Simplify in Steps
Part of the Factors & Fractions section of Coddy's Pre-Algebra journey. Lesson 25 of 58.
You do not need the GCF to simplify. Any factor the top and the bottom share can be divided out, and then you look again. 40/60: both are even, so halve them, 20/30. Both are even again: 10/15. Now both end in 0 or 5, so divide by 5: 2/3.
Why does this land in the same place as the GCF? Dividing by 2, then 2, then 5 divides by 2 × 2 × 5, which is 20, in total, and 20 is the GCF of 40 and 60. The steps just split the GCF into small pieces that are easy to spot.
Stop when the top and the bottom share no factor except 1: 2 and 3 share none, so 2/3 is finished. Quick checks for a shared factor: both even means 2, both ending in 0 or 5 means 5, and both with digits that add up to a multiple of 3 means 3.
Challenge
Simplify 36/48 in steps. Both numbers are even, so start by halving. Type one line per step until the fraction is in lowest terms.
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