Before Science, Let’s Revisit Arithmetic2 – Fraction operations (addition, subtraction, multiplication, and division)
Fractions often seem complicated, but with a clear understanding of how they work, you can handle them confidently. In this post, we’ll explore the four basic operations on fractions and explain why each rule works.
1. Addition of Fractions
Example:
1/3 + 1/4 = 7/12
Why it works:
To add fractions with different denominators, find the least common denominator (LCD).
LCD of 3 and 4 is 12
Convert:
1/3 = 4/12
1/4 = 3/12Add:
4/12 + 3/12 = 7/12 ✅
2. Subtraction of Fractions
Example:
7/8 – 3/4 = 1/8
Why it works:
LCD of 8 and 4 is 8
Convert:
3/4 = 6/8Subtract:
7/8 – 6/8 = 1/8 ✅
3. Multiplication of Fractions
Example:
(3/10) × (5/6) = 1/4
Why it works:
Multiply the numerators and denominators:
(3 × 5) / (10 × 6) = 15 / 60Simplify:
15 / 60 = 1 / 4 ✅
4. Division of Fractions
Example:
(2/9) ÷ (1/3) = 2/3
Why it works:
Division is the same as multiplying by the reciprocal:
(2/9) ÷ (1/3) = (2/9) × (3/1) = 6/9 = 2/3 ✅
Bonus: Why do we multiply by the reciprocal when dividing?
Suppose you have:
Then:
To solve for x, multiply both sides by the reciprocal of (c/d):
This shows why dividing by a fraction equals multiplying by its reciprocal.
Conclusion
Understanding the logic behind each fraction operation—not just memorizing steps—makes math more intuitive and enjoyable. With practice, fractions become a powerful tool, not a source of confusion.
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