Adding Fractions: 1/4 + 1/3 + 1/6 as a Fraction
Understanding the Concept
Fractions are a fundamental concept in mathematics, and adding them can be a bit tricky. In this article, we will explore how to add the fractions 1/4, 1/3, and 1/6 to find their sum as a fraction.
Step-by-Step Solution
To add these fractions, we need to find a common denominator. The least common multiple (LCM) of 4, 3, and 6 is 12. So, we will convert each fraction to have a denominator of 12.
Step 1: Convert 1/4 to have a denominator of 12
1/4 = 3/12
Step 2: Convert 1/3 to have a denominator of 12
1/3 = 4/12
Step 3: Convert 1/6 to have a denominator of 12
1/6 = 2/12
Step 4: Add the fractions
Now, we can add the fractions:
3/12 + 4/12 + 2/12 = 9/12
Simplifying the Fraction
The resulting fraction is 9/12. We can simplify this fraction 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 fraction is:
3/4
Conclusion
In conclusion, the sum of the fractions 1/4, 1/3, and 1/6 is 3/4. By following the steps outlined above, you can add fractions with different denominators and simplify the result to obtain a single fraction.
