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How to Simplify Fractions With Letters

Fractions are confusing enough for many students, but throw in a few variables, letters that represent unknown values, and most just throw their hands up in surrender. The good thing about simplifying fractions with letters is that the rules of simplifying, or reducing, are the same as the rules for standard fractions. In order to simplify the fractions, there must be a common term between both the numerator and the denominator that can cancel out of the problem and leave the lowest possible remainder as the simplified answer.

Instructions

  1. Simplifying Basic Fractions with Variables

    • 1

      Simplify 4b/2b. Divide both terms by 2 for 2b/b. The fraction b/b will simplify to 1, so 2 x 1 = 2, which is the simplified answer.

    • 2

      Examine the expression 15b/3. Since fractions are another form of division problem, you can reduce the solution by dividing. Divide the numerator by the denominator: (15 x b) ÷ 5 = 3b, which is the simplified answer.

    • 3

      Examine the expression 60f/48h. Sixty and 48 are both multiples of 12. Divide both terms by 12 for 5f/4h.

    Simplifying Fractions with Variables and Exponents

    • 4

      Simplify x^4/x^2. Exponent division rules tell you to subtract the exponents. Subtract 4 -- 2 = 2, so x^4/x^2 simplifies to x^2.

    • 5

      Examine the expression: 2t/3 x 12/t. Multiply straight across for 24t/3t, which simplifies to 8t.

    • 6

      Simplify x^2/x + y^3/y^2. Follow the rules of exponents for the simplified solution of x + y.

    Simplifying Fractions with Variables and Polynomials

    • 7

      Examine the expression (r^2 -- 9)/(4r^2 + 16r + 12) x (r + 1)/(r + 4). This is a very complex fraction problem since the first fraction has a binomial as the numerator and a trinomial as the denominator and the second fraction has a binomial in both the numerator and denominator.

    • 8

      Factor out the numerator: r^2 -- 9 = (r + 3)(r -- 3). This will be the numerator. Factor out the denominator: 4r^2 + 16r + 12 = 4(r^2 + 4r + 3), which factors further to 4(r + 3)(r + 1). This is the denominator.

    • 9

      Write the new fraction problem: (r + 3)(r -- 3)/4(r + 3)(r + 1) x (r + 1)/(r + 4.) Simplify the expression to read as one fraction, written as a product of the terms: (r + 3)(r -- 3)(r + 1) over 4(r + 3)(r + 1)(r + 4).

    • 10

      Notice that the numerator and denominator have two common terms, (r + 3) and (r + 1). Since (r + 3) ÷ (r + 3) and (r + 1) ÷ (r + 1) both equal 1, the terms will cancel out. Cross them out and write 1 in their places. Your problem should read: (1)(r -- 3)(1) over 4(r + 4).

    • 11

      Multiply across for the simplified solution (r -- 3) over 4(r + 4)

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