Adding Fractions with Different Denominators
In this article, we will explore how to add fractions with different denominators. Specifically, we will calculate the sum of the following fractions:
1/2 + 1/4 + 1/8 + 1/16 + 1/32
Step 1: Find the Least Common Multiple (LCM)
To add these fractions, we need to find the least common multiple (LCM) of the denominators. The denominators are 2, 4, 8, 16, and 32.
The LCM of these numbers is 32. Therefore, we need to convert each fraction to have a denominator of 32.
Step 2: Convert Each Fraction to Have a Denominator of 32
Let's convert each fraction to have a denominator of 32:
- 1/2 = 16/32
- 1/4 = 8/32
- 1/8 = 4/32
- 1/16 = 2/32
- 1/32 = 1/32 (no conversion needed)
Step 3: Add the Fractions
Now that all the fractions have the same denominator, we can add them:
16/32 + 8/32 + 4/32 + 2/32 + 1/32 = 31/32
Result
The sum of the fractions is 31/32.
Conclusion
In this article, we learned how to add fractions with different denominators by finding the least common multiple (LCM) of the denominators and converting each fraction to have the LCM as the denominator. By doing so, we were able to calculate the sum of the given fractions, which is 31/32.
