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This lesson covers key decimal and percentage skills for AQA GCSE Mathematics. You will learn how to perform operations with decimals, calculate percentages of amounts, find percentage increase and decrease, and express one quantity as a percentage of another. These skills are essential for both exam papers and real-life applications.
Line up the decimal points and add/subtract as with whole numbers.
Worked Example: Calculate 3.47 + 12.6
3.47
+ 12.60
-------
16.07
Answer: 16.07
Method: Ignore the decimal points, multiply as whole numbers, then put the decimal point back in.
Worked Example: Calculate 2.3 x 0.14
Step 1: 23 x 14 = 322
Step 2: Count the total number of decimal places in the original numbers:
Step 3: Place the decimal point: 0.322
To divide by a decimal, multiply both numbers by a power of 10 to make the divisor a whole number.
Worked Example: Calculate 4.56 divided by 0.3
Step 1: Multiply both by 10: 45.6 divided by 3
Step 2: 45.6 / 3 = 15.2
Exam Tip: When multiplying decimals, always check your answer is reasonable. For instance, 2.3 x 0.14 must be less than 2.3 (because you are multiplying by something less than 1).
Break the percentage into parts you can easily calculate.
| Percentage | How to Find It |
|---|---|
| 50% | Divide by 2 |
| 25% | Divide by 4 |
| 10% | Divide by 10 |
| 5% | Find 10% and halve it |
| 1% | Divide by 100 |
Worked Example: Find 35% of 240.
Use the multiplier: convert the percentage to a decimal and multiply.
Find 17.5% of 560.
17.5% = 0.175
0.175 x 560 = 98
Exam Tip: On the calculator paper, always use the multiplier method. It is faster and less prone to errors than building up from 10% and 1%.
A jacket costs 85 pounds. It is reduced by 20%. Find the sale price.
| Change | Multiplier |
|---|---|
| Increase of 15% | 1.15 |
| Increase of 3% | 1.03 |
| Increase of 120% | 2.20 |
| Decrease of 20% | 0.80 |
| Decrease of 5% | 0.95 |
| Decrease of 33% | 0.67 |
A jacket costs 85 pounds. It is reduced by 20%. Find the sale price.
Multiplier = 1 - 0.20 = 0.80
85 x 0.80 = 68 pounds
graph LR
A["Original Amount"] --> B{"Increase or Decrease?"}
B -->|Increase| C["Multiplier = 1 + percentage/100"]
B -->|Decrease| D["Multiplier = 1 - percentage/100"]
C --> E["Original x Multiplier = New Amount"]
D --> E
A house is worth 250,000 pounds. Its value increases by 4.5%. What is the new value?
Multiplier = 1 + 0.045 = 1.045
250,000 x 1.045 = 261,250 pounds
Exam Tip: Learn the multiplier method — it is essential for compound interest and growth/decay problems later in the course.
Formula: (the part / the whole) x 100
A student scored 42 out of 60 on a test. What percentage is this?
(42 / 60) x 100 = 0.7 x 100 = 70%
Last year a shop sold 840 items. This year it sold 966 items. Express the increase as a percentage of last year's sales.
Percentage change = (change / original) x 100
This formula works for both increases and decreases.
A phone was bought for 480 pounds and sold for 372 pounds. Find the percentage loss.
Exam Tip: Always divide by the original value, not the new value. This is the most common mistake in percentage change questions.
A reverse percentage question gives you the value after a percentage change and asks you to find the original.
After a 15% increase, a laptop costs 690 pounds. Find the original price.
Step 1: The current price represents 115% of the original (100% + 15% = 115%).
Step 2: Find 1%: 690 / 115 = 6
Step 3: Find 100%: 6 x 100 = 600 pounds
Original x 1.15 = 690
Original = 690 / 1.15 = 600 pounds
A coat is on sale at 20% off. The sale price is 56 pounds. What was the original price?
The sale price is 80% of the original (100% - 20% = 80%).
Original = 56 / 0.80 = 70 pounds
Exam Tip: Reverse percentage questions always tell you the value AFTER the change. To find the original, identify what percentage the given value represents and divide by that multiplier.
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