Fraction solve for x calculator
To solve x over 8 equals 3 over 4, multiply the two numbers that are not diagonally opposite x, then divide by the one that is. The boxes above do the multiply step.
12 × 12 = 144
Adding 12 to itself 12 times gives the same answer.
What this page solves
Two shapes of problem, not algebra in general. It handles proportions — one fraction equal to another, with x in any of the four positions — and simple linear equations with fractional coefficients, such as x/3 + 2 = 5. It is not a general solver: powers of x, quadratics, two unknowns, and x appearing in more than one term on both sides all need a different method than the one below.
The rule that always works
Write the problem as one fraction equals another fraction. Then find the number sitting diagonally opposite x. Multiply the other two numbers together in the boxes above, and divide that answer by the diagonal one. That is all cross-multiplication is.
When x is on top
x/8 = 3/4. Diagonally opposite x is the 4. The other two are 8 and 3, so multiply them: 24. Divide 24 by 4 and x = 6. Check it: 6/8 does reduce to 3/4.
When x is underneath
5/x = 2/6. Diagonally opposite x is the 2. The other two are 5 and 6, so multiply them: 30. Divide 30 by 2 and x = 15. Check it: 5/15 is one third, and so is 2/6.
When the answer looks wrong
- Test it before you trust it. Put your answer back into the original equation. If the two fractions do not reduce to the same thing, the multiply and the divide were swapped.
- One fraction per side first. Cross-multiplying only works on a single fraction each side, so combine anything added or subtracted first with the fraction adding calculator.
- A messy answer is often the right answer. If the division does not come out whole, leave it as a fraction rather than rounding. Turning it back into a division is covered in division into fraction.
- Watch the minus sign. A negative on either side stays with the number it belongs to through both steps.
More of these are listed in the calculators index.