Number
Percentages
3rd Class · 4th Class · 5th Class · 6th Class
- ✓Understand the meaning of a percentage and its symbol.
- ✓Convert between percentages, fractions, and decimals.
- ✓Calculate a percentage of a given quantity.
- ✓Solve simple problems involving percentages in everyday contexts.
Key concepts
A percentage is a way of expressing a number as a fraction of 100. The word 'per cent' means 'per hundred' or 'out of one hundred'. We use the symbol '%' to show a percentage. For example, 50% means 50 out of 100, or 50/100.
To change a percentage to a fraction, we write the percentage number over 100 and simplify the fraction if possible. For example, 25% is 25/100, which simplifies to 1/4. To change a fraction to a percentage, we multiply the fraction by 100%.
To change a percentage to a decimal, we divide the percentage number by 100. This means moving the decimal point two places to the left. For example, 75% is 75 ÷ 100 = 0.75. To change a decimal to a percentage, we multiply the decimal by 100%. This means moving the decimal point two places to the right.
To find a percentage of a quantity, first convert the percentage to a fraction (by dividing by 100) or a decimal (by dividing by 100). Then, multiply this fraction or decimal by the given quantity. Remember that 'of' in maths usually means multiply.
Key facts to remember
- 1The symbol '%' means 'per hundred' or 'out of one hundred'.
- 2100% represents the whole amount or a full quantity.
- 3To change a percentage to a fraction, divide by 100 and simplify.
- 4To change a percentage to a decimal, divide by 100 (move the decimal point two places to the left).
- 5To change a fraction or decimal to a percentage, multiply by 100% (move the decimal point two places to the right for decimals).
- 6To find a percentage 'of' a quantity, convert the percentage to a fraction or decimal and then multiply by the quantity.
- 7Common percentages: 50% = 1/2 = 0.5, 25% = 1/4 = 0.25, 10% = 1/10 = 0.1.
Worked examples
Example 1
Convert 40% to a fraction in its simplest form and to a decimal.
Answer
40% = 2/5 (fraction) and 0.4 (decimal)
Example 2
Calculate 25% of €120.
Answer
€30
Both methods give the same answer. Choose the one you find easier.
Example 3
In a class of 30 students, 60% are boys. How many boys are in the class?
Answer
There are 18 boys in the class.
Common mistakes
- ✗Forgetting to divide or multiply by 100 when converting between percentages, fractions, and decimals.
- ✗Incorrectly moving the decimal point when converting (e.g., moving it one place instead of two).
- ✗Not understanding that 'of' means multiplication when finding a percentage of a quantity.
- ✗Calculating the percentage of the wrong amount or misreading the question.
- ✗Not simplifying fractions to their simplest form when required.
Exam tips
- ★Always read the question carefully to understand what is being asked.
- ★Show all your working steps clearly, even for simple calculations. This helps you get partial marks if your final answer is incorrect.
- ★If you are unsure, try converting the percentage to a fraction first, as it can sometimes be easier to work with.
- ★Check your answer to make sure it makes sense in the context of the problem. For example, 50% of 100 should be 50, not 5 or 500.
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