Converting Mixed Numbers to Improper Fractions and Adding Them
In this article, we will learn how to add two mixed numbers: 2 1/2 and 3 1/3. To do this, we need to convert each mixed number to an improper fraction and then add them.
Converting Mixed Numbers to Improper Fractions
A mixed number is a combination of a whole number and a fraction. To convert a mixed number to an improper fraction, we need to multiply the whole number part by the denominator and then add the numerator.
2 1/2 as an Improper Fraction
To convert 2 1/2 to an improper fraction, we multiply 2 by 2 (the denominator) and add 1 (the numerator):
2 × 2 = 4 4 + 1 = 5
So, 2 1/2 as an improper fraction is 5/2.
3 1/3 as an Improper Fraction
To convert 3 1/3 to an improper fraction, we multiply 3 by 3 (the denominator) and add 1 (the numerator):
3 × 3 = 9 9 + 1 = 10
So, 3 1/3 as an improper fraction is 10/3.
Adding the Improper Fractions
Now that we have converted both mixed numbers to improper fractions, we can add them:
5/2 + 10/3
To add these fractions, we need to find the least common multiple (LCM) of the denominators, which is 6. We can convert both fractions to have a denominator of 6:
15/6 + 20/6
Now we can add the numerators:
15 + 20 = 35
So, the result of adding 2 1/2 and 3 1/3 as a fraction is 35/6.
Simplifying the Fraction
We can simplify the fraction 35/6 by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 1. Therefore, the simplified fraction is still 35/6.
Conclusion
In conclusion, we have successfully added 2 1/2 and 3 1/3 as a fraction by converting them to improper fractions, adding them, and simplifying the result. The final answer is 35/6.
