Understanding Ratios in Math

Reducing Ratios to Simplest Form

You'll find ratio simplification everywhere in maths, so mastering this skill now will save you loads of time later. The key is finding the highest common factor of both numbers and dividing through.

For basic ratios like 15:18, spot that both numbers share a factor of 3. Divide both sides: 15÷3 = 5 and 18÷3 = 6, giving you 5:6 in its simplest form.

When dealing with decimals in ratios, multiply both sides by 10 (or 100) first to eliminate decimal places. For 2.4:3.6, multiply by 10 to get 24:36, then divide by 12 to reach the simplest form of 2:3.

Mixed units need converting to the same unit before simplifying. For 24mm:1.2cm, convert 1.2cm to 12mm first, giving 24:12, which simplifies to 2:1.

Quick tip: Always check if you can divide both numbers by the same factor - start with obvious ones like 2, 3, 5, or 10!

Writing Ratios as Fractions

Converting ratios to fractions is actually simpler than it looks - you just need to know what you're comparing. This skill is crucial for probability questions and percentage problems.

To write one part as a fraction of another part, simply put the first number over the second. If you have a ratio of 3:5, then the first part as a fraction of the second part is 3/5.

For finding one part as a fraction of the total, add up both parts of the ratio first. With 3:5, the total is 8, so the first part represents 3/8 of the whole, and the second part represents 5/8.

Remember: Part-to-part fractions use the original ratio numbers, but part-to-whole fractions need you to find the total first!