Year 8: Finding values based on multiple ratios

What are ratios?

A ratio compares two amounts. It's usually written as a colon (:) between the two numbers, like 2:3. This means for every 2 of something, there are 3 of something else.

Finding values with multiple ratios

Sometimes you'll be given a problem with more than one ratio. Here’s how to solve them:

Step 1: Understand the problem

Clearly identify what you’re trying to find out. What is the unknown value?

Step 2: Set up equations

Create equations based on the ratios given. For example, if you have ratios a:b and c:d, you can create equations like:

• $a/b=c/d$

Step 3: Solve for the unknown

Now you have an equation you can solve for the unknown variable. Use algebraic techniques like cross-multiplication or substitution.

Example:

If a:$b=2$:3 and b:$c=3$:4, find a:c.

1. From a:$b=2$:3, we get $a=(2/3)b$

2. Substitute $b=(3/4)c$ into $a=(2/3)b$. So, $a=(2/3)\times (3/4)c=(2/4)c=(1/2)c$

3. Therefore, a:$c=(1/2)c$ : $c=1$:2