Clearing One Denominator
Part of the Fundamentals section of Coddy's Math journey. Lesson 36 of 64.
x/5 + 2 = 6 can be solved as a two-step equation (subtract 2, multiply by 5). There is a habit worth learning here that pays off when fractions multiply: clear the denominator first. Multiply every term on both sides by 5:
5 × x/5 + 5 × 2 = 5 × 6
x + 10 = 30
x = 20
Every term gets multiplied, not just the fraction: the 2 became 10 and the 6 became 30. Miss one and the balance tips. After the multiplication there are no fractions left, and the rest is the equation-solving you already know.
Challenge
Solve 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