Simplifying Ratios

MAIN IDEA

Ratios compare the sizes of two groups. We can simplify a ratio if both parts share a common factor

Ratio

A comparison of two numbers (like 60 to 24)

Simplified Ratio

The same comparison, but using smaller numbers

GCF

Greatest Common Factor, the biggest number both parts share

RULES FOR SIMPLIFYING

Check if both numbers share a common factor → Divide both parts by the same number → If possible, use the GCF to simplify in one step → Your ratio is simplest when both parts share no common factors (except 1)

EXAMPLE: Simplify 60 blueberries to 24 cherries

Step 1: Find the GCF of 60 and 24 → GCF = 12 | Step 2: Divide both parts by 12 → 60 ÷ 12 = 5 and 24 ÷ 12 = 2

Answer

The simplified ratio is 5 blueberries to 2 cherries

FINAL TIP

Always double check your simplified ratio. If the numbers still share a factor, divide again