Ratios and Rates

Lesson

In Keeping it Simple, we introduced the concept of simplifying ratios. Remember what we are trying to do is express ratios in the lowest possible whole numbers. So if our ratios have fractions, decimals, numbers with common factors or mixed units of measurements, we can simplify them.

We can also simplify ratios that have algebraic variables (in other words letters not numbers) in just the same way.

**Question**: Simplify the ratio $3x:5x$3`x`:5`x`

**Think:** $x$`x` is a common factor of $3x$3`x` and $5x$5`x` because it represents the same value on both sides.

**Do:**

$3x:5x$3x:5x |
$=$= | $3:5$3:5 | divide both sides by $x$x |

Remember to check both the numbers and algebraic values to see if they can be simplified.

Simplify the ratio $10x:20x^2$10`x`:20`x`2

Simplify the ratio $75xy:55xy$75`x``y`:55`x``y`.

Apply direct and inverse relationships with linear proportions

Apply numeric reasoning in solving problems