Percentages

Percentages

Percentages are a way of expressing a number as a fraction of 100. They are widely used in various fields, such as finance, statistics, and everyday life. Understanding percentages is essential for analysing data and making informed decisions.

Understanding Percentages

A percentage is a ratio that compares a number to 100. For example, 25% (read as twenty-five percent) means 25 out of 100. To convert a percentage to a decimal, divide it by 100. For example:

25% = 25 ÷ 100 = 0.25

Similarly, to convert a decimal back to a percentage, multiply by 100:

0.25 × 100 = 25%

Calculating Percentages

To find a percentage of a number, use the following formula:

Percentage = (Part / Whole) × 100

For example, if you want to find 20% of 150, follow these steps:

1. Convert the percentage to a decimal: 20% = 20 ÷ 100 = 0.20.
2. Multiply the decimal by the whole number: 0.20 × 150 = 30.

Thus, 20% of 150 is 30.

Finding the Whole from a Percentage

Sometimes, you may know the percentage and the part, and you need to find the whole. Use the formula:

Whole = Part / (Percentage / 100)

For example, if 30 is 20% of a number, you can find the whole number as follows:

1. Convert the percentage to a decimal: 20% = 20 ÷ 100 = 0.20.
2. Use the formula: Whole = 30 / 0.20 = 150.

The whole number is 150.

Percentage Increase and Decrease

Percentage increase and decrease are common in finance and sales. To calculate the increase or decrease in percentage, use these formulas:

Percentage Increase = (New Value - Old Value) / Old Value × 100

Percentage Decrease = (Old Value - New Value) / Old Value × 100

Example of Percentage Increase

Suppose the price of a shirt increases from R200 to R250. To find the percentage increase:

1. Calculate the difference: R250 - R200 = R50.
2. Use the formula: Percentage Increase = (R50 / R200) × 100 = 25%.

The price increased by 25%.

Example of Percentage Decrease

If the price of a shirt decreases from R250 to R200, the percentage decrease is calculated as follows:

1. Calculate the difference: R250 - R200 = R50.
2. Use the formula: Percentage Decrease = (R50 / R250) × 100 = 20%.

The price decreased by 20%.

Applications of Percentages

Percentages are used in various real-life situations. Here are some common applications:

• Finance: Interest rates on loans and savings accounts are often expressed as percentages.
• Sales: Discounts during sales are typically given as percentages off the original price.
• Statistics: Data is often presented as percentages to show proportions or comparisons.

Working with Percentage Problems

When solving percentage problems, follow these steps:

1. Read the problem carefully.
2. Identify the known values (part, whole, percentage).
3. Choose the appropriate formula.
4. Perform the calculations step by step.

Example Problem

A store has a sale where all items are 15% off. If an item originally costs R400, how much do you pay after the discount?

1. Calculate the discount amount: 15% of R400.
2. Convert percentage to decimal: 15% = 0.15.
3. Calculate the discount: 0.15 × R400 = R60.
4. Subtract the discount from the original price: R400 - R60 = R340.

You pay R340 after the discount.

Practice Problems

To become proficient with percentages, practice solving various problems. Here are some examples:

1. What is 35% of R600?
2. If you scored 45 out of 60 on a test, what percentage did you achieve?
3. A product costs R500 and is on sale for 20% off. What is the sale price?
4. The population of a town increased from 8,000 to 10,000. What was the percentage increase?

Summary

• A percentage is a ratio comparing a number to 100.
• To calculate a percentage of a number, use the formula: Percentage = (Part / Whole) × 100.
• To find the whole from a part and percentage, use the formula: Whole = Part / (Percentage / 100).
• Percentage increase and decrease are calculated using specific formulas.
• Practice is essential for mastering percentage problems.

Check your understanding

1. What is 50% of R800?
2. If a car's value decreased from R120,000 to R90,000, what is the percentage decrease?
3. How do you convert 75% to a decimal?
4. A student scored 70 out of 80 on a test. What percentage did they achieve?