How Do You Solve Proportions?

How Do You Solve Proportions?

Solve simple mathematical proportions by writing the ratios as fractions, setting these fractions equal to each other, cross-multiplying and then solving for any variables. A simple ratio to solve is 2:x = 3:9, which means "2 is to x as 3 is to 9."

  1. Set the proportions as fractions

    Write both of the ratios as fractions in the equation. Convert 2:x to 2/x and then 3:9 to 3/9. If you want, 3/9 can be reduced to 1/3, since both the numerator and denominator divide equally by three.

  2. Cross-multiply the ratios

    Using 2/x = 3/9, cross-multiply in an "X" pattern across the equals sign to form a linear equation. In this case, take 9x2 and 3x. The equation becomes 3x = 18. The reduced fraction of 1/3 yields the equation x = 6 when you multiply 1x and 3x2.

  3. Solve the equation

    Solve for x in the linear equation by dividing both sides by three. The result is x = 6, thereby making the final proportion 2:6 = 3:9. The reduced fraction 1/3 standing in for 3/9 solves the proportion faster. Ratios can be written in three basic ways, such as 2 to 6, 2:6 and 2/6. Each of these relationships between 2 and 6 means the exact same thing in this instance.