7.3 Ratios in their Simplest Form

We reduce a ratio to its simplest form by dividing both terms by their HCF (highest common factor).

• Poster A: 80 : 60. The HCF of 80 and 60 is 20. Dividing, \;80 : 60 = 4 : 3.
• Poster D: 120 : 90. The HCF is 30, so \;120 : 90 = 4 : 3.

Both reduce to 4 : 3, confirming A and D are proportional. And poster C: 40 : 30 = 4 : 3 as well.

What about the two odd ones?

• Poster B: 60 : 40 = 3 : 2.
• Poster E: 80 : 80 = 1 : 1.

Neither 3:2 nor 1:1 equals 4:3, so B and E are not proportional to the others, exactly what our eyes reported.

Proportion When two ratios are the same in their simplest form, we say they are in proportion (or proportional), and write them with the double colon ::. Thus a : b :: c : d \quad\text{means}\quad a:b \text{ and } c:d \text{ are proportional.} For example, 80 : 60 :: 40 : 30 and 80 : 60 :: 120 : 90.

Use the explorer below to type any two ratios and see at a glance whether they are in proportion.

Are these two ratios proportional?

: :: :

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