** Adding Fractions: 1/2 + 1/3 + 5/6 **
When we need to add fractions, we must ensure that they have the same denominator. In this case, we want to add 1/2, 1/3, and 5/6. To do this, we'll find the least common multiple (LCM) of the denominators, which are 2, 3, and 6.
Finding the Least Common Multiple (LCM)
To find the LCM, we'll 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 first number that appears in all three lists is 6. Therefore, the LCM is 6.
Converting to Equivalent Fractions
Now, we'll convert each fraction to have a denominator of 6:
- 1/2 = 3/6
- 1/3 = 2/6
- 5/6 = 5/6 (no change needed)
Adding the Fractions
Finally, we can add the fractions:
3/6 + 2/6 + 5/6 = 10/6
Simplifying the Result
We can simplify the result by dividing both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 10 and 6 is 2. So, we can simplify the result as follows:
10 ÷ 2 = 5 6 ÷ 2 = 3
Therefore, the simplified result is:
5/3
And that's the answer!
