Wages and Salaries
A wage is paid by the hour; a salary is a fixed amount for the year. This NSW Year 9 Core maths subtopic works out pay both ways and converts between weekly, fortnightly, monthly and yearly amounts using \(1\) year \(= 52\) weeks. It is Stage 5 Core content under NESA outcome MA5‑FIN‑C‑01.
You will find a weekly wage from an hourly rate and the hours worked, turn a salary such as \(\$67\,600\) a year into a fortnightly, monthly or daily amount, and find hours worked from total pay. You will also work out hours from start and finish times with an unpaid lunch break, combine two pay rates in one week, and compare two jobs by putting both on the same time basis, as when deciding whether a salary or an hourly rate pays more. It is part of Year 9 Core Earning Money.
Every question with a fully worked solution.
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Theory
A wage is paid by the hour. A salary is a fixed amount for a year, paid in equal parts. This Year 9 maths page shows how to work out pay from an hourly rate and a timesheet, how to split a salary into weekly, fortnightly and monthly pay, how to work backwards, and how to compare two jobs.
A wage is paid for each hour worked. The amount per hour is the hourly rate.
A salary is a fixed amount for a whole year. It is paid in equal parts, such as each week, each fortnight or each month. The yearly amount is also called per annum (p.a.).
Unless told otherwise, use \(1\) year \(= 52\) weeks \(= 26\) fortnights \(= 12\) months. A fortnight is two weeks.
A timesheet shows when a shift starts and finishes. An unpaid break, such as lunch, is taken off the time worked.
Write part of an hour as a decimal: \(15\) min \(= 0.25\) h, \(30\) min \(= 0.5\) h and \(45\) min \(= 0.75\) h.
A wage:
Working backwards is a division:
| From a yearly salary | Divide by | To go back |
|---|---|---|
| to a monthly amount | \(12\) | \(\times 12\) |
| to a fortnightly amount | \(26\) | \(\times 26\) |
| to a weekly amount | \(52\) | \(\times 52\) |
| to a daily amount | \(365\) (if told to) | \(\times 365\) |
How to work out pay
- Find the hours worked: finish time minus start time, minus any unpaid break. Write minutes as a decimal of an hour.
- Multiply the hours by the rate. If there are two rates, do each part and add.
- Convert a salary by dividing by \(52\), \(26\) or \(12\). For month to week, go to a year first.
- Compare jobs on the same basis, and give money to two decimal places.
From 8:30 am to 4:45 pm is \(8\) h \(15\) min. Take off the unpaid break.
| \(\text{per day}\) | \(=\) | \(8 \text{ h } 15 \text{ min} - 45 \text{ min}\) |
| \(\) | \(=\) | \(7 \text{ h } 30 \text{ min} = 7.5 \text{ h}\) |
| \(\text{per week}\) | \(=\) | \(7.5 \times 5 = 37.5\) |
Pay is the rate times the hours:
| \(\text{pay}\) | \(=\) | \(26.80 \times 37.5\) |
| \(\) | \(=\) | \(\mathbf{1005.00}\) |
Dan's weekly wage is $1005.00.
(i) a week
(ii) a fortnight
(iii) a month?
Divide by the number of pays in a year.
| \(\text{weekly}\) | \(=\) | \(71\,500 \div 52 = \mathbf{1375.00}\) |
| \(\text{fortnightly}\) | \(=\) | \(71\,500 \div 26 = \mathbf{2750.00}\) |
| \(\text{monthly}\) | \(=\) | \(71\,500 \div 12\) |
| \(\) | \(=\) | \(5958.333\ldots\) |
| \(\) | \(\approx\) | \(\mathbf{5958.33}\) |
So $1375.00 a week, $2750.00 a fortnight and $5958.33 a month. A fortnight is two weeks, so the fortnightly pay is double the weekly pay.
(i) Ella earned $693 in a week at $23.10 an hour. How many hours did she work?
(ii) Raj is paid $4550 a month. How much is that a week?
(i) Hours are the pay divided by the rate.
| \(\text{hours}\) | \(=\) | \(\dfrac{693}{23.10}\) |
| \(\) | \(=\) | \(\mathbf{30}\) |
(ii) A month is not a whole number of weeks. Go to a year first, then divide by \(52\).
| \(\text{yearly}\) | \(=\) | \(4550 \times 12 = 54\,600\) |
| \(\text{weekly}\) | \(=\) | \(54\,600 \div 52\) |
| \(\) | \(=\) | \(\mathbf{1050.00}\) |
Raj earns $1050.00 a week.
Put both jobs on the same basis: per week.
| \(\text{Job A}\) | \(=\) | \(66\,300 \div 52 = 1275.00\) |
| \(\text{Job B}\) | \(=\) | \(34.20 \times 38 = 1299.60\) |
| \(\text{difference}\) | \(=\) | \(1299.60 - 1275.00\) |
| \(\) | \(=\) | \(\mathbf{24.60}\) |
Job B pays more, by $24.60 a week.
Common pitfalls
Frequently asked questions
What is the difference between a wage and a salary?
A wage is paid for each hour worked, so the pay changes with the hours. A salary is a fixed amount for the year, paid in equal parts whatever the hours.
How do you work out a weekly wage?
Multiply the hourly rate by the number of hours worked in the week. At $26.80 an hour for \(37.5\) hours, the wage is $1005.00.
How many fortnights are in a year?
There are \(26\) fortnights in a year, because a year has \(52\) weeks and a fortnight is \(2\) weeks.
How do you convert a monthly salary to weekly pay?
Multiply the monthly amount by \(12\) to get the yearly salary, then divide by \(52\).
How do you work out hours worked from a start and finish time?
Count the time from start to finish, then subtract any unpaid break. Change the minutes into a decimal of an hour before multiplying by the rate.