Final answer:
To subtract the mixed numbers 5 1/8 and 2 3/4, convert them to improper fractions, find a common denominator, subtract, and convert the result back to a mixed number. The difference is 2 3/8.
Step-by-step explanation:
To find the difference between 5 1/8 and 2 3/4, we must first convert these mixed numbers into improper fractions. The mixed number 5 1/8 can be converted by multiplying the whole number 5 by the denominator 8 and adding the numerator 1, resulting in 41/8. On the other hand, the mixed number 2 3/4 is converted by multiplying the whole number 2 by the denominator 4 and adding the numerator 3, resulting in 11/4.
Next, we need a common denominator to subtract these two fractions. The least common denominator (LCD) for 8 and 4 is 8. Since 11/4 is not with an 8 in the denominator, we need to convert it. We do this by multiplying both the numerator and the denominator by 2, which gives us 22/8.
Now we can subtract the fractions: 41/8 - 22/8 equals 19/8. Since 19/8 is an improper fraction, we can convert it back to a mixed number by dividing 19 by 8, which is 2 with a remainder of 3. So, the mixed number is 2 3/8.
Therefore, the difference between 5 1/8 and 2 3/4 is 2 3/8.