A Fraction Coefficient
Part of the Fundamentals section of Coddy's Algebra journey. Lesson 35 of 64.
The equation 2/3 x = 8 says that two thirds of a number is 8. The coefficient of x is the fraction 2/3. To undo a coefficient, you divide both sides by it. Dividing by 2/3 is the same as multiplying by its reciprocal, 3/2, because 2/3 × 3/2 = 1. So multiply both sides by 3/2:
3/2 × 2/3 x = 3/2 × 8
x = 12
Multiplying by the reciprocal turned the coefficient into 1 and left x on its own. Check the answer: two thirds of 12 is 8.
You can also do this in two smaller steps. Multiply both sides by 3 to get 2x = 24, then divide both sides by 2 to get x = 12. Both ways give the same answer. In both, you are done when the coefficient in front of x is 1.
Challenge
MediumSolve 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