Ratios, Percentages & Financial Maths
Match Percentages to Fractions
Draw a line from each percentage to its fraction.
Calculate the Percentage
Circle the correct answer.
25% of 80
10% of 150
50% of 64
30% of 90
Simplify the Ratio
Draw a line from each ratio to its simplest form.
Share in a Ratio
Circle the correct answer.
Share $30 in ratio 1:2. Smaller share =
Share $40 in ratio 3:1. Larger share =
Share $60 in ratio 1:3. Larger share =
Share $90 in ratio 2:1. Larger share =
Percentage Increase or Decrease?
Sort each situation as a percentage increase or decrease.
Financial Percentages
Circle the correct answer.
A shirt costs $40. GST is 10%. Final price?
A book is $25. It goes on sale for 20% off. New price?
You earn $80 pocket money. You save 25%. How much saved?
A $60 item has 15% discount. Sale price?
Ratio & Percentage Word Problems
Show all working.
Orange juice and water are mixed in ratio 2:3. If you use 400 mL of juice, how much water do you need?
A $350 bike is on sale for 30% off. What do you save, and what is the sale price?
A class has 15 boys and 10 girls. Write the ratio of boys to girls in simplest form.
Equivalent Ratios
Match each ratio to an equivalent ratio.
Finding the Original Price
Work backwards to find the original price before a discount.
A shirt is on sale for $36 after a 10% discount. Original price?
Shoes cost $56 after a 20% discount. Original price?
A bag costs $90 after a 25% discount. Original price?
Rate Problems — Speed, Distance, Time
Match each rate problem to its answer.
Dividing Quantities in a Ratio
Show full working for each problem.
Three friends — Alex, Blake and Cameron — share prize money of $360 in ratio 2:3:4. How much does each receive?
Concrete is mixed from cement, sand and gravel in ratio 1:2:3. How much of each is needed to make 480 kg?
Percentage Error
Percentage error = (|estimate − actual| ÷ actual) × 100%. Circle the correct answer.
Estimated 50 cm, actual 40 cm
Estimated 120 g, actual 100 g
Estimated 95, actual 100
GST Calculations
Australia's GST is 10%. Solve each problem.
A camera costs $550 plus GST. What is the total price?
A laptop costs $1320 including GST. What was the price before GST?
A plumber charges $180/hour plus GST. What is the total for 2.5 hours of work?
Best Value — Unit Rates
Find the unit rate for each and sort from best to worst value.
Proportion Problems
Use proportion to solve each problem.
If 5 pencils cost $3.50, how much do 8 pencils cost?
A car travels 300 km on 24 L of petrol. How far can it travel on 40 L?
A recipe uses 150 g of sugar for 12 biscuits. How much sugar for 20 biscuits?
Simple Interest
Use I = P × r × t where I = interest, P = principal, r = rate per year, t = time in years.
Calculate the simple interest on $2000 at 5% p.a. for 3 years.
How long does it take for $1000 at 4% p.a. simple interest to grow to $1200?
Financial Literacy — Budget
Create and analyse a simple budget.
Your weekly income is $80 from part-time work. You spend 40% on food, 25% on transport, 20% on entertainment and save the rest. Calculate each amount and the amount saved.
If you want to save $500 by the end of the year (52 weeks), what fraction of your weekly income do you need to save each week?
Rates in Everyday Life
Match each rate description to its value.
Ratio in Cooking
Use ratio and proportion to solve these cooking problems.
Pancake batter: flour : milk : egg = 3 : 2 : 1. To make enough for 12 people you need 3 cups of flour. How much milk and how many eggs?
A cordial is diluted 1:5 with water. How much water do you need to make 720 mL of drink?
Compound Interest Investigation
Use a year-by-year table to investigate compound interest.
Complete a table for a $1000 investment at 6% p.a. compound interest for 5 years. Show: Year, Start Balance, Interest (6%), End Balance.
How does the final amount compare to a simple interest account at the same rate?
Financial Planning — Salary and Tax
Apply percentage skills to real financial scenarios.
A plumber earns $75 000 per year. They pay 25% income tax. What is their take-home pay per year? Per fortnight?
After a 12% pay rise, a worker earns $84 000. What was their salary before the rise?
Exchange Rates
Use exchange rates and percentage change to solve.
AUD $1 = USD $0.65. Convert AUD $250 to USD.
A holiday costs 3000 euros. If AUD $1 = €0.60, what is the cost in AUD?
Last year AUD $1 = JPY 85. This year AUD $1 = JPY 95. By what percentage has the AUD strengthened against the yen?
Rule of 72 Investigation
Test the Rule of 72 with actual compound interest calculations.
For $1000 at 9% compound interest, use the rule of 72 to predict when the balance doubles. Then calculate the actual balance after 8 years. How close is the rule?
Investigating Percentage Chains
Investigate the effect of repeated percentage changes.
Start with $100. Apply +10%, then −10%. What do you end with? Why isn't it $100?
Start with $100. Apply −20%, then +25%. What do you end with? What percentage brought you back up?
Ratio Applications — Sort by Category
Sort each real-world situation by the type of ratio or rate involved.
Golden Ratio Investigation
Calculate successive ratios in the Fibonacci sequence.
Divide each Fibonacci number by the previous one: 2/1, 3/2, 5/3, 8/5, 13/8, 21/13, 34/21. Write all results as decimals. What number are they approaching?
Find an example of the golden ratio in architecture, art, or nature. Describe it.
Comparing Loan Offers
Use simple and compound interest to compare two loan options.
Loan A: $5000 at 8% simple interest for 3 years. Total repayment = ?
Loan B: $5000 at 7% compound interest for 3 years. Total repayment = ?
Which loan costs more? By how much?
Survey Data and Ratios
Analyse survey data using ratios and percentages.
A survey of 120 students: 45 prefer sport, 35 prefer art, 40 prefer music. Express each as: (a) a fraction of the total (b) a percentage (c) a ratio compared to sport.
If the survey was scaled to a school of 840 students, how many would you expect to prefer each activity?
Design a Sale
Design and analyse a promotional sale.
You own a shop. Design a sale with at least 3 items. For each item, set a discount (in %), show the original price, discount amount, and sale price.
If your cost price for each item is 60% of the original selling price, calculate your profit or loss on each item at the sale price.
Reflection: Ratios, Percentages and Money
Summarise your understanding.
Give two real-world situations where ratios are used. Explain what the ratio means in each.
Explain the difference between percentage increase and compound growth. Give an example of each.
Why is it important to know whether a ratio compares part:part or part:whole?
Percentage Hunt
Look for real-life examples of percentages and ratios at home or in shops.
- 1Find 3 food labels showing percentages (e.g., fat content, daily value). Record and compare them.
- 2Look at a supermarket catalogue or website. Find a sale item and calculate how much you save.
- 3Mix a drink (e.g., cordial and water) in ratio 1:4. How much of each did you use?
- 4Check a bank or savings account (with a parent). What interest rate does it offer? Is it simple or compound?
- 5Use the Rule of 72 to estimate how long it would take to double a $1000 deposit at different interest rates.
Extending — Compound Interest Investigation
Investigate the power of compound interest.
You invest $1 000 at 5% per annum compound interest. Calculate the balance after 1, 2, 5, and 10 years. Show all working.
Compare to simple interest: at 5% p.a. simple interest on $1 000, what is the balance after 10 years? How much more does compound interest earn?