Cross-Multiplying
Part of the Fundamentals section of Coddy's Algebra journey. Lesson 39 of 64.
Sometimes an equation is one fraction equal to another, like x/4 = 3/8. You can multiply both sides by both denominators to clear everything at once. The shortcut is called cross-multiplying: the top of the left fraction times the bottom of the right equals the top of the right fraction times the bottom of the left.
8x = 12
x = 3/2
Check the answer: (3/2)/4 = 3/8. The answer is a fraction. A solution does not have to be a whole number.
Cross-multiplying is the same as multiplying both sides by both denominators, as long as neither denominator is zero. Use it only when each side is a single fraction. In x/4 + 1 = 3/8 the left side has two terms, so first add them into one fraction, or multiply every term by the common denominator 8.
Challenge
MediumSolve the equation x/6 = 5/4 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