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) * (3/4)c = (2/4)c = (1/2)c

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

Practice is key: Work through many examples to get comfortable with this method.