Question
Simplify \( \frac{1}{4}(8 m-4 n)+\frac{1}{3}(6 m+3 n) \) \( -4 m \) \( \frac{1}{4} m \) \( 4 m \)
Ask by Bolton Hodges. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified expression is \( 4m \).
Solution
To simplify the expression (1/4)(8m - 4n) + (1/3)(6m + 3n):
1. Distribute the coefficients:
(1/4)·8m = 2m
(1/4)·(-4n) = -n
(1/3)·6m = 2m
(1/3)·3n = n
2. Combine like terms:
2m - n + 2m + n = 4m
Thus, the simplified expression is 4m.
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Simplify this solution Beyond the Answer
To simplify the expression \( \frac{1}{4}(8 m-4 n)+\frac{1}{3}(6 m+3 n) \), we start by distributing the fractions: 1. Distributing \( \frac{1}{4} \): \[ \frac{1}{4}(8 m - 4 n) = 2 m - n \] 2. Distributing \( \frac{1}{3} \): \[ \frac{1}{3}(6 m + 3 n) = 2 m + n \] Now combine the two results: \[ (2 m - n) + (2 m + n) = 4 m \] Thus, the simplified result is \( 4 m \).
