Cancel First
Part of the Factors & Fractions section of Coddy's Pre-Algebra journey. Lesson 35 of 58.
(4/15) × (5/6) multiplies to (4 × 5)/(15 × 6), which is 20/90, and then you still have to simplify it. There is a shorter road: simplify before you multiply.
Every top ends up on the top of the product and every bottom on the bottom, so any top can be simplified with any bottom, even the other fraction's. 4 and 6 share a 2: they become 2 and 3. 5 and 15 share a 5: they become 1 and 3. The product is now (2/3) × (1/3), which is 2/9.
This is called cancelling. It is the same division by a shared factor that simplifying does, done while the numbers are still small. If you cancel every shared factor first, the product comes out in lowest terms. Two tops can never cancel with each other, though: dividing two tops changes the value.
Challenge
Work out (4/9) × (3/8). Cancel first, then multiply.
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