Class 5 — Mathematics

Percentages

Class 5

✓By the end of this lesson students will be able to understand the meaning of 'percent' as 'out of hundred'.
✓By the end of this lesson students will be able to express a fraction as a percentage.
✓By the end of this lesson students will be able to find a percentage of a given quantity.
✓By the end of this lesson students will be able to solve simple real-life problems involving percentages.

Key concepts

What is Percent?

The word 'percent' means 'per hundred' or 'out of hundred'. It is denoted by the symbol '%'. For example, 15% means 15 out of 100. If you score 90% in a test, it means you scored 90 marks out of every 100 marks possible.

Link to Fractions

A percentage can always be written as a fraction with a denominator of 100. For example, 25% can be written as 25/100. To convert a fraction into a percentage, we multiply the fraction by 100%.

Fraction to Percentage: (Fraction) × 100%

Percent of a Quantity

To find a percentage of a given quantity, we first convert the percentage into a fraction (by dividing by 100) and then multiply it by the quantity. For example, to find 10% of 50, we write 10% as 10/100 and then multiply (10/100) by 50.

Percentage of Quantity: (Percentage/100) × Quantity

Key facts to remember

1The word 'percent' means 'per hundred' or 'out of hundred'.
2The symbol for percent is '%'.
3100% represents the whole or the entire quantity.
4To convert a fraction to a percentage, multiply the fraction by 100%.
5To find a percentage of a quantity, convert the percentage to a fraction (divide by 100) and then multiply by the quantity.

Worked examples

Example 1

Express 3/4 as a percentage.

ITo convert a fraction to a percentage, we multiply the fraction by 100%.

II3/4 = (3/4) × 100%

IIISimplify the expression:

IV3/4 × 100% = 3 × (100 ÷ 4)%

V3 × 25% = 75%

Answer

75%

Remember to include the '%' symbol in your final answer.

Example 2

Find 20% of 60.

IFirst, convert the percentage into a fraction:

II20% = 20/100

IIINow, multiply this fraction by the given quantity:

IV20/100 × 60

VSimplify the expression:

VI(20 × 60) / 100

VII1200 / 100

VIII12

Answer

When finding a percentage of a quantity, the answer is a number, not a percentage.

Example 3

In a basket of 50 fruits, 30% are mangoes. How many mangoes are there in the basket?

ITotal number of fruits = 50

IIPercentage of mangoes = 30%

IIITo find the number of mangoes, we need to calculate 30% of 50.

IVConvert 30% to a fraction: 30/100

VMultiply the fraction by the total number of fruits:

VI(30/100) × 50

VIISimplify the expression:

VIII(30 × 50) / 100

91500 / 100

1015

Answer

There are 15 mangoes in the basket.

Always write the final answer in a complete sentence for word problems.

Common mistakes

✗Forgetting to write the '%' symbol when the answer is a percentage.
✗Incorrectly writing a percentage as a fraction (e.g., writing 20% as 20 instead of 20/100).
✗Making errors in simplifying fractions or multiplication.
✗Confusing the percentage value with the actual quantity (e.g., thinking 20% of 50 is 20, not 10).

Exam tips

★Always show all your working steps clearly, as marks are often awarded for method.
★Remember to include the '%' symbol in your final answer if the question asks for a percentage.
★Simplify fractions before performing multiplication to make calculations easier and reduce errors.
★Read the question carefully to understand what is being asked – whether it's a percentage or a quantity.

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