Learn: Ratio and Proportion

Welcome!Today we'll explore ratio and proportion. These are essential concepts for solving problems involving comparisons and scaling. Let's break it down step by step!

What is a Ratio?A ratio compares two or more quantities, showing how many times one value contains another. For example, the ratio 3:2 means for every 3 of one item, there are 2 of another.

What is Proportion?Proportion is the equality of two ratios. It shows that two fractions or comparisons are equivalent. For example, if 1:2 = 2:4, this is a proportion.

Simplifying RatiosTo simplify a ratio, divide both parts by their greatest common divisor (GCD). For example, the ratio 12:16 simplifies to 3:4 because both numbers can be divided by 4.

Direct ProportionIn a direct proportion, as one quantity increases, the other increases at the same rate. For example, if 3 pens cost £6, then 6 pens cost £12.

Inverse ProportionIn an inverse proportion, as one quantity increases, the other decreases. For example, if 4 workers complete a task in 6 hours, 2 workers will take 12 hours to complete the same task.

Using Ratios in Real LifeRatios are used in recipes, maps, and mixing solutions. For example, if a recipe calls for 2 parts flour to 1 part sugar, you can scale it by doubling or halving the amounts.

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