Subtracting Mixed Numbers with Unlike Denominators
In this article, we will learn how to subtract mixed numbers with unlike denominators, specifically the problem 5 1/2 - 2 5/8.
Understanding Mixed Numbers
Before we dive into the subtraction problem, let's briefly review what mixed numbers are. A mixed number is a combination of a whole number and a fraction. For example, 5 1/2 is a mixed number where 5 is the whole number and 1/2 is the fraction.
Converting Mixed Numbers to Improper Fractions
To subtract mixed numbers with unlike denominators, we need to convert them to improper fractions. An improper fraction is a fraction where the numerator is greater than the denominator. We can convert a mixed number to an improper fraction by multiplying the whole number part by the denominator and then adding the numerator.
Let's convert our mixed numbers:
5 1/2
- Whole number part: 5
- Fraction part: 1/2
- Denominator: 2
- Improper fraction: (5 x 2) + 1 = 11/2
2 5/8
- Whole number part: 2
- Fraction part: 5/8
- Denominator: 8
- Improper fraction: (2 x 8) + 5 = 21/8
Subtracting Improper Fractions
Now that we have converted our mixed numbers to improper fractions, we can subtract them:
11/2 - 21/8
To subtract these fractions, we need to find a common denominator. The least common multiple (LCM) of 2 and 8 is 8. So, we can convert the first fraction to have a denominator of 8:
11/2 = 44/8
Now we can subtract:
44/8 - 21/8 = 23/8
Converting the Result Back to a Mixed Number
Finally, we can convert the improper fraction back to a mixed number:
23/8 = 2 7/8
Therefore, the result of subtracting 5 1/2 and 2 5/8 is 2 7/8.
I hope this article has helped you understand how to subtract mixed numbers with unlike denominators. Remember to convert the mixed numbers to improper fractions, find a common denominator, subtract the fractions, and then convert the result back to a mixed number.
