Adding Fractions – Step-by-Step
Adding fractions is one of the most important fraction skills. The key rule is simple: you can only add fractions that have the same denominator. Everything else follows from this.
Case 1 – Like Fractions (Same Denominator)
Add the numerators. Keep the denominator. Simplify if possible.
(3 + 2)/8 = 5/8. Already simplified. Answer: 5/8.
Case 2 – Unlike Fractions (Different Denominators)
Find the LCM of the denominators. Convert both fractions. Then add.
LCM(3,4) = 12. 1/3 = 4/12. 1/4 = 3/12. 4/12 + 3/12 = 7/12. Answer: 7/12.
LCM(5,8) = 40. 2/5 = 16/40. 3/8 = 15/40. 16/40 + 15/40 = 31/40. Answer: 31/40.
Case 3 – Mixed Numbers
Method A: Add whole parts and fraction parts separately.
Method B: Convert to improper fractions first, then add.
Method A: Wholes: 2+1=3. Fractions: 1/2+1/3. LCM=6: 3/6+2/6=5/6. Total: 3⅞.
Convert: 15/4 + 8/3. LCM=12: 45/12 + 32/12 = 77/12 = 6 5/12. Answer: 6 5/12.
Case 4 – Adding Fractions and Whole Numbers
Adding Three or More Fractions
LCM(2,3,6) = 6. 3/6 + 2/6 + 1/6 = 6/6 = 1.
Key Takeaways
- Same denominators: add numerators, keep denominator.
- Different denominators: find LCM, convert, then add.
- Always simplify the answer.
- If the result is improper, convert to a mixed number.
Practice Questions
- 5/9 + 2/9
- 1/4 + 2/3
- 3/5 + 7/10 + 1/2
- 2¾ + 1⅞
- A jug holds 3/8 L of juice and another holds 5/6 L. How much juice in total?