Learn: Ratio and Proportion

Welcome!Today we'll explore Ratio and Proportion. Ratios compare two quantities, and proportions help us solve problems where two ratios are equal. Let's dive in!

What is a Ratio?A ratio compares two quantities, showing how many times one quantity is related to another. It can be written as 2:3, 2 to 3, or 2/3. For example, if there are 2 apples and 3 oranges, the ratio of apples to oranges is 2:3.

What is Proportion?A proportion is an equation that states two ratios are equal. For example, 2:3 = 4:6 means that 2 apples to 3 oranges is the same ratio as 4 apples to 6 oranges.

Simplifying RatiosTo simplify a ratio, divide both parts of the ratio by their highest common factor (HCF). For example, 12:16 simplifies to 3:4 since the HCF of 12 and 16 is 4.

Using Ratios in Real LifeRatios are used in recipes, maps, and mixing solutions. For example, if a recipe says 'mix flour and sugar in a 2:1 ratio', it means for every 2 parts of flour, use 1 part sugar.

Dividing Quantities in a Given RatioTo divide a quantity in a given ratio, first add the parts of the ratio together. Find the value of one part by dividing the total by the sum of the ratio, then multiply this value by each part of the ratio. For example, to divide £60 into a 2:3 ratio, calculate (60 ÷ (2+3)) = £12. Then, 2 parts = £24 and 3 parts = £36.

Percentage ChangePercentage change measures how much a value increases or decreases compared to its original value. Use the formula: Percentage change = \frac{\text{{Change}}}{\text{{Original}}} \times 100

Direct ProportionTwo quantities are in direct proportion when they increase or decrease together at the same rate. For example, if you buy more apples, you pay more money. The formula is: y \propto x or y = kx (where k is the constant of proportionality).

Inverse ProportionTwo quantities are in inverse proportion when one increases while the other decreases. For instance, if you increase the number of workers on a job, the time to complete the job decreases. The formula is: y \propto \frac{1}{x} or y = \frac{k}{x}.

Review Time!Great work! You've learned about ratios, proportions, percentage change, and direct/inverse proportion. Now let's test your understanding with a few questions.

Well done!You’ve completed the lesson on Ratio and Proportion. Keep practising to master this topic and apply it to real-world situations. Great work today!