\( \frac{2}{3}-\frac{2}{12}= \) Find a common denominator

To subtract the fractions \( \frac{2}{3} - \frac{2}{12} \), you'll first need to find a common denominator. Here's how you can do it step by step: ### Step 1: Identify the Denominators The denominators of the two fractions are 3 and 12. ### Step 2: Find the Least Common Denominator (LCD) The **Least Common Denominator (LCD)** is the smallest number that both denominators can divide into evenly. - Multiples of **3**: 3, 6, 9, **12**, 15, ... - Multiples of **12**: 12, 24, 36, ... The smallest common multiple is **12**. So, the LCD is **12**. ### Step 3: Convert Each Fraction to Have the LCD 1. **Convert \( \frac{2}{3} \) to have a denominator of 12:** - Multiply both the numerator and the denominator by 4 (because \( 3 \times 4 = 12 \)): \[ \frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12} \] 2. **Convert \( \frac{2}{12} \) to have a denominator of 12:** - This fraction already has the denominator 12, so it remains \( \frac{2}{12} \). ### Step 4: Subtract the Fractions Now that both fractions have the same denominator, subtract the numerators: \[ \frac{8}{12} - \frac{2}{12} = \frac{8 - 2}{12} = \frac{6}{12} \] ### Step 5: Simplify the Result Simplify \( \frac{6}{12} \) by dividing both the numerator and the denominator by their greatest common divisor (which is 6): \[ \frac{6 \div 6}{12 \div 6} = \frac{1}{2} \] ### Final Answer \[ \frac{2}{3} - \frac{2}{12} = \frac{1}{2} \]