How to Add or Subtract Fractions: A Step-by-Step Guide

Understanding Fractions

Before we dive into adding and subtracting fractions, let’s clarify what a fraction is. A fraction consists of a numerator (the top number) and a denominator (the bottom number). For example, in the fraction 1/2, 1 is the numerator and 2 is the denominator.

Adding Fractions

Step 1: Determine if the Denominators are the Same

To add fractions, the first step is to check if the denominators are the same.

• If they are the same, proceed to Step 3.
• If they are different, move to Step 2.

Step 2: Find a Common Denominator

If the denominators are not the same, you need to find a common denominator. This could be the least common multiple (LCM) of the two denominators.

• For example, to add 1/3 and 1/4, the LCM of 3 and 4 is 12.

Step 3: Adjust the Fractions

Convert each fraction to have the common denominator:

• For 1/3 to convert to a denominator of 12, multiply both the numerator and denominator by 4: 1/3 = 4/12
• For 1/4, multiply both the numerator and denominator by 3: 1/4 = 3/12

Step 4: Add the Numerators

Now that both fractions have the same denominator, add the numerators together:

4/12 + 3/12 = (4 + 3)/12 = 7/12

Step 5: Simplify the Fraction

If needed, simplify the fraction. In this case, 7/12 is already in its simplest form.

Subtracting Fractions

Step 1: Determine if the Denominators are the Same

Just like addition, check if the denominators are the same:

• If yes, proceed to Step 3.
• If no, go to Step 2.

Step 2: Find a Common Denominator

If the denominators are different, find the LCM to get the common denominator.

Step 3: Adjust the Fractions

Convert each fraction to have the common denominator using the same techniques as in addition.

Step 4: Subtract the Numerators

Now, subtract the numerators:

4/12 - 3/12 = (4 - 3)/12 = 1/12

Step 5: Simplify the Fraction

Finally, check if the result can be simplified. In this case, 1/12 is already simplified.

Conclusion

Adding and subtracting fractions may seem complex at first, but by following these steps, you can master the process. Just remember to find a common denominator when necessary, adjust the fractions, and then perform the addition or subtraction of the numerators!