How Many Fit
Part of the Factors & Fractions section of Coddy's Pre-Algebra journey. Lesson 39 of 58.
A division asks a question: how many of one number fit into another? 12 / 3 is 4 because four 3s fit into 12. Ask the same question with a fraction: 3 ÷ 1/4 asks how many quarters fit into 3.
3 wholes, each holding 4 quarters: 12 quarters in all.
Each whole holds 4 quarters, so 3 wholes hold 12 quarters. 3 ÷ 1/4 is 12. In the same way, 2 ÷ 1/3 is 6, because each whole holds 3 thirds.
Notice that the answer is bigger than the number you started with. That surprises people, because dividing by a whole number makes things smaller. But when the pieces are smaller than 1, more of them fit than there are wholes, so dividing by a fraction below 1 makes the answer bigger.
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
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