Understanding and Working with Ratios

Ratios are your tool for comparing two quantities and showing their relative sizes. Think of them like a recipe - if you need 2 cups of flour to 3 cups of milk, that's a 2:3 ratio.

You can make ratios simpler by finding the greatest common divisor (GCD) and dividing both numbers by it. For example, 6:9 becomes 2:3 when you divide both sides by 3. This makes calculations much easier!

Ratios work just like fractions too. The ratio 3:4 can be written as 3/4, which helps when you're doing calculations. Sometimes you'll need ratios in the form n:1 or 1:n - just divide both terms by one of them, like turning 4:8 into 1:2.

Top Tip: Always check if you can simplify your ratio first - it makes everything else much easier!

Sharing Amounts and Solving Problems

When you need to share amounts using ratios, there are three main situations you'll face. If you know the total amount, add up the ratio parts, divide the total by this sum, then multiply by each part.

Got one part but need the other? Use the ratio relationship to find your multiplier, then calculate the missing piece. When you only know the difference between parts, divide this difference by the difference in the ratio to find your multiplier.

Word problems become straightforward once you identify the ratio and what information you're given. Set up your equation based on the ratio relationship and solve step by step.

Combining ratios means finding a common term between them. Adjust both ratios so they share this term, then write them as one extended ratio. It's like finding a common denominator in fractions!

Remember: Take your time reading word problems - identifying what you know and what you need to find makes the maths much clearer.