Question

solve for $w$.
$w+\frac{2}{5}=7\frac{2}{3}$
$w=\square$

Explanation:

Step1: Isolate w by subtracting $\frac{2}{5}$

$w = 7\frac{2}{3} - \frac{2}{5}$

Step2: Convert mixed number to improper fraction

$7\frac{2}{3} = \frac{7\times3 + 2}{3} = \frac{23}{3}$

Step3: Find common denominator (15) for subtraction

$\frac{23}{3} = \frac{23\times5}{15} = \frac{115}{15}$, $\frac{2}{5} = \frac{2\times3}{15} = \frac{6}{15}$

Step4: Subtract the fractions

$w = \frac{115}{15} - \frac{6}{15} = \frac{109}{15}$

Step5: Convert to mixed fraction (optional)

$\frac{109}{15} = 7\frac{4}{15}$

Answer:

$w = 7\frac{4}{15}$ or $\frac{109}{15}$