Students typically encounter fractions with missing numbers during a unit on ratios and proportions in a high school algebra course. The missing number is represented by a variable, which is an alphabetic letter that serves as a placeholder when solving the problem. The quickest way to find the missing number in a fraction is to use cross products. A cross product is found by multiplying the diagonal terms of each fraction and setting them equal. This procedure requires a degree of basic algebraic background knowledge.

### One Missing Number

Multiply the numerator of the first fraction by the denominator of the second. For instance, suppose you want to find the missing number, x, in the fraction problem x/8 = 5/4. Multiply x by 4 to get 4x.

Multiply the denominator of the first fraction by the numerator of the second. In the previous example, multiply 8 by 5, obtaining 40.

Set the result of Step 1 equal to the result of Step 2. In the example, write 4x = 40.

Divide both sides by the coefficient. The coefficient is the number appearing to the left of the variable. In 4x = 40, divide both sides by 4, obtaining a solution of x = 10.

Check your answer by substituting it in for the variable in the original problem. Using a calculator, divide the first fraction’s numerator by its denominator. Write down this decimal. Then divide the second fraction’s numerator by its denominator. If the decimals match, your solution is correct.

### Two Missing Numbers

Multiply the numerator of the first fraction by the denominator of the second. For instance, suppose you need to find missing numbers in the fraction problem 6/y = 3/(y – 2). Calculate 6*(y – 2) to get 6y – 12.

Multiply the denominator of the first fraction by the numerator of the second. In the example, multiply y by 3, obtaining 3y.

Set the result of Step 1 equal to the result of Step 2. In the example, write 6y – 12 = 3y.

Add or subtract the variable term on the side with two terms from both sides of the equation. In 6y – 12 = 3y, subtract 6y from both sides, resulting in -12 = -3y.

Divide both sides by the coefficient. In -12 = -3y, divide both sides by -3 to get y = 4.

Check your answer by substituting it in for both variables in the original problem and simplifying using a calculator, as described in Section 1.