Having trouble finding missing numerators and denominators in fraction addition and subtraction number sentences? Learn how to find that missing number and solve the equation in this lesson on fraction addition and subtraction number sentences.

Reviewing Fractions

In this lesson, we’ll learn to find the missing numerator or denominator in fraction addition and subtraction sentences. but first, let’s quickly review the parts of a fraction:

  • The numerator is the top number in a fraction. For example, 7 would be our numerator in the fraction 7/8.
  • The denominator is the bottom number in a fraction. For example, 8 would be our denominator in the fraction 7/8.

To solve missing numerator and denominator problems we need to know that in addition and subtraction number sentences the denominator stays the same, and the answers must always be simplified, or reduced to their lowest terms.

Find the Missing Denominator in an Addition or Subtraction Sentence

Let’s look at an example: 4/15 + 1/15 = 1/_____

When we add the numerators 4 + 1, we find the sum to be 5. So our first answer would be 5/15 (remember the denominator stays the same). But we must simplify the fraction if possible. To do this we must divide both the numerator and denominator by the least common multiple, or the smallest number that can be divided into the numerator and denominator, in this case 5. So when we divide both 5 and 15 by 5, we get a new numerator of 1 (5/5 = 1) and new denominator of 3 (15/5 = 3) This makes our new fraction 1/3.

So the missing denominator in the number sentence would be 3.

Find the Missing Numerator in an Addition or Subtraction Sentence

Let’s look at another number sentence 8/8 – _____/8 = 1/2.

Look at the answer in the number sentence above, 1/2. We must figure out what number we can multiply that denominator by to make it equal to the denominator of the first fraction in the number sentence, which is 8. So, what number can we multiply 2 by to give us 8: 2 x _____ = 8. The answer would be 4. So we must multiply both the numerator and denominator of the answer by 4.

  • Multiply the numerator first: 1 * 4 = 4. The new numerator is 4.
  • Multiply the denominator next: 2 * 4 = 8. The new denominator is 8.

So the new answer is 4/8. Now the new number sentence is 8/8 – _____ /8 = 4/8. Now, simply ignore the denominators and look at only the numerators to solve the problem: 8 – _____ = 4. The answer would be 4. The final answer with the number sentence is 8/8 – 4/8 = 1/2.

Addition sentences are worked out the same way. Let’s look at an example:

_____/16 + 2/16 = 3/8

We follow the same steps and look at the answer first: 3/8. What number can we multiply that denominator by to make it equal the denominator of the first fraction: 16. 8 x _____ = 16? The answer would be 2. 8 * 2 = 16.

Multiply both the numerator and denominator of the answer by 2.

3 * 2 = 6

8 * 2 = 16

The new answer is 6/16. The new number sentence is _____/16 + 2/16 = 6/16.

Now, we only look at the numerators: _____ + 2 = 6. The answer would be 4. Therefore, the missing numerator is 4.

The final number sentence is 4/16 + 2/16 = 3/8.

Lesson Summary

Finding a missing number within an addition or a subtraction number sentence starts with making sure the answer and the first two fractions have the same denominator. To do this, we multiply both the numerator and denominator of the answer by the number that would make the denominators the same. Always remember, when adding and subtracting fractions, the denominators remain the same and the answer must be simplified.