Reggie writes the expression m + 8 × (2/3). Which expression is equivalent to the one Reggie writes?
Responses
A (8×2 ÷ 3) + m(8×2 ÷ 3) + m
B m + (8×3 ÷ 2)m + (8×3 ÷ 2)
C 8 + m(2 ÷ 3)8 + m(2 ÷ 3)
D (m+8)(2 ÷ 3)
C 8 + m(2 ÷ 3)
To find the equivalent expression, we need to simplify m + 8 × (2/3).
Step 1: Simplify 8 × (2/3) by multiplying the numerators and the denominators:
8 × (2/3) = (8 × 2) / 3 = 16/3.
Now we have m + 16/3.
Step 2: Rewrite the sum using a common denominator:
m + 16/3 = (3m/3) + (16/3) = (3m + 16) / 3.
The answer is D, (m+8)(2 ÷ 3), which is equivalent to (3m + 16) / 3.
To find the equivalent expression to the one Reggie writes, we need to simplify the expression m + 8 × (2/3).
The first step is to simplify the multiplication within the parentheses.
8 × (2/3) can be rewritten as (8 × 2) ÷ 3.
So, the expression becomes m + (16 ÷ 3).
To simplify further, we can divide 16 by 3.
16 ÷ 3 equals 5 (with a remainder of 1).
So, the expression becomes m + 5 + (1 ÷ 3).
The last step is to divide 1 by 3, which equals 1/3.
Therefore, the final equivalent expression is m + 5 + 1/3.
Checking the answer choices:
A. (8 × 2 ÷ 3) + m is not equivalent to the expression Reggie writes.
B. m + (8 × 3 ÷ 2) is not equivalent to the expression Reggie writes.
C. 8 + m (2 ÷ 3) is not equivalent to the expression Reggie writes.
D. (m + 8)(2 ÷ 3) is not equivalent to the expression Reggie writes.
None of the answer choices are equivalent, so the answer is None of the Above.