Adding Mixed Fractions: 2 1/3 plus 1 3/4 as a Fraction
Understanding Mixed Fractions
Before we dive into adding mixed fractions, let's quickly review what they are. A mixed fraction is a combination of a whole number and a fraction. For example, 2 1/3 is a mixed fraction, where 2 is the whole number and 1/3 is the fraction.
Converting to Improper Fractions
To add mixed fractions, we need to convert them to improper fractions. An improper fraction is a fraction where the numerator (the top number) is greater than or equal to the denominator (the bottom number).
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 = 6 6 + 1 = 7
So, 2 1/3 as an improper fraction is 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 = 4 4 + 3 = 7
So, 1 3/4 as an improper fraction is 7/4.
Adding the Improper Fractions
Now that we have both mixed fractions converted to improper fractions, we can add them.
7/3 + 7/4
To add these fractions, we need to find 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.
7/3 = 28/12 7/4 = 21/12
Now, we can add the fractions:
28/12 + 21/12 = 49/12
Simplifying the Result
Our result, 49/12, is an improper fraction. We can simplify it by dividing both the numerator and the denominator by their greatest common divisor (GCD).
The GCD of 49 and 12 is 1, so we can't simplify the fraction further.
Final Answer
2 1/3 plus 1 3/4 as a fraction is equal to 49/12.
