Clearing Fractions
Part of the Polynomials & Rational Expressions section of Coddy's Algebra 2 journey. Lesson 37 of 54.
An equation with fractions does not have to keep them. Take x/2 + x/5 = 14. Both 2 and 5 go into 10, so multiply both sides by 10. Every term is multiplied: 10 × x/2 is 5x, 10 × x/5 is 2x, and 10 × 14 is 140.
5x + 2x = 140
Now it is an ordinary equation: 7x is 140, so x is 20. Why is this allowed? Multiplying both sides by the same nonzero number keeps them equal for exactly the same x, so no solution is gained or lost. The number to use is the least common denominator, the smallest number every bottom goes into, which keeps the numbers small.
The common mistake is to multiply only the fractions and leave the 14 alone. Every term on both sides gets multiplied.
Challenge
Solve x/3 + x/4 = 7.
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 Polynomials & Rational Expressions
1Polynomial Long Division
How Long Division WorksOne Term at a TimeA Remainder Left OverA Missing TermDividing by a QuadraticRecap: Long Division7Adding and Subtracting
Same BottomDifferent BottomsSubtractingFactor the Bottoms FirstRecap: Adding Fractions2Remainders and Factors
The Remainder TheoremThe Factor TheoremFinding a Missing NumberUsing a Known FactorRecap: Remainders and Factors5Sign Charts
Between the RootsOutside the RootsA Negative Leading TermReading a Sign ChartRecap: Sign Charts8Rational Equations
Clearing Fractionsx in the BottomCross-MultiplyingA False AnswerOne True, One FalseRecap: Rational Equations