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 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.

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.