Practice Maths

Calculating Percentages of Amounts

The Core Method

To find a percentage of an amount, convert the percentage to a decimal (divide by 100), then multiply by the amount.

Key Terms

percentage of an amount
the result of applying a percentage to a quantity (e.g. 20% of $80 = $16)
decimal multiplier
the decimal form of a percentage, found by dividing by 100 (e.g. 35% → 0.35); used to calculate percentages by multiplication
1% method
a mental strategy where you find 1% of an amount by dividing by 100, then scale up to the target percentage
10% strategy
a mental maths technique where 10% is found by dividing by 10, then used as a building block for other percentages
benchmark percentage
a commonly used percentage — such as 10%, 25%, or 50% — that corresponds to a simple fraction and can be calculated mentally
Strategy 1: The 1% Method Divide the total by 100 to find 1%. Then multiply by the percentage you need.
Example: Find 7% of $400.  1% is $4.  7% is 7 × $4 = $28.

Strategy 2: The 10% Method (Mental Maths)

  • Find 10% by dividing by 10.
  • Find 5% by halving the 10% value.
  • Find 20% by doubling the 10% value.

Worked Example

Find 35% of $80.

Step 1: Convert 35% to a decimal by dividing by 100.
35 ÷ 100 = 0.35

Step 2: Multiply the decimal by the amount.
0.35 × $80

Step 3: Calculate the answer.
0.35 × $80 = $28

Why Do We Calculate Percentages of Amounts?

Finding a percentage of an amount is one of the most useful maths skills in real life. You need it for working out discounts in a sale ("20% off!"), calculating a GST amount, finding a test score, or splitting a bill with a tip. Understanding the method properly means you can handle any percentage problem, not just the simple ones.

The Decimal Method (Works Every Time)

The most reliable method is: convert the percentage to a decimal, then multiply by the amount.

To convert a percentage to a decimal, divide by 100 (move the decimal point two places left).

  • 20% of $45: 20 ÷ 100 = 0.20, then 0.20 × $45 = $9.00
  • 15% of 80 km: 15 ÷ 100 = 0.15, then 0.15 × 80 = 12 km
  • 35% of 200 students: 0.35 × 200 = 70 students

This method works for any percentage — even tricky ones like 17.5% or 3%.

The 10% Strategy (Great for Mental Maths)

To find 10% of any number, simply divide it by 10. From there, you can build up other percentages by multiplying or adding:

  • 10% of $60 = $6
  • 20% = double the 10% → $12
  • 5% = half the 10% → $3
  • 15% = 10% + 5% → $6 + $3 = $9
  • 30% = 3 × 10% → $18

This is especially useful when you want a quick estimate or don’t have a calculator.

Worked Example: Shopping Discount

A jacket costs $120 and is on sale for 25% off. How much do you save, and what is the sale price?

  • Step 1: Find 25% of $120 → 0.25 × $120 = $30 saved
  • Step 2: Sale price = $120 − $30 = $90

Alternatively, the sale price is 75% of the original (100% − 25% = 75%), so: 0.75 × $120 = $90.

Key Mistake to Avoid: To find a percentage of an amount, always turn the percentage into a decimal first by dividing by 100. Then multiply. For example, 7% of 300 = 0.07 × 300 = 21. Many students write 7 × 300 (forgetting to convert) and get 2100 — always divide by 100 first!

Practice Questions

  1. The 1% Method Fluency

    Find 1% of the amount first, then multiply to find the target percentage:

    1. Find 3% of $800.
    2. Find 7% of $1200.
    3. Find 5% of $460.
    4. Find 9% of $300.
    5. Find 4% of $2500.

  2. Common Benchmarks: 25% Fluency

    Calculate 25% (Hint: 25% = 14, so divide by 4):

    1. 25% of 800 grams.
    2. 25% of $44.
    3. 25% of 360 km.
    4. 25% of $196.

  3. Common Benchmarks: 20% Fluency

    Calculate 20% (Hint: 20% = 15, so divide by 5):

    1. 20% of $350.
    2. 20% of 150 kilometres.
    3. 20% of $85.
    4. 20% of 1500 mL.

  4. The 10% Jump Fluency

    Find 10% by dividing by 10, then use it to find the target percentage:

    1. Find 30% of 70.
    2. Find 40% of 240.
    3. Find 20% of 450.
    4. Find 60% of 80.
    5. Find 80% of 350.

  5. Combining Percentages Understanding

    Combine benchmark values (50%, 10%, 5%, or 1%) to find each total:

    1. 60% of $120.
    2. 11% of $500.
    3. 35% of $80.
    4. 45% of $200.

  6. Mental Halving Understanding

    Find 5% by first finding 10% and halving the result:

    1. 5% of $160.
    2. 5% of $420.
    3. 5% of $90.
    4. 5% of $340.

  7. The 15% Tip Understanding

    Calculate 15% by finding 10% + 5%:

    1. 15% of $200.
    2. 15% of $60.
    3. 15% of $80.

  8. Shopping Discounts Understanding

    Calculate how much money you save on each item:

    1. Shoes cost $80. There is a 20% off sale. How much do you save?
    2. A jacket costs $120. It is 25% off. How much do you save?
    3. A backpack costs $65. It is 30% off. How much do you save?

  9. Mixed Units Problem Solving

    Convert the units first, then calculate the percentage:

    1. Calculate 75% of 2 litres. (Hint: Convert to 2000 mL first.)
    2. Calculate 40% of 1.5 kg. (Hint: Convert to 1500 g first.)
    3. Calculate 30% of 4.5 km. (Hint: Convert to 4500 m first.)

  10. Sale Price with GST Problem Solving

    A jacket is originally priced at $180. It is discounted by 30%, and then 10% GST is added to the sale price.

    1. Find the sale price after the 30% discount.
    2. Calculate the final price after 10% GST is added to the sale price.
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