Clearing One Denominator
Part of the Fundamentals section of Coddy's Algebra journey. Lesson 36 of 64.
To solve x/5 + 2 = 6, you could subtract 2 from both sides and then multiply both sides by 5. There is another way. You can clear the denominator first: multiply every term on both sides by 5. This removes the fraction before you get x on its own.
5 × x/5 + 5 × 2 = 5 × 6
x + 10 = 30
x = 20
Multiplying by 5 removed the fraction, and the rest is an equation with whole numbers.
Every term gets multiplied by 5, not only the fraction. The 2 became 10 and the 6 became 30. If you miss a term, the two sides are no longer equal. After the multiplication there are no fractions left, and you solve the rest the way you already know.
Challenge
MediumSolve the equation x/3 + 4 = 10 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