Multiply by the Reciprocal
Part of the Factors & Fractions section of Coddy's Pre-Algebra journey. Lesson 40 of 58.
Flip a fraction upside down and you get its reciprocal: the reciprocal of 2/5 is 5/2. To divide by a fraction, multiply by its reciprocal. 7/10 ÷ 2/5 becomes (7/10) × (5/2), which is 35/20, and that simplifies to 7/4.
Why does flipping work? Dividing by 1/5 asks how many fifths fit, and 5 fit in every whole, so it is the same as multiplying by 5. Dividing by 2/5 counts pieces twice as big, so half as many fit: multiply by 5, then halve. Multiplying by 5 and halving is multiplying by 5/2.
Only the divisor, the fraction you divide by, is flipped; the first fraction stays as it is. On the board a division is written with a fraction bar, so a fraction divided by a fraction shows as one fraction stacked over another.
Challenge
Work out 2/3 ÷ 4/9. The board writes it with a fraction bar, 2/3 over 4/9. Flip the divisor, multiply, 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