Question

You and your classmates are asked to simplify the expression below. One of your classmates incorrectly claims that the expression simplifies to 13 1/8 . What is the correct value of the expression? what error did your classmate likely make?

2/3 + 1/2 ( 8 + 3 1/4 )

Answer 1

The expression 2/3 + 1/2 ( 8 + 3 1/4 ) simplifies to 4 7/24 after proper order of operations and converting the mixed number to an improper fraction. The common mistake could involve misapplying the order of operations or mishandling the fractions.

Step-by-step explanation:

The correct simplification of the expression 2/3 + 1/2 ( 8 + 3 1/4 ) involves first computing the term within the parentheses, after which we multiply by 1/2 before adding 2/3. The error your classmate likely made was in not correctly applying the order of operations or perhaps incorrectly converting mixed numbers to improper fractions.

Step-by-Step Explanation:

1. Convert the mixed number 3 1/4 to an improper fraction: 3 1/4 = 13/4.
2. Perform the addition inside the parentheses: 8 + 13/4 = 32/4 + 13/4 = 45/4.
3. Multiply this result by 1/2: (1/2)(45/4) = 45/8.
4. Add 2/3 to the result: (2/3) + (45/8). To add these fractions, find a common denominator.
5. The common denominator for 3 and 8 is 24, so rewrite the fractions: (16/24) + (90/24).
6. Now add the fractions: 106/24, which simplifies to 4 7/24.

Therefore, the correct value of the expression is 4 7/24, not 13 1/8 as your classmate claimed.