A Fraction Coefficient
Part of the Fundamentals section of Coddy's Math journey. Lesson 35 of 64.
2/3 x = 8 means "two thirds of a number is 8". The coefficient is the fraction 2/3, and a coefficient is undone by dividing by it. Dividing by 2/3 is the same as multiplying by its reciprocal, 3/2, because 2/3 × 3/2 = 1:
3/2 × 2/3 x = 3/2 × 8
x = 12
Check: two thirds of 12 is 8.
Two smaller moves reach the same place: multiply both sides by 3 (2x = 24), then divide by 2. Whichever you choose, the target shape is the same as ever: a coefficient of 1 in front of x.
Challenge
Solve the equation 3/5 x = 12 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