Basic Math Examples

$\frac{n}{16} - \frac{8}{n} \div \frac{1}{8} + \frac{1}{n}$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

To divide by a fraction, multiply by its reciprocal.

$\frac{n}{16} - (\frac{8}{n} \cdot 8) + \frac{1}{n}$

Step 1.2

Multiply $\frac{8}{n} \cdot 8$ .

Tap for more steps...

Step 1.2.1

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

$\frac{n}{16} - \frac{8 \cdot 8}{n} + \frac{1}{n}$

Step 1.2.2

Multiply $8$ by $8$ .

$\frac{n}{16} - \frac{64}{n} + \frac{1}{n}$

Step 2

Combine fractions.

Tap for more steps...

Step 2.1

Combine the numerators over the common denominator.

$\frac{n}{16} + \frac{- 64 + 1}{n}$

Step 2.2

Simplify the expression.

Tap for more steps...

Step 2.2.1

Add $- 64$ and $1$ .

$\frac{n}{16} + \frac{- 63}{n}$

Step 2.2.2

Move the negative in front of the fraction.

$\frac{n}{16} - \frac{63}{n}$

Step 3

To write $\frac{n}{16}$ as a fraction with a common denominator, multiply by $\frac{n}{n}$ .

$\frac{n}{16} \cdot \frac{n}{n} - \frac{63}{n}$

Step 4

To write $- \frac{63}{n}$ as a fraction with a common denominator, multiply by $\frac{16}{16}$ .

$\frac{n}{16} \cdot \frac{n}{n} - \frac{63}{n} \cdot \frac{16}{16}$

Step 5

Write each expression with a common denominator of $16 n$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 5.1

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

$\frac{n \cdot n}{16 n} - \frac{63}{n} \cdot \frac{16}{16}$

Step 5.2

Multiply $\frac{63}{n}$ by $\frac{16}{16}$ .

$\frac{n \cdot n}{16 n} - \frac{63 \cdot 16}{n \cdot 16}$

Step 5.3

Reorder the factors of $n \cdot 16$ .

$\frac{n \cdot n}{16 n} - \frac{63 \cdot 16}{16 n}$

Step 6

Combine the numerators over the common denominator.

$\frac{n \cdot n - 63 \cdot 16}{16 n}$

Step 7

Simplify the numerator.

Tap for more steps...

Step 7.1

Multiply $n$ by $n$ .

$\frac{n^{2} - 63 \cdot 16}{16 n}$

Step 7.2

Multiply $- 63$ by $16$ .

$\frac{n^{2} - 1008}{16 n}$