Adding Mixed Numbers: 2 1/3 + 1 3/4
In this article, we will learn how to add two mixed numbers, 2 1/3 and 1 3/4, and express the result in fraction form.
Understanding Mixed Numbers
A mixed number is a combination of a whole number and a fraction. For example, 2 1/3 is a mixed number, where 2 is the whole number and 1/3 is the fraction.
Converting Mixed Numbers to Improper Fractions
To add mixed numbers, we need to convert them into improper fractions first. An improper fraction is a fraction where the numerator is greater than or equal to the denominator.
Converting 2 1/3 to an Improper Fraction
To convert 2 1/3 to an improper fraction, we multiply the whole number part (2) by the denominator (3) and then add the numerator (1).
(2 × 3) + 1 = 7
So, 2 1/3 is equal to 7/3.
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) + 3 = 7
So, 1 3/4 is equal to 7/4.
Adding the Improper Fractions
Now that we have converted both mixed numbers to improper fractions, we can add them.
7/3 + 7/4
To add these fractions, we need to find the least common multiple (LCM) of the denominators, which is 12. Then, we can convert both fractions to have a denominator of 12.
7/3 = 28/12 7/4 = 21/12
Now, we can add the fractions:
28/12 + 21/12 = 49/12
Simplifying the Result
The result of the addition is an improper fraction, 49/12. If we want to express it as a mixed number, we can divide the numerator by the denominator:
49 ÷ 12 = 4 with a remainder of 1
So, the result of the addition is 4 1/12.
In conclusion, 2 1/3 + 1 3/4 is equal to 4 1/12 in mixed number form or 49/12 in improper fraction form.
