Adding Mixed Numbers with Fractions: 1 2/3 + 2 3/4 as a Fraction
When dealing with mixed numbers and fractions, it's essential to understand how to add them correctly. In this article, we'll explore how to add 1 2/3 and 2 3/4 as a fraction.
Converting Mixed Numbers to Improper Fractions
To add mixed numbers, we need to convert them to improper fractions first. An improper fraction is a fraction where the numerator is greater than the denominator.
Converting 1 2/3
To convert 1 2/3 to an improper fraction, we multiply the whole number part (1) by the denominator (3) and then add the numerator (2):
1 × 3 + 2 = 5
So, 1 2/3 is equal to:
5/3
Converting 2 3/4
Similarly, to convert 2 3/4 to an improper fraction, we multiply the whole number part (2) by the denominator (4) and then add the numerator (3):
2 × 4 + 3 = 11
So, 2 3/4 is equal to:
11/4
Adding the Fractions
Now that we have converted both mixed numbers to improper fractions, we can add them:
5/3 + 11/4
To add these fractions, we need to find the least common multiple (LCM) of the denominators, which is 12. We'll convert both fractions to have a denominator of 12:
5/3 = 20/12
11/4 = 33/12
Now we can add the fractions:
20/12 + 33/12 = 53/12
Simplifying the Result
The result of the addition is an improper fraction, 53/12. We can simplify it by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 1:
53/12
So, 1 2/3 + 2 3/4 as a fraction is equal to:
53/12
In conclusion, adding mixed numbers with fractions requires converting them to improper fractions and then adding them. By following these steps, you'll be able to add mixed numbers with fractions with ease.
