Adding Mixed Numbers: 1 2/3 + 1 3/4 as a Fraction
When working with mixed numbers, it's essential to understand how to add them correctly. In this article, we'll explore how to add 1 2/3 and 1 3/4 as a fraction.
Step 1: Convert 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 or equal to the denominator.
1 2/3 as an Improper Fraction
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 as an improper fraction is:
5/3
1 3/4 as an Improper Fraction
To convert 1 3/4 to an improper fraction, we multiply the whole number part (1) by the denominator (4) and then add the numerator (3):
1 × 4 + 3 = 7
So, 1 3/4 as an improper fraction is:
7/4
Step 2: Add the Improper Fractions
Now that we have converted both mixed numbers to improper fractions, we can add them:
5/3 + 7/4
To add these fractions, we need a common denominator. The least common multiple (LCM) of 3 and 4 is 12. So, we'll convert both fractions to have a denominator of 12:
5/3 = 20/12 7/4 = 21/12
Now, we can add the fractions:
20/12 + 21/12 = 41/12
The Result
The result of adding 1 2/3 and 1 3/4 as a fraction is:
41/12
In summary, to add 1 2/3 and 1 3/4 as a fraction, we convert them to improper fractions, find a common denominator, and then add the fractions. The result is 41/12.
