Step 1: Determine the Denominators
To add fractions, we need to have a common denominator. In this case, we have 1/8 and 1/2. The denominator of 1/8 is 8, and the denominator of 1/2 is 2. To find the least common multiple (LCM) of 8 and 2, we can list the multiples of each number:- Multiples of 8: 8, 16, 24, 32, 40
- Multiples of 2: 2, 4, 6, 8, 10
Step 2: Convert Fractions to Have a Common Denominator
1/2 × 4/4 = 4/8
So, 1/2 is equal to 4/8. Now we can rewrite the original problem as:1/8 + 4/8
Step 3: Add the Numerators
Now that both fractions have the same denominator, we can add the numerators:1 + 4 = 5
Step 4: Simplify the Result (Optional)
In this case, the fraction 5/8 is already in its simplest form. However, if we had a fraction with a common factor in the numerator and the denominator, we could simplify it. For example, if we had 10/20, we could simplify it by dividing both the numerator and the denominator by 10:10 ÷ 10 = 1
20 ÷ 10 = 2
10/20 = 1/2
Comparison of Fraction Operations
| Operation | Example | Result |
|---|---|---|
| Adding Fractions with Different Denominators | 1/8 + 1/2 | 5/8 |
| Adding Fractions with the Same Denominator | 1/8 + 1/8 | 2/8 = 1/4 |
| Adding Fractions with a Common Factor | 1/20 + 1/20 | 2/20 = 1/10 |