Final answer:
To solve 5 5/6 - 3 3/4 2 1/2, convert all mixed numbers to improper fractions, perform the multiplication first, then convert the result to a mixed number, find a common denominator to subtract the second mixed number, and simplify to get the answer 2 17/24.
Step-by-step explanation:
To solve the expression 5 5/6 - 3 3/4 2 1/2, first convert the mixed numbers to improper fractions. For 5 5/6, the improper fraction is 35/6. For 3 3/4, the improper fraction is 15/4. Now, we should remember the order of operations, which states we need to perform multiplication before subtraction. So, we will first multiply 15/4 by 2 1/2, which is the same as 5/2 when converted to an improper fraction.
Multiplying 15/4 by 5/2, we get 15/4 × 5/2 = 75/8. Next, convert this to a mixed number to subtract it from 5 5/6. The mixed number for 75/8 is 9 3/8.
Now we can subtract the two mixed numbers: 35/6 - 9 3/8. To subtract these, they must both have the same denominator. The least common denominator of 6 and 8 is 24. Convert to have the same denominator: 35/6 = 140/24 and 9 3/8 = 75/24. Subtracting gives us 140/24 - 75/24 = 65/24, which simplifies to the mixed number 2 17/24. So, the answer to 5 5/6 - 3 3/4 × 2 1/2 is 2 17/24.