 New Zealand
Level 6 - NCEA Level 1

Simplifying Ratios with Algebraic Terms

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.

Examples

Question 1

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

Think: $x$x is a common factor of  $3x$3x and $5x$5x 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.

Question 2

Simplify the ratio $10x:20x^2$10x:20x2

Question 3

Simplify the ratio $75xy:55xy$75xy:55xy.

Outcomes

NA6-1

Apply direct and inverse relationships with linear proportions

91026

Apply numeric reasoning in solving problems