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.

Build · Skill Drill

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

Stuck? Revisit lesson § Key Formulas (Weekly × 52 = Annual; Annual ÷ 26 = Fortnightly).

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.

Stuck? Revisit lesson § Worked Example 4, Annual → Hourly.

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

Stuck? Convert both options to annual first, then compare.

5. Self-check the easy 3

Tick the first three once you've checked your method works.

For 4.2 ($1,080/week) I multiplied by 52, not 12 or 26, to get the annual amount.

For 4.3 ($84,500/year) I divided by 26, not 24, to get the fortnightly amount.

For 4.4 ($72,000/year) I divided by 12, not 4 × weekly, to get the monthly amount.

How did this worksheet feel?

Got it Partly Lost

What I'll revisit before next class:

Answers, Do not peek before attempting

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.