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 I find the least common denominator when working with complex fractions that include variables?
    Christopher
    Top Answerer
    To find the least common denominator (LCD), factor all denominators in the complex fraction, including variable expressions. Identify the unique factors and use the highest power for each. Multiply these factors to get the LCD, which is then used to simplify the complex fraction.
  • Question
    How do I solve (1/2) divided by (√2/2)?
    Donagan
    Top Answerer
    To solve (1/2) ÷ (√2/2), multiply by the reciprocal: (1/2) × (2/√2) = 2/(2√2). Then, multiply both the numerator and denominator by √2 to get 2√2/4 = √2/2. Alternatively, approximate √2 as 1.414, so the expression becomes (0.5)/(0.707) = 0.707, which is approximately equal to √2/2.
  • Question
    How do I simplify (3 - 3/x) divided by (1/2 - 1/x)?
    Donagan
    Top Answerer
    To simplify (3 - 3/x) ÷ (1/2 - 1/x), rewrite it as (3x - 3)/x ÷ (x - 2)/(2x). Multiply by the reciprocal to get [(3x - 3)/x] × [(2x)/(x - 2)] = (6x² - 6x)/(x² - 2x) = (6x - 6)/(x - 2).
  • Question
    How do I solve 47/9 divided by 8/5?
    Donagan
    Top Answerer
    (47/9) ÷ (8/5) = (47/9)(5/8) = 235/72 = 3 19/72.
  • 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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