Learn: Percentages

Welcome!Today we'll learn about percentages, a key concept in maths. Percentages are used in everyday life, from calculating discounts to working out interest rates. Let's break it down step by step!

What are percentages?A percentage is a way of expressing a number as a fraction of 100. For example, 25% means 25 out of 100, or 25 divided by 100, which equals 0.25. Percentages are useful for comparing values and are often seen in sales, statistics, and financial calculations.

Converting percentages to decimalsTo convert a percentage to a decimal, divide the percentage by 100. For example, 25% becomes 0.25 (25 ÷ 100 = 0.25). This is useful for calculations involving percentages, such as finding a fraction of a number.

Calculating percentages of an amountTo find a percentage of an amount, multiply the amount by the decimal equivalent of the percentage. For example, to find 20% of £50, multiply £50 by 0.2 (50 × 0.2 = £10).

Increasing and decreasing by a percentageTo increase an amount by a percentage, multiply the amount by (1 + decimal equivalent of the percentage). For example, to increase £100 by 20%, calculate £100 × 1.2 = £120.To decrease an amount by a percentage, multiply the amount by (1 - decimal equivalent of the percentage). For example, to decrease £100 by 20%, calculate £100 × 0.8 = £80.

Reverse percentagesReverse percentages are used when you need to find the original amount before a percentage increase or decrease. To find the original amount after an increase, divide the new amount by (1 + the percentage as a decimal). For example, if the new price is £120 after a 20% increase, divide £120 by 1.2 to get the original price: £120 ÷ 1.2 = £100.

Review Time!Great work! You've learned about percentages, including how to calculate them, convert them, and work with increases, decreases, and reverse percentages. Let's test your understanding with a few questions.