Adding Mixed Numbers: 2 1/2 plus 1 3/4 as a Fraction
When dealing with mixed numbers, adding them can be a bit tricky. In this article, we will explore how to add 2 1/2 and 1 3/4 as a fraction.
Converting Mixed Numbers to Improper Fractions
To add mixed numbers, we need to convert them into improper fractions. An improper fraction is a fraction where the numerator is greater than the denominator.
Converting 2 1/2 to an Improper Fraction
To convert 2 1/2 to an improper fraction, we multiply the whole number part (2) by the denominator (2) and then add the numerator (1).
2 × 2 = 4 4 + 1 = 5
So, 2 1/2 as an improper fraction is 5/2.
Converting 1 3/4 to 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 = 4 4 + 3 = 7
So, 1 3/4 as an improper fraction is 7/4.
Adding the Improper Fractions
Now that we have converted both mixed numbers to improper fractions, we can add them.
5/2 + 7/4
To add these fractions, we need to find the least common multiple (LCM) of the denominators, which are 2 and 4. The LCM of 2 and 4 is 4. So, we can rewrite the fractions with a denominator of 4.
10/4 + 7/4
Now, we can add the fractions.
10 + 7 = 17
So, 10/4 + 7/4 = 17/4.
Converting the Result Back to a Mixed Number
To convert the result back to a mixed number, we divide the numerator by the denominator.
17 ÷ 4 = 4 with a remainder of 1
So, 17/4 = 4 1/4.
The Final Answer
Therefore, 2 1/2 plus 1 3/4 as a fraction is 4 1/4.
