Two Denominators
Part of the Fundamentals section of Coddy's Algebra journey. Lesson 37 of 64.
The equation x/2 + x/3 = 10 says that half a number plus a third of it is 10. It has two denominators, 2 and 3. To clear both, multiply every term by a number that both 2 and 3 divide into. The smallest such number is their least common multiple, which is 6:
6 × x/2 + 6 × x/3 = 6 × 10
3x + 2x = 60
5x = 60
x = 12
One multiplication by 6 removed both fractions. Check the answer: 12/2 + 12/3 = 6 + 4 = 10.
Any common multiple of the denominators clears the fractions, as long as it is not zero. The least common multiple keeps the numbers small. You can also add the two fractions first: x/2 + x/3 is 5/6 x, so the equation becomes 5/6 x = 10. Then divide both sides by 5/6. Both methods give x = 12.
Challenge
MediumSolve the equation x/2 + x/5 = 14 for x.
Try it yourself
Solve for x
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Fundamentals
1What an Equation Is
The EquationFinding the UnknownThe Same to Both SidesSolved Means AloneRecap: First Equations4Two-Step Equations
Two Layers to UndoSubtract, Then DivideAdd, Then DivideA Division InsideNegatives in Two StepsRecap: Two-Step Equations7Fractions in Equations
A Fraction CoefficientClearing One DenominatorTwo DenominatorsA Fraction Around a SumCross-MultiplyingRecap: Fractions2One-Step Equations
Undoing AdditionUndoing SubtractionUndoing MultiplicationUndoing DivisionInverse OperationsRecap: One-Step Equations5Tidying First
Like TermsTerms and Numbers MixedThe Distributive PropertyDistributing a SubtractionTidy, Then SolveRecap: Tidying First