Different Denominators
Part of the Factors & Fractions section of Coddy's Pre-Algebra journey. Lesson 29 of 58.
1/3 + 1/5 cannot be added as it stands. Thirds and fifths are different sizes, and you can only count pieces that are the same size. So first rename both fractions with the same denominator.
The new denominator must be a multiple of 3 and of 5, so that both fractions can be renamed. 15 works: 1/3 is 5/15, top and bottom times 5, and 1/5 is 3/15, top and bottom times 3. Now the pieces match: 5/15 + 3/15 is 8/15.
On the board, the renamed line 5/15 + 3/15 is accepted straight away, because renaming never changes a value. Any common multiple of the denominators will do, and multiplying the two denominators always gives one.
Challenge
Work out 1/4 + 1/6. Rename both fractions over a common denominator first, then add.
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 Fractions3GCF and LCM
Greatest Common FactorGCF from Prime FactorsLeast Common MultipleLCM from Prime FactorsGCF or LCM?Recap: GCF and LCM6Adding and Subtracting
Same DenominatorDifferent DenominatorsSubtracting FractionsThe Least Common DenominatorNegative ResultsRecap: Adding and Subtracting