Dividing by a Whole Number
Part of the Factors & Fractions section of Coddy's Pre-Algebra journey. Lesson 41 of 58.
A whole number is a fraction over 1, so its reciprocal is 1 over it: 2 is 2/1, and its reciprocal is 1/2. That makes 4/7 ÷ 2 the same as (4/7) × (1/2), which is 4/14, or 2/7 in lowest terms.
It matches what dividing by 2 means: sharing between two, taking half. And half of 4/7 is (1/2) × (4/7), the same multiplication you met in the last chapter, since of means multiply.
When the top divides evenly by the whole number, there is a shortcut: divide the top. 4 sevenths shared between 2 is 2 sevenths. Either way, never divide the bottom: that makes the pieces bigger, so the fraction would grow instead of shrinking.
Challenge
Work out 3/5 ÷ 6. The board writes it with a fraction bar, 3/5 over 6. Multiply by the reciprocal of 6, then simplify.
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 Fractions8Dividing Fractions
How Many FitMultiply by the ReciprocalDividing by a Whole NumberHow Many BagsRecap: Dividing Fractions