Basic Math Examples

$- \frac{27}{8} n - \frac{3}{2} + \frac{29}{6} n$

Step 1

Simplify each term.

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Step 1.1

Combine $n$ and $\frac{27}{8}$ .

$- \frac{n \cdot 27}{8} - \frac{3}{2} + \frac{29}{6} n$

Step 1.2

Move $27$ to the left of $n$ .

$- \frac{27 \cdot n}{8} - \frac{3}{2} + \frac{29}{6} n$

Step 1.3

Combine $\frac{29}{6}$ and $n$ .

$- \frac{27 n}{8} - \frac{3}{2} + \frac{29 n}{6}$

Step 2

To write $- \frac{27 n}{8}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{27 n}{8} \cdot \frac{3}{3} + \frac{29 n}{6} - \frac{3}{2}$

Step 3

To write $\frac{29 n}{6}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{27 n}{8} \cdot \frac{3}{3} + \frac{29 n}{6} \cdot \frac{4}{4} - \frac{3}{2}$

Step 4

Write each expression with a common denominator of $24$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{27 n}{8}$ by $\frac{3}{3}$ .

$- \frac{27 n \cdot 3}{8 \cdot 3} + \frac{29 n}{6} \cdot \frac{4}{4} - \frac{3}{2}$

Step 4.2

Multiply $8$ by $3$ .

$- \frac{27 n \cdot 3}{24} + \frac{29 n}{6} \cdot \frac{4}{4} - \frac{3}{2}$

Step 4.3

Multiply $\frac{29 n}{6}$ by $\frac{4}{4}$ .

$- \frac{27 n \cdot 3}{24} + \frac{29 n \cdot 4}{6 \cdot 4} - \frac{3}{2}$

Step 4.4

Multiply $6$ by $4$ .

$- \frac{27 n \cdot 3}{24} + \frac{29 n \cdot 4}{24} - \frac{3}{2}$

Step 5

Combine the numerators over the common denominator.

$\frac{- 27 n \cdot 3 + 29 n \cdot 4}{24} - \frac{3}{2}$

Step 6

Simplify each term.

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Step 6.1

Simplify the numerator.

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Step 6.1.1

Factor $n$ out of $- 27 n \cdot 3 + 29 n \cdot 4$ .

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Step 6.1.1.1

Factor $n$ out of $- 27 n \cdot 3$ .

$\frac{n (- 27 \cdot 3) + 29 n \cdot 4}{24} - \frac{3}{2}$

Step 6.1.1.2

Factor $n$ out of $29 n \cdot 4$ .

$\frac{n (- 27 \cdot 3) + n (29 \cdot 4)}{24} - \frac{3}{2}$

Step 6.1.1.3

Factor $n$ out of $n (- 27 \cdot 3) + n (29 \cdot 4)$ .

$\frac{n (- 27 \cdot 3 + 29 \cdot 4)}{24} - \frac{3}{2}$

Step 6.1.2

Multiply $- 27$ by $3$ .

$\frac{n (- 81 + 29 \cdot 4)}{24} - \frac{3}{2}$

Step 6.1.3

Multiply $29$ by $4$ .

$\frac{n (- 81 + 116)}{24} - \frac{3}{2}$

Step 6.1.4

Add $- 81$ and $116$ .

$\frac{n \cdot 35}{24} - \frac{3}{2}$

Step 6.2

Move $35$ to the left of $n$ .

$\frac{35 n}{24} - \frac{3}{2}$