Adding and Subtracting Fractions in Algebra

Fractions can be difficult to deal with, but they can be made easy to understand. Whether you’re a student or a parent helping with homework, this guide will break it down step by step. Let's make algebra easier!

Step 1: Find the Common Denominator The denominator is the bottom number of a fraction. To add or subtract, the denominators must match. If they’re different, find the least common multiple (LCM).

Example: 1/4 + 1/6 → The LCM of 4 and 6 is 12.

Adjust both fractions so they have the same denominator: 1/4 = 3/12 1/6 = 2/12

Step 2: Add or Subtract the Numerators Once the denominators match, add or subtract the top numbers (numerators).

3/12 + 2/12 = 5/12

If subtracting: 3/12 - 2/12 = 1/12

Step 3: Simplify If Needed If the fraction can be reduced, do it. Find the greatest common factor (GCF) and divide.

Example: 6/8 → Divide both by 2 → 3/4

Tips for Success

• If adding mixed numbers, convert to improper fractions first.

• Always simplify your final answer.

• If stuck, ask a math tutor for help!

What about fractions with variables?

The same steps work. Example: x/3 + x/6. The common denominator is 6. Change x/3 into 2x/6. Now add: 2x/6 + x/6 = 3x/6. Simplify to x/2.

Another one: 1/x + 1/2. The common denominator is 2x. That gives 2/(2x) + x/(2x). Add the tops to get (2 + x)/(2x).

A mistake to avoid

Do not add the bottom numbers. 1/2 + 1/3 is not 2/5. The right answer is 5/6. Change them to 3/6 and 2/6, then add.

Practice problems

1. 2/5 + 1/10. Answer: 1/2.

2. 3/4 minus 1/6. Answer: 7/12.

3. x/4 + x/2. Answer: 3x/4.

Mastering fractions is key in algebra. Practice and keep it simple. Math gets easier with time!