Simplifying Fractions
Part of the Factors & Fractions section of Coddy's Pre-Algebra journey. Lesson 24 of 58.
12/30 has a simpler name. 12 and 30 are both divisible by 6, their greatest common factor. Divide the top and the bottom by 6: 12 divided by 6 is 2, and 30 divided by 6 is 5. So 12/30 is 2/5.
Why is that allowed? It is the last lesson run backwards: multiply the top and the bottom of 2/5 by 6 and you are back at 12/30. Dividing both by the same number makes the pieces bigger and fewer, and the amount stays exactly the same.
A fraction is in lowest terms when its top and bottom share no factor except 1. 2 and 5 share none, so 2/5 is finished. Dividing by the GCF gets there in one step, because it removes every shared factor at once. The board accepts a line like 6/15, since its value is right, but it will not call the problem finished until the fraction is in lowest terms.
Challenge
Write 18/24 in lowest terms. Find the GCF of the top and the bottom, divide both by it, and type the result.
Try it yourself
Simplify the expression
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Factors & Fractions
1Factors and Multiples
What a Factor IsFactor PairsDivisibility RulesMultiplesPrime or CompositeRecap: Factors and Multiples4What a Fraction Is
Parts of a WholeFractions on the LineA Fraction of a NumberImproper FractionsRecap: What a Fraction Is7Multiplying Fractions
Top Times TopCancel FirstWhole Times FractionA Fraction of a FractionRecap: Multiplying Fractions10Fractions in Stories
Part of a GroupWhat Is LeftSharing a FractionScaling a RecipeRecap: Fraction Stories2Prime Factorization
Factor TreesUsing ExponentsOne Tree per NumberBigger NumbersRecap: Prime Factorization5Equivalent Fractions
Same Amount, New NameSimplifying FractionsSimplify in StepsComparing FractionsRecap: Equivalent Fractions