Solving the Fraction Problem: 1/2 + 1/3 + 1/6
In this article, we will solve the fraction problem 1/2 + 1/3 + 1/6. To do this, we need to find the least common multiple (LCM) of the denominators and then add the fractions.
Step 1: Find the Least Common Multiple (LCM)
The denominators of the fractions are 2, 3, and 6. To find the LCM, we need to list the multiples of each denominator:
- Multiples of 2: 2, 4, 6, 8, 10, ...
- Multiples of 3: 3, 6, 9, 12, 15, ...
- Multiples of 6: 6, 12, 18, 24, 30, ...
The smallest number that appears in all three lists is 6, so the LCM is 6.
Step 2: Convert the Fractions
Now that we have found the LCM, we need to convert each fraction to have a denominator of 6:
- 1/2 = 3/6 (multiply numerator and denominator by 3)
- 1/3 = 2/6 (multiply numerator and denominator by 2)
- 1/6 = 1/6 (no change needed)
Step 3: Add the Fractions
Now that all the fractions have the same denominator, we can add them:
3/6 + 2/6 + 1/6 = 6/6 = 1
Therefore, the solution to the problem 1/2 + 1/3 + 1/6 is 1.
