Percent Equations
Part of the Fundamentals section of Coddy's Math journey. Lesson 44 of 64.
"20% of a number is 15." Percent means per hundred, so 20% is 20/100, which is 1/5 or 0.2, and "of" is multiplication:
20% × x = 15
Rewrite the percent as a fraction over 100 and it is a fraction-coefficient equation: 1/5 x = 15, multiply both sides by 5, x = 75. Check: a fifth of 75 is 15.
Every "what number" percent question has this shape. "12 is 30% of what?" is 30% × x = 12; "what is 15% of 80" is x = 15% × 80 and needs no solving at all, only arithmetic. Write the sentence as an equation and the moves take over.
Challenge
Solve the equation 25% × 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 Equations2One-Step Equations
Undoing AdditionUndoing SubtractionUndoing MultiplicationUndoing DivisionInverse OperationsRecap: One-Step Equations5Tidying First
Like TermsTerms and Numbers MixedThe Distributive PropertyDistributing a SubtractionTidy, Then SolveRecap: Tidying First8Decimals and Percent
Decimal CoefficientsTwo-Step with DecimalsAdding a PercentPercent EquationsRecap: Decimals