How to Cross Multiply

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Cross Multiply

Cross-multiplication is a handy math skill to know. It is a way to solve an equation that involves a variable as part of two fractions set equal to each other. The variable is a placeholder for an unknown number or quantity, and cross multiplying reduce the proportion to one simple equation, allowing you to solve for the variable in question. It is also useful when you’re trying to solve a ratio. Here is how you can do cross multiplication.

Cross-Multiplication with a Single Variable

  1. Multiply the numerator of the left-hand fraction by the denominator of the right-hand fraction.
    (For Example: The equation is 2/x = 10/13.)
    Now, multiply 2 * 13 = 26

  2. Multiply the numerator of the right-hand fraction by the denominator of the left-hand fraction. 
    Now, multiply x * 10 = 10x

  3. Set the two products equal to each other. 
    Just set 26 equal to 10x. 26 = 10x

  4. Solve the variable. 
    Find a common denominator and diving both 26 and 10 by a number that divides evenly into both numbers. In this case, you can divide them by 2; 26/2 = 13 and 10/2 = 5. You’re left with 13 = 5x. Now, to isolate x, divide both sides of the equation by 5. So, 13/5 = 5/5, or 13/5 = x. You can divide both sides of the equation by 10 to get 26/10 = 10/10, or 2.6 = x to get an answer in decimal form. 

Cross-Multiplication with a Two of the Same Variable

  1. Multiply the numerator of the left-hand fraction by the denominator of the right-hand fraction.
    (For Example: (x + 3)/2 = (x + 1)/4.)
    Now, Multiply (x + 3) by 4 to get 4(x +3). Distribute the 4 to get 4x + 12.

  2. Multiply the numerator of the right-hand fraction by the denominator of the left-hand fraction.
    Now, Multiply (x +1) x 2 = 2(x +1). Distribute the 2 and you get 2x + 2.

  3. Set the two products equal to each other and combine the like terms.
    Just set 4x + 12 equal to 2x + 2.
    Combine the x terms and the constant terms on opposite sides of the equation. On the left side, 4x – 2x = 2x, so you have 2x remaining. On the right side 2-12 = -10. Now, you’re left with 2x = -10.

  4. Solve the equation. Divide both sides of the equation by 2. 2x/2 = -10/2. After cross multiplying, you have found that x = -5.

    We can check the equation byb plugging in -5. If you plug -5 back into the original equation, you’ll get -1 = -1.

Source: WikiHow