Simplifying Fractions: 1/4 + 1/6 + 1/3
When adding fractions, it's essential to have the same denominator. Let's break down the process of simplifying the given fraction: 1/4 + 1/6 + 1/3.
Finding the Least Common Multiple (LCM)
To add these fractions, we need to find the least common multiple (LCM) of the denominators, which are 4, 6, and 3.
The multiples of 4 are: 4, 8, 12, 16, ... The multiples of 6 are: 6, 12, 18, 24, ... The multiples of 3 are: 3, 6, 9, 12, ...
The first number that appears in all three lists is 12, so the LCM is 12.
Converting Each Fraction to Have a Denominator of 12
Now, let's convert each fraction to have a denominator of 12:
- 1/4 = 3/12 (multiply numerator and denominator by 3)
- 1/6 = 2/12 (multiply numerator and denominator by 2)
- 1/3 = 4/12 (multiply numerator and denominator by 4)
Adding the Fractions
Now that all fractions have the same denominator, we can add them:
3/12 + 2/12 + 4/12 = 9/12
Simplifying the Result
The resulting fraction is 9/12. We can simplify it further by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 3:
9 ÷ 3 = 3 12 ÷ 3 = 4
So, the simplified result is:
3/4
There you have it! The simplified fraction of 1/4 + 1/6 + 1/3 is 3/4.
