Simplifying Fractions: 1/3 + 1/5 + 1/2
When dealing with fractions, it's essential to understand how to add them together. In this article, we'll explore how to simplify the expression 1/3 + 1/5 + 1/2 as a single fraction.
Step 1: Find the Least Common Multiple (LCM)
To add these fractions, we need to find the least common multiple (LCM) of the denominators, which are 3, 5, and 2. The LCM of these numbers is 30. This means we'll convert each fraction to have a denominator of 30.
Step 2: Convert Each Fraction
1. Convert 1/3 to a fraction with a denominator of 30
To do this, we'll multiply both the numerator and denominator by 10:
1/3 = (1 × 10) / (3 × 10) = 10/30
2. Convert 1/5 to a fraction with a denominator of 30
To do this, we'll multiply both the numerator and denominator by 6:
1/5 = (1 × 6) / (5 × 6) = 6/30
3. Convert 1/2 to a fraction with a denominator of 30
To do this, we'll multiply both the numerator and denominator by 15:
1/2 = (1 × 15) / (2 × 15) = 15/30
Step 3: Add the Fractions
Now that each fraction has a denominator of 30, we can add them together:
(10/30) + (6/30) + (15/30) = (10 + 6 + 15)/30 = 31/30
Simplified Fraction
The simplified fraction is:
31/30
This is the result of adding 1/3, 1/5, and 1/2 as a single fraction.
