Understanding Cross-Multiplication in Proportions

Cross-multiplication is a helpful way to solve problems involving ratios in Year 10 Math. Here’s how to use this technique step-by-step:

Step 1: Set Up the Proportion

Start with a proportion that shows two ratios are equal.

For example, you might see something like this:

$\frac{a}{b} = \frac{c}{d}$

Make sure the two fractions are lined up correctly.

Step 2: Cross-Multiply

Cross-multiplication means you multiply the top number of one fraction by the bottom number of the other fraction.

Here’s how to do it:

• Multiply a (the top number of the first fraction) by d (the bottom number of the second fraction).

• Multiply b (the bottom number of the first fraction) by c (the top number of the second fraction).

Now, you will have this equation:

$a \times d = b \times c$

Step 3: Solve the Equation

Next, you’ll want to rearrange this equation to find the unknown variable (like a, b, c, or d).

For example, if you need to find c, you can change the equation to:

$c = \frac{a \times d}{b}$

Step 4: Check Your Solution

Once you have the answer, plug it back into the original ratios. This helps you make sure both sides are equal and that your work is accurate.

Example

Let’s say you have this proportion:

$\frac{3}{4} = \frac{x}{8}$

Using cross-multiplication, you would do:

$3 \times 8 = 4 \times x$

This gives you:

$24 = 4x$

To find x, divide both sides by 4:

$x = 6$

Remember, always double-check your results to make sure they match the original ratios!