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

### Step 1

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.

### Step 2

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

### Step 3

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

### Step 4

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.

### Step 5

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

### Step 1

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.

### Step 2

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

### Step 3

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

### Step 4

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.

### Step 5

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

### Step 6

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