Adding Mixed Numbers: 1 2/3 + 2 1/6 as a Fraction
When working with mixed numbers, it's essential to understand how to add them correctly. In this article, we'll focus on adding 1 2/3 and 2 1/6 as a fraction.
Converting Mixed Numbers to Improper Fractions
Before we dive into adding these mixed numbers, let's convert them into improper fractions.
1 2/3
To convert 1 2/3 into an improper fraction, we multiply the whole number part (1) by the denominator (3) and then add the numerator (2).
1 × 3 = 3 3 + 2 = 5
So, 1 2/3 as an improper fraction is 5/3.
2 1/6
Similarly, to convert 2 1/6 into an improper fraction, we multiply the whole number part (2) by the denominator (6) and then add the numerator (1).
2 × 6 = 12 12 + 1 = 13
So, 2 1/6 as an improper fraction is 13/6.
Adding Improper Fractions
Now that we have converted both mixed numbers into improper fractions, we can add them.
5/3 + 13/6
To add these fractions, we need to find the least common multiple (LCM) of the denominators, which is 6. We'll convert both fractions to have a denominator of 6:
5/3 = 10/6 (multiply numerator and denominator by 2) 13/6 (no change needed)
Now we can add:
10/6 + 13/6 = 23/6
Simplifying the Result
Our final answer is 23/6. This is an improper fraction, and we can simplify it by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 1 in this case.
So, 1 2/3 + 2 1/6 = 23/6.
By following these steps, you can add mixed numbers and simplify the result to obtain the correct answer as an improper fraction.
