Splitting the Fraction
Part of the Exponents & Polynomials section of Coddy's Algebra journey. Lesson 54 of 64.
Division distributes over addition from the other side: a sum divided by something is each term divided by it. (6x^2 + 9x)/3 splits into 6x^2/3 + 9x/3, two small divisions instead of one large one.
Each piece is coefficient arithmetic: 6/3 = 2 and 9/3 = 3, so the quotient is 2x^2 + 3x. The powers of x ride through untouched, because the divisor 3 carries no x to cancel.
The check is multiplication, as it has been since Fundamentals: 3(2x^2 + 3x) = 6x^2 + 9x. Division and distribution are the same fact read in opposite directions.
Challenge
MediumDivide: (10x^2 + 8x)/2.
Try it yourself
Simplify the expression
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Exponents & Polynomials
1What a Power Is
Repeated MultiplicationSquares and CubesPowers of Negative NumbersWhere the Minus LivesRecap: First Powers4Power of a Power
A Power Raised AgainWhy Exponents MultiplyProduct Rule or Power Rule?The Rule in LettersRecap: Power of a Power2The Product Rule
Multiplying Same BasesWith CoefficientsMore Than Two FactorsThe Rule in LettersRecap: The Product Rule5Product and Quotient Powers
Every Factor Gets the PowerWith a Number InsideA Power of a QuotientAll Three Rules TogetherRecap: Products and Quotients8What a Polynomial Is
Terms with PowersThe DegreeLike Terms, Only StrongerRecap: Meet the Polynomials11Dividing by a Monomial
Splitting the FractionDividing by a Variable TermBigger SplitsCancel with CareRecap: Dividing3The Quotient Rule
Dividing Same BasesWhy Exponents SubtractWith CoefficientsThe Rule in LettersRecap: The Quotient Rule6Zero and Negative Exponents
The Zero ExponentZero at WorkNegative Means ReciprocalWriting Without NegativesPowers of TenRecap: Zero and Negative