Cross-Multiplying
Part of the Fundamentals section of Coddy's Math journey. Lesson 39 of 64.
When an equation is one fraction equal to another, x/4 = 3/8, multiplying both sides by both denominators clears everything at once. The shortcut is cross-multiplying: top of the left times bottom of the right equals top of the right times bottom of the left.
8x = 12
x = 3/2
Check: (3/2)/4 = 3/8. The answer is a fraction, and that is fine: solutions do not have to be whole numbers.
Cross-multiplying is only a shortcut for "multiply both sides by both denominators", so it is legal exactly when the equation is a single fraction on each side. x/4 + 1 = 3/8 is not that shape; clear denominators there instead.
Challenge
Solve 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