1/2 + 1/3 + 1/7 as a Fraction
In this article, we will explore how to add the fractions 1/2, 1/3, and 1/7 and express the result 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 2, 3, and 7. The LCM of 2, 3, and 7 is 42. Therefore, we need to convert each fraction to have a denominator of 42.
Step 2: Convert Each Fraction
1. Convert 1/2 to have a denominator of 42
To convert 1/2 to have a denominator of 42, we need to multiply the numerator and denominator by 21.
1/2 = (1 × 21) / (2 × 21) = 21/42
2. Convert 1/3 to have a denominator of 42
To convert 1/3 to have a denominator of 42, we need to multiply the numerator and denominator by 14.
1/3 = (1 × 14) / (3 × 14) = 14/42
3. Convert 1/7 to have a denominator of 42
To convert 1/7 to have a denominator of 42, we need to multiply the numerator and denominator by 6.
1/7 = (1 × 6) / (7 × 6) = 6/42
Step 3: Add the Fractions
Now that we have converted each fraction to have a denominator of 42, we can add them:
(21/42) + (14/42) + (6/42) = ?
To add these fractions, we add the numerators and keep the denominator the same:
(21 + 14 + 6) / 42 = 41/42
Result
The result of adding 1/2, 1/3, and 1/7 as a fraction is:
41/42
Therefore, the sum of 1/2, 1/3, and 1/7 is equal to 41/42.
