consumer arithmetic is the mathematics of everyday money: earning it, spending it and comparing deals. Two ideas sit underneath almost every calculation in this topic. A rate compares two quantities measured in different units, such as dollars per hour, cents per litre or kilometres per hour. A percentage is a rate out of 100, so 12% means 12 out of every 100, or the decimal 0.12.

To find a percentage of an amount, convert the percentage to a decimal and multiply. To write one amount as a percentage of another, divide and multiply by 100.

People are paid in several different ways, and you need to recognise each one.

• Salary: a fixed annual amount, usually paid weekly (divide by 52), fortnightly (divide by 26) or monthly (divide by 12), regardless of the exact hours worked.
• Wage: payment at an hourly rate. Hours beyond the normal working week are often paid as overtime at time-and-a-half (1.5 × the hourly rate) or double time (2 × the hourly rate).
• Allowances: extra fixed amounts for special conditions, such as working in heat, using your own tools or being on call.
• Commission: a percentage of the value of sales, sometimes added to a small fixed payment called a retainer.
• Piecework: a fixed amount paid for each item completed or delivered.

A common trap is converting between weekly and monthly pay. A month is not exactly four weeks, so never multiply a weekly wage by 4 to get a monthly amount. Instead, convert to an annual figure first (× 52), then divide by 12. When comparing jobs, always convert both to the same period before deciding which pays more.

Always show the separate parts of a pay calculation, label each part, and round money to the nearest cent only at the final step.