Fractions cause more confusion than almost any other arithmetic topic — mostly because of the steps when denominators differ. Once you see why each step exists, the method becomes straightforward.
Adding Fractions: Same Denominator
When denominators are the same: just add the numerators.
- 2/7 + 3/7 = 5/7
Adding Fractions: Different Denominators
Step 1: Find the LCD (Lowest Common Denominator) — the smallest number both denominators divide into.
- 1/3 + 1/4: denominators are 3 and 4. LCD = 12.
Step 2: Convert each fraction to the LCD.
- 1/3 = 4/12 (multiply top and bottom by 4)
- 1/4 = 3/12 (multiply top and bottom by 3)
Step 3: Add the numerators, keep the denominator.
- 4/12 + 3/12 = 7/12
Subtracting Fractions
Same process — subtract numerators instead of adding:
- 3/4 − 1/6: LCD = 12
- 9/12 − 2/12 = 7/12
Multiplying Fractions
Multiply numerators together and denominators together. No need to find LCD.
- 2/3 × 3/5 = 6/15 = 2/5 (simplified)
Dividing Fractions
Multiply by the reciprocal of the second fraction (flip it):
- 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6
Simplifying Fractions
Divide both numerator and denominator by their GCD (Greatest Common Divisor).
- 12/18: GCD of 12 and 18 is 6.
- 12÷6 / 18÷6 = 2/3
Finding the GCD manually: list factors of each number and find the largest one they share. Or use the LCM & GCD Calculator.
Mixed Numbers
Convert to improper fractions before calculating:
- 1½ + 2¼ = 3/2 + 9/4 = 6/4 + 9/4 = 15/4 = 3¾
Use Fraction Calculator for any fraction arithmetic. For finding LCM and GCD, see how to find the LCM and GCD of numbers.
Fractions in Everyday Pakistani Context
Fractions appear in cooking measurements (half a cup, three-quarters of a teaspoon), land measurements (half kanal, quarter marla), and any situation involving sharing or splitting. The underlying arithmetic is the same regardless of context — find the LCD when adding different-denominator fractions, multiply numerators across when multiplying, flip and multiply when dividing. If the manual steps are time-consuming, Fraction Calculator handles any operation instantly, showing the steps alongside the result.
Improper Fractions vs Mixed Numbers
An improper fraction has a numerator larger than the denominator (7/4). A mixed number expresses it with a whole part and a fraction (1¾). Converting: 7 ÷ 4 = 1 remainder 3, giving 1¾. Either form is arithmetically correct; mixed numbers are more readable for people, improper fractions are easier to compute with. Fraction Calculator accepts and outputs both forms.
