Adding Mixed Numbers: 4 1/2 + 3 3/4 as a Fraction
When dealing with mixed numbers, it's essential to understand how to add them correctly. In this article, we'll explore how to add 4 1/2 and 3 3/4 as a fraction.
Converting Mixed Numbers to Improper Fractions
To add mixed numbers, we need to convert them to improper fractions. An improper fraction is a fraction where the numerator is greater than or equal to the denominator.
Converting 4 1/2 to an Improper Fraction
4 1/2 can be written as:
4 1/2 = 4 + 1/2 = 8/2 + 1/2 = 9/2
Converting 3 3/4 to an Improper Fraction
3 3/4 can be written as:
3 3/4 = 3 + 3/4 = 12/4 + 3/4 = 15/4
Adding the Improper Fractions
Now that we have converted both mixed numbers to improper fractions, we can add them:
9/2 + 15/4
To add these fractions, we need to find the least common multiple (LCM) of 2 and 4, which is 4. So, we'll convert 9/2 to have a denominator of 4:
9/2 = 18/4
Now we can add the fractions:
18/4 + 15/4 = 33/4
Simplifying the Result
The result of the addition is an improper fraction, 33/4. We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 1.
So, the final result is:
33/4
Conclusion
In conclusion, adding mixed numbers involves converting them to improper fractions, finding the least common multiple, and then adding the fractions. In this case, 4 1/2 + 3 3/4 as a fraction is equal to 33/4.
