Sixth Grade · Math · week 2

Equivalent ratios and simplest form

Determine whether two ratios are equivalent and reduce a ratio to simplest form using the greatest common factor.

Two ratios are equivalent if they compare amounts in the same way - one is a scaled-up or scaled-down copy of the other. 2:3 and 6:9 are equivalent because multiplying both numbers of 2:3 by 3 gives 6:9.

To check if two ratios are equivalent, see whether there is ONE number you can multiply (or divide) both parts of the first ratio by to get the second ratio.

A ratio is in simplest form when the two numbers share no common factor except 1. Divide both numbers by their greatest common factor (GCF) to simplify: 8:12 has GCF 4, so simplest form is 2:3.

📋 For the teacher
Teach it (10–15 min):
  • Review GCF quickly if it is rusty - it is the biggest number that divides both parts evenly.
  • Show the "same multiplier" test: what times 4 gives 10? There is not a whole number, so simplify both ratios instead and compare.
  • Simplify both ratios to lowest terms and compare - it is the most reliable check.
  • Praise checking work by simplifying rather than guessing.
Talk about it:
  • How do you know two ratios are NOT equivalent?
  • Why does dividing both numbers by the GCF keep the ratio the same?
  • Can you find two equivalent ratios in the kitchen, like cups of two ingredients?

Mastery looks like: They simplify a ratio using the GCF and correctly decide whether two given ratios are equivalent.

Common stumbles: Simplifying only one number in the ratio; dividing by a common factor that is not the GREATEST one and stopping too early.

See it visually

Interactive, spoken-aloud tools that show this idea in motion.

FractionsSlice bars and circles into equal parts and compare them.try →
Homework for this lessonType it, write it with a stylus, or print it for pencil & paper.open →
Records attendance + 15 min of Math for this learner.
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