Q&A for How to Simplify Complex Fractions

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  • Question
    How do I solve 5/6 divided by 1 1/4?
    Donagan
    Top Answerer
    That's 5/6 divided by 5/4, which is solved by multiplying 5/6 by 4/5, which is 20/30 or 2/3.
  • Question
    How do I solve 4/1/4 - 5/2?
    Donagan
    Top Answerer
    4/1/4 is 4 divided by ¼. That's equal to (4)(4) = 16. Then 16 - 5/2 = 16 - 2½ = 13½ or 27/2.
  • Question
    How do I solve 3 2/3 = 2 x/3?
    Donagan
    Top Answerer
    First change the left side to an improper fraction: 3 2/3 = 11/3. Then change the right side to (2x)/3. Now solve for x: 11/3 = 2x/3. Multiply both sides by 3, so that 11 = 2x, and x = 5½.
  • Question
    How do you solve (6/x)/(x^3+x)?
    I_l1ke_gam3s
    Community Answer
    This cannot be solved because it's not an equation.
  • Question
    How do I simplify one that has a decimal instead?
    Donagan
    Top Answerer
    If a number is expressed as a decimal rather than a fraction, no simplification is required.
  • Question
    How do I solve x-(1/3) / 3-(1/x)?
    Donagan
    Top Answerer
    Solving means finding the value of the variable, so you can't solve this expression, but you can simplify it. Multiply the full fraction by (3x / 3x). [x - (1/3)] / [3 - (1/x)](3x / 3x) = (3x² - x) / (9x - 3) = x(3x - 1) / 3(3x - 1) = x/3.
  • Question
    How do I solve ((1/x)+1)/((1/x^2)-1)?
    Donagan
    Top Answerer
    You won't solve it, you'll simplify it. Multiply the full fraction by (x²/x²): [(1/x) + 1] / [(1/x²) - 1](x² / x²) = (x + x²) / (1 - x²) = x(1 + x) / (1 - x)(1 + x) = x / (1 - x).
  • Question
    How do you solve x/1+(1/x)?
    Donagan
    Top Answerer
    That expression cannot be solved or simplified.
  • Question
    How do you solve 1/2 divided by square root 3 over 6?
    Donagan
    Top Answerer
    (1/2) / (√3 / 6) = (1/2)(6 / √3) = 6 / 2√3 = 3 / √3. Now rationalize the denominator by multiplying the fraction by (√3 / √3) : (3 / √3)(√3 / √3) = (3√3) / (√3)(√3) = (3√3) / 3 = √3.
  • Question
    How to solve 19/19/6?
    Donagan
    Top Answerer
    First we identify the numerator as 19 and the denominator as 19/6. When we divide by a fraction, we multiply the numerator by the reciprocal of the denominator. Thus, (19)(6/19) = 6.
  • Question
    X- 1/(x+1) /(x-1) I tried using this method but got the wrong answer. Do I multiply each term by (x+1)(x-1)?
    Donagan
    Top Answerer
    No. [(x-1) / (x+1)] / (x-1) = (x-1) / [(x+1)((x-1)] = 1 / (x+1).
  • Question
    Can I cross cancel one expression from another expression of two different fractions before I flip my fraction and multiply? Say in the instance (2/14) / (10/2), can I cross cancel right at this point?
    Donagan
    Top Answerer
    The first thing to do is always reducing or simplifying fractions to make things easier. In this case 2/14 reduces to 1/7, and 10/2 becomes 5. Thus you have 1/7 divided by 5, which is the same as multiplying 1/7 by 1/5, which is 1/35.
  • Question
    How do I solve x to the second power minus 1 divided by 3x-1?
    Donagan
    Top Answerer
    (x² - 1) is not evenly divisible by (3x - 1) and simply remains (x² - 1) / (3x - 1). It's not solvable, because it's not part of an equation.
  • Question
    What is the rule for simplifying stacked fractions with an odd number terms, like a/b/c?
    Donagan
    Top Answerer
    Think of this as a numerator (a) being divided by a fraction (b/c). When you divide by a fraction, multiply the numerator by the reciprocal of the denominator. Thus you multiply (a) by (c/b) to get (ac)/b.
  • Question
    How do I solve 3/x - 1?
    Donagan
    Top Answerer
    Since this expression is not an equation, it can't be "solved." It can be simplified slightly: (3/x) - 1 = (3/x) - (x/x) = (3-x) / x. However, this form is not any more useful than the original expression, so there's really no point in making the change.
  • Question
    How do I solve (x/3 - 2) - x + 4/2 - x/6?
    Donagan
    Top Answerer
    You can't "solve" this expression, but you can simplify it: (x/3) - (2) - (x) + (4/2) - (x/6) = (2x/6) - 2 - (6x/6) + (2) - (x/6) = [(2x - 6x - x) / 6] + (-2 + 2) = [(-5x) / 6] + 0 = -5x / 6. (This is not a solution. A solution is something like x = 10. Expressions can be "solved" only when they are equations.)
  • Question
    How do I solve 2/7 divided by 14?
    Donagan
    Top Answerer
    Dividing by 14 is the same as multiplying by 1/14. (2/7) multiplied by (1/14) equals 2/98 or 1/49. Note that dividing a fraction by a whole number is the same as multiplying the denominator by that whole number.
  • Question
    How do I solve (1/3)6 + (2/3)6?
    Donagan
    Top Answerer
    Looking at it logically, just as one-third of a cake plus two-thirds of the same cake amounts to the full cake, one-third of 6 plus two-thirds of 6 equals 6. Doing the multiplication, (1/3)(6) = 6/3. (2/3)(6) = 12/3. 6/3 + 12/3 = 18/3 = 6.
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