Adding Mixed Numbers: 1 3/4 + 1 2/8
In this article, we will explore how to add mixed numbers, specifically 1 3/4 and 1 2/8.
Understanding Mixed Numbers
Before we dive into the calculation, let's quickly review what mixed numbers are. A mixed number is a combination of a whole number and a fraction. In our example, 1 3/4 is a mixed number where 1 is the whole number and 3/4 is the fraction.
Converting Mixed Numbers to Improper Fractions
To add mixed numbers, it's often easier to convert them to improper fractions first. An improper fraction is a fraction where the numerator is greater than the denominator.
Converting 1 3/4 to an Improper Fraction
To convert 1 3/4 to an improper fraction, we multiply the whole number (1) by the denominator (4) and then add the numerator (3):
1 × 4 + 3 = 7
So, 1 3/4 is equal to 7/4.
Converting 1 2/8 to an Improper Fraction
To convert 1 2/8 to an improper fraction, we multiply the whole number (1) by the denominator (8) and then add the numerator (2):
1 × 8 + 2 = 10
So, 1 2/8 is equal to 10/8.
Adding the Improper Fractions
Now that we have converted both mixed numbers to improper fractions, we can add them:
7/4 + 10/8
To add these fractions, we need to find the least common multiple (LCM) of 4 and 8, which is 8. So, we can rewrite the fractions with a denominator of 8:
7/4 = 14/8 10/8 = 10/8
Now we can add the fractions:
14/8 + 10/8 = 24/8
Simplifying the Result
Finally, we can simplify the result by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 4:
24 ÷ 4 = 6 8 ÷ 4 = 2
So, the result of adding 1 3/4 and 1 2/8 is 3 1/2.
Conclusion
In this article, we have learned how to add mixed numbers by converting them to improper fractions and then adding them. By following these steps, we can easily add mixed numbers and simplify the results.
