When I was in Year 9 math, comparing different ratios felt a bit tricky at first. But after some practice, I found a few helpful tricks to make it easier to understand ratios and compare them. Here are some tips that really worked for me:

1. Change to a Fraction

One easy way to compare ratios is by turning them into fractions. For example, if you have a ratio like 2:3 and another like 4:5, change them like this:

• For 2:3, write it as $\frac{2}{3}$.
• For 4:5, write it as $\frac{4}{5}$.

Now, it’s easier to compare these fractions. You can either find a common denominator or change them to decimals.

2. Find the Decimal Version

Calculating the decimal version of a ratio can make things much clearer, especially with bigger numbers. Using the same examples:

• $\frac{2}{3} \approx 0.67$
• $\frac{4}{5} = 0.80$

Now it’s super clear—$0.67 < 0.80$, so 2:3 is less than 4:5.

3. Cross-Multiplication

If you want to compare two ratios, cross-multiplication is a cool trick. Let’s say you want to compare 3:4 and 5:6. Set it up like this:

$$\text{Compare } \quad \frac{3}{4} \quad \text{and} \quad \frac{5}{6}$$

Now, cross-multiply:

• $3 \times 6 = 18$
• $4 \times 5 = 20$

Since $18 < 20$, we know that $3:4 < 5:6$.

4. Simplifying Ratios

Sometimes, you can simplify the ratios before comparing them. If you have 12:16 and 9:12, simplify them like this:

• 12:16 simplifies to 3:4 (by dividing both by 4).
• 9:12 simplifies to 3:4 (by dividing both by 3).

Now you see they are equal!

5. Use Visuals

Sometimes it helps to see the ratios visually. Drawing pie charts or bar graphs can give you a better picture of how the ratios compare. For example, if you have ratios that make up parts of a whole, drawing them can show how they relate. This is super helpful in group projects or presentations when you want everyone to see the comparison quickly.

6. Practice with Real-Life Examples

Lastly, try using ratios in everyday situations—like cooking, sports stats, or shopping deals. The more you use ratios in real life, the easier it will be to compare them in math.

Overall, comparing ratios is all about finding a method that works for you. Keep practicing these tips, and soon it will feel like second nature!