Mathematics Standard • Year 11 • Module 3 • Lesson 1
Wages, Salaries and Pay Periods
Build fluency in pay-period conversions — hourly, weekly, fortnightly, monthly and annual — one step at a time.
1. Quick recall
Answer each question in the space provided. 1 mark each
Q1.1 Fill in the number of pay periods in one year:
Weeks per year = ____ Fortnights per year = ____ Months per year = ____
Q1.2 State in one sentence the main difference between a wage and a salary.
Q1.3 Complete the conversion arrow with the operation needed:
Weekly pay ____________ Annual salary ____________ Fortnightly pay
2. Worked example — comparing two job offers
Follow each line. Every step has a reason on the right.
Problem. Job A pays $61,360 per year. Job B pays $24.80 per hour for 38 hours per week. Which job pays more annually, and by how much?
Step 1 — Identify the unit asked for.
Compare both jobs as annual amounts.
Reason: comparison is fair only when both options are in the same unit.
Step 2 — Job A is already annual.
Job A = $61,360 / year
Step 3 — Convert Job B to weekly, then annual.
Weekly = $24.80 × 38 = $942.40
Annual = $942.40 × 52 = $49,004.80
Reason: hourly × hours per week × 52.
Step 4 — Compare and state.
$61,360 − $49,004.80 = $12,355.20
Conclusion. Job A pays more by $12,355.20 per year.
3. Faded example — convert annual salary to hourly rate
An apprentice earns a salary of $58,968 per year and works 36 hours per week. Calculate the equivalent hourly rate, to the nearest cent. Fill the blanks. 3 marks
Step 1 — Convert annual to weekly:
Weekly = $58,968 ÷ ____ = $ ____________
Step 2 — Divide weekly by hours per week:
Hourly = $ __________ ÷ 36 = $ ____________ (full calculator value)
Step 3 — Round to the nearest cent:
Hourly rate ≈ $ ____________ per hour
Conclusion. Hourly rate ≈ $ ____________ /hr.
4. Graduated practice — pay period calculations
Show your working in the space below each part. Keep dollar amounts to 2 decimal places unless told otherwise.
Foundation — single-step conversions (4 questions)
| Q | Problem | Answer |
|---|---|---|
| 4.1 1 | An hourly rate of $23.50 is paid for 38 hours per week. Calculate the weekly wage. | |
| 4.2 1 | A weekly wage is $1,080. Calculate the annual salary. | |
| 4.3 1 | An annual salary is $84,500. Calculate the fortnightly pay. | |
| 4.4 1 | An annual salary is $72,000. Calculate the monthly pay. |
Standard — typical HSC difficulty (6 questions)
Show at least one line of substitution and clearly label your final answer with units.
4.5 Priya works 38 hours per week at $26.40 per hour. Calculate her annual income. 2 marks
4.6 A graduate earns a salary of $74,880 per year, paid fortnightly. Calculate the fortnightly pay. 2 marks
4.7 A worker is paid $1,372.80 per week. Calculate the equivalent monthly pay (to the nearest cent). 2 marks
4.8 An annual salary of $67,704 is paid for a 36-hour week. Calculate the equivalent hourly rate, to the nearest cent. 2 marks
4.9 A salary of $89,440 is paid fortnightly. Calculate the fortnightly pay. 2 marks
4.10 Marcus earns $84,500 per year. State (i) his weekly pay and (ii) his monthly pay, to the nearest cent. 2 marks
Extension — compare two jobs / reverse-calculate (2 questions)
4.11 Job A pays $63,500 per year. Job B pays $31.25 per hour for 38 hours per week. Which job pays more annually, and by how much? Write a one-sentence conclusion. 3 marks
4.12 A worker earning $1,200 per week was offered a new role at $32.50 per hour for the same 38-hour week. By how much per year is the new role better paid? 3 marks
5. Self-check the easy 3
Tick the first three once you've checked your method works.
How did this worksheet feel?
What I'll revisit before next class:
Q1.1 — Periods per year
Weeks = 52. Fortnights = 26. Months = 12.
Q1.2 — Wage vs salary
A wage is paid per hour worked (more hours = more pay); a salary is a fixed annual amount that does not change with hours worked.
Q1.3 — Conversion arrow
Weekly × 52 Annual ÷ 26 Fortnightly.
Q3 — Faded example (annual to hourly)
Step 1: Weekly = $58,968 ÷ 52 = $1,134.00.
Step 2: Hourly = $1,134.00 ÷ 36 = $31.50 exactly.
Step 3: Already exact, no further rounding required.
Conclusion: Hourly rate = $31.50/hr.
Q4.1 — Weekly wage
W = $23.50 × 38 = $893.00 per week.
Q4.2 — Weekly to annual
A = $1,080 × 52 = $56,160.00 per year.
Q4.3 — Annual to fortnightly
F = $84,500 ÷ 26 = $3,250.00 per fortnight.
Q4.4 — Annual to monthly
M = $72,000 ÷ 12 = $6,000.00 per month.
Q4.5 — Priya's annual income
Weekly = $26.40 × 38 = $1,003.20.
Annual = $1,003.20 × 52 = $52,166.40 per year.
Q4.6 — Graduate fortnightly
F = $74,880 ÷ 26 = $2,880.00 per fortnight.
Q4.7 — Weekly to monthly
Annual = $1,372.80 × 52 = $71,385.60.
Monthly = $71,385.60 ÷ 12 = $5,948.80 per month.
Q4.8 — Annual salary to hourly rate
Weekly = $67,704 ÷ 52 = $1,302.00.
Hourly = $1,302.00 ÷ 36 = $36.166... ≈ $36.17/hr.
Q4.9 — Salary to fortnightly
F = $89,440 ÷ 26 = $3,440.00 per fortnight.
Q4.10 — Marcus weekly and monthly
(i) Weekly = $84,500 ÷ 52 = $1,625.00.
(ii) Monthly = $84,500 ÷ 12 = $7,041.666... ≈ $7,041.67.
Q4.11 — Job A vs Job B
Job A = $63,500 per year (already annual).
Job B weekly = $31.25 × 38 = $1,187.50; annual = $1,187.50 × 52 = $61,750.00.
Difference = $63,500 − $61,750 = $1,750.
Job A pays more by $1,750 per year.
Q4.12 — Current vs new role
Current annual = $1,200 × 52 = $62,400.
New weekly = $32.50 × 38 = $1,235.00; annual = $1,235.00 × 52 = $64,220.00.
Difference = $64,220 − $62,400 = $1,820 better per year in the new role.