Content

• Steps
• Method 1 of 2: Cross-multiplication with unknown in one side of the equation
• Method 2 of 2: Cross-multiplication with unknown on both sides of the equation
• Tips

Cross multiplication is a way to solve an equation, both sides of which are fractions and the unknown value is included in the numerator or denominator of one of them (or both). Cross-multiplication will allow you to get rid of fractions and bring the equation to a simpler form. This method is especially useful for solving proportions.

Steps

Method 1 of 2: Cross-multiplication with unknown in one side of the equation

1. 1 Multiply the numerator of the left fraction by the denominator of the right. For example, we are given the equation 2 / x = 10/13. Multiply 2 by 13.2 * 13 = 26.
2. 2 Multiply the numerator of the right fraction by the denominator of the left. Now multiply x by 10. x * 10 = 10x. You can change the first step and this one. It doesn't matter what you multiply first and what second; the main thing is to multiply diagonally the numerator of one fraction with the denominator of the other.
3. 3 Equate the answers. Note that 26 is 10x. 26 = 10x. The sequence in which the responses are recorded does not matter. You can swap them - equality will still be preserved. Just write down each answer in its entirety in the form in which you received it (10x is 10x, not 10, not x and not 10 + x).
   • So, if you solve the equation 2 / x = 10/13, then you get 2 * 13 = x * 10, or 26 = 10x.
4. 4 Solve the equation to find the unknown. To solve the equation 26 = 10x, you can start by looking for the greatest common factor. Find the number that divides 26 and 10. This will be 2; 26/2 = 13 and 10/2 = 5. Remaining 13 = 5x. Now leave only x on the right side, dividing both sides by 5. So 13/5 = 5x / 5, or x = 13/5. If you want a decimal answer, you can simply divide both sides of the equation by 10: 26/10 = 10x / 10, or x = 2.6.

Method 2 of 2: Cross-multiplication with unknown on both sides of the equation

1. 1 Multiply the numerator of the left fraction by the denominator of the right. For example, we are given the following equation: (x + 3) / 2 = (x + 1) / 4... Multiply (x + 3) on the 4, it will turn out 4 (x +3). Open the brackets, you get 4x + 12.
2. 2 Multiply the numerator of the right fraction by the denominator of the left. Do the same as described above. It will turn out: (x +1) x 2 = 2 (x +1). Open the brackets, we get 2x + 2.
3. 3 Write down the answers received in the form of equality and transfer the unknowns into one part. You've got the equation 4x + 12 = 2x + 2. Transfer all x to one part and the known values ​​to the other.
   • Let's move 2x To 4x... Subtracting from both sides of the equation 2x, on the left you get "4x - 2x + 12 = 2x + 12", and on the right there will be only 2.
   • Now let's move 12 To 2... Subtracting from both parts 12, then only 2x, and on the right you get 2 - 12 = -10.
   • The equation turned out 2x = -10.
4. 4 Solve the equation. To do this, it remains only to find the unknown, dividing both parts by 2. 2x / 2 = -10/2; we get x = -5... For verification, you can substitute this value in the original equation. It will turn out -1 = -1.

Tips

• The result can be verified by plugging it into the original equation. If you get a correct equality, for example 1 = 1, then you have solved the equation correctly. If equals is not true, for example 0 = 1, you made a mistake. For example, in the example from Part 1 of this article, plug 2.6 into the equation: 2 / (2.6) = 10/13. Multiply the left side by 5/5 to get 10/13 = 10/13. This equality is correct, so 2.6 is the correct answer.
• If in the same example you got, say, 5, then when you substitute this value, you get 2/5 = 10/13. If you multiply the left side by 5/5, you get 10/25 = 10/13. This equality is not correct, so you made a mistake in the cross-multiplication.