Fraction Addition
Adding fractions is straightforward once you understand one key rule: you can only add fractions that refer to the same-sized parts. That means the denominators must match.
Adding Fractions with the Same Denominator
When denominators are equal, simply add the numerators and keep the denominator.
⅓ + ⅓ = ⅔ (1+1=2, denominator stays 3)
2/7 + 3/7 = 5/7 (2+3=5, denominator stays 7)
Adding Fractions with Different Denominators
When denominators differ, you must find the lowest common denominator (LCD) — the smallest number that both denominators divide into exactly. Then convert each fraction to that denominator before adding.
Example: 1/3 + 1/4
- LCD of 3 and 4 = 12.
- Convert: 1/3 = 4/12 and 1/4 = 3/12.
- Add: 4/12 + 3/12 = 7/12.
1/3 + 1/4 = 4/12 + 3/12 = 7/12
Example: 2/5 + 3/10
- LCD of 5 and 10 = 10.
- Convert: 2/5 = 4/10.
- Add: 4/10 + 3/10 = 7/10.
2/5 + 3/10 = 4/10 + 3/10 = 7/10
Simplifying the Answer
Always check whether the resulting fraction can be simplified. Divide numerator and denominator by their highest common factor (HCF).
3/6 + 1/6 = 4/6 → simplify by dividing by 2 → 2/3
Adding Three Fractions
Find the LCD of all three denominators, convert all, then add the numerators.
1/2 + 1/3 + 1/6 → LCD=6 → 3/6 + 2/6 + 1/6 = 6/6 = 1
Key Takeaways
- Same denominator: add numerators, keep denominator.
- Different denominators: find LCD, convert, then add.
- Always simplify (reduce) the answer if possible.
- If the result is an improper fraction (numerator > denominator), convert to a mixed number.
Practice Questions
- Calculate 2/9 + 4/9.
- Add 1/4 + 1/2.
- Calculate 2/3 + 3/5.
- Add 1/2 + 1/3 + 1/6 and simplify.
- A recipe needs 3/8 cup of sugar and 1/4 cup of honey. What is the total amount of sweetener?