Basic Math Examples

$\frac{7 n}{16} + \frac{19 n}{3} - \frac{17}{6}$

Step 1

Find the common denominator.

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Step 1.1

Multiply $\frac{7 n}{16}$ by $\frac{3}{3}$ .

$\frac{7 n}{16} \cdot \frac{3}{3} + \frac{19 n}{3} - \frac{17}{6}$

Step 1.2

Multiply $\frac{7 n}{16}$ by $\frac{3}{3}$ .

$\frac{7 n \cdot 3}{16 \cdot 3} + \frac{19 n}{3} - \frac{17}{6}$

Step 1.3

Multiply $\frac{19 n}{3}$ by $\frac{16}{16}$ .

$\frac{7 n \cdot 3}{16 \cdot 3} + \frac{19 n}{3} \cdot \frac{16}{16} - \frac{17}{6}$

Step 1.4

Multiply $\frac{19 n}{3}$ by $\frac{16}{16}$ .

$\frac{7 n \cdot 3}{16 \cdot 3} + \frac{19 n \cdot 16}{3 \cdot 16} - \frac{17}{6}$

Step 1.5

Multiply $\frac{17}{6}$ by $\frac{8}{8}$ .

$\frac{7 n \cdot 3}{16 \cdot 3} + \frac{19 n \cdot 16}{3 \cdot 16} - (\frac{17}{6} \cdot \frac{8}{8})$

Step 1.6

Multiply $\frac{17}{6}$ by $\frac{8}{8}$ .

$\frac{7 n \cdot 3}{16 \cdot 3} + \frac{19 n \cdot 16}{3 \cdot 16} - \frac{17 \cdot 8}{6 \cdot 8}$

Step 1.7

Reorder the factors of $16 \cdot 3$ .

$\frac{7 n \cdot 3}{3 \cdot 16} + \frac{19 n \cdot 16}{3 \cdot 16} - \frac{17 \cdot 8}{6 \cdot 8}$

Step 1.8

Multiply $3$ by $16$ .

$\frac{7 n \cdot 3}{48} + \frac{19 n \cdot 16}{3 \cdot 16} - \frac{17 \cdot 8}{6 \cdot 8}$

Step 1.9

Multiply $3$ by $16$ .

$\frac{7 n \cdot 3}{48} + \frac{19 n \cdot 16}{48} - \frac{17 \cdot 8}{6 \cdot 8}$

Step 1.10

Multiply $6$ by $8$ .

$\frac{7 n \cdot 3}{48} + \frac{19 n \cdot 16}{48} - \frac{17 \cdot 8}{48}$

Step 2

Combine the numerators over the common denominator.

$\frac{7 n \cdot 3 + 19 n \cdot 16 - 17 \cdot 8}{48}$

Step 3

Simplify each term.

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Step 3.1

Multiply $3$ by $7$ .

$\frac{21 n + 19 n \cdot 16 - 17 \cdot 8}{48}$

Step 3.2

Multiply $16$ by $19$ .

$\frac{21 n + 304 n - 17 \cdot 8}{48}$

Step 3.3

Multiply $- 17$ by $8$ .

$\frac{21 n + 304 n - 136}{48}$

Step 4

Add $21 n$ and $304 n$ .

$\frac{325 n - 136}{48}$