Q&A for How to Simplify Complex Fractions

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.

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.

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.

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.

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).

(47/9) ÷ (8/5) = (47/9)(5/8) = 235/72 = 3 19/72.

This cannot be solved because it's not an equation.

If a number is expressed as a decimal rather than a fraction, no simplification is required.

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.

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).

That expression cannot be solved or simplified.

(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.

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.

No. [(x-1) / (x+1)] / (x-1) = (x-1) / [(x+1)((x-1)] = 1 / (x+1).

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.

(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.

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.

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.

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.)

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.

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.