Learn: Ratio and Proportion

Welcome!Today, we'll explore ratio and proportion, an important concept in iGCSE Mathematics. These ideas help us compare quantities and solve problems involving parts and wholes.

What is a Ratio?A ratio compares two or more values. For example, if there are 2 apples and 3 oranges in a basket, the ratio of apples to oranges is 2:3. Ratios help us describe how quantities relate to each other.

What is Proportion?Proportion is when two ratios are equal. For example, if £2 buys 4 apples, then £4 will buy 8 apples. The two ratios, 2:4 and 4:8, are equivalent. Proportion helps us solve problems involving scaling or sharing quantities.

Dividing a Quantity in a Given RatioTo divide a quantity in a given ratio, add the parts of the ratio, then divide the quantity by this total. Multiply each part by the result to find its share. For example, to divide £60 in a 2:3 ratio, add 2+3=5, divide £60 by 5 = £12, then multiply £12 by 2 (first part) and £12 by 3 (second part).

Working with PercentagesA percentage is a way to express a number as a part of 100. For example, 25% is the same as 25 out of 100, or 0.25 as a decimal. Percentages are useful for comparisons and calculating increases or decreases.

Calculating Percentage ChangeTo calculate percentage change, subtract the old value from the new value to get the change. Then divide the change by the original value and multiply by 100. For example, if a price increases from £50 to £60, the change is £10. The percentage change is (10 ÷ 50) × 100 = 20%.

Review Time!Great work! You've learned about ratios, proportions, and percentages. Now let's test your understanding with a few questions.