Basic Math Examples

$\frac{\frac{16}{m - 1}}{\frac{16}{5} + \frac{16}{25}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{16}{m - 1} \cdot \frac{1}{\frac{16}{5} + \frac{16}{25}}$

Step 2

Simplify the denominator.

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Step 2.1

To write $\frac{16}{5}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{16}{m - 1} \cdot \frac{1}{\frac{16}{5} \cdot \frac{5}{5} + \frac{16}{25}}$

Step 2.2

Write each expression with a common denominator of $25$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.2.1

Multiply $\frac{16}{5}$ by $\frac{5}{5}$ .

$\frac{16}{m - 1} \cdot \frac{1}{\frac{16 \cdot 5}{5 \cdot 5} + \frac{16}{25}}$

Step 2.2.2

Multiply $5$ by $5$ .

$\frac{16}{m - 1} \cdot \frac{1}{\frac{16 \cdot 5}{25} + \frac{16}{25}}$

Step 2.3

Combine the numerators over the common denominator.

$\frac{16}{m - 1} \cdot \frac{1}{\frac{16 \cdot 5 + 16}{25}}$

Step 2.4

Simplify the numerator.

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Step 2.4.1

Multiply $16$ by $5$ .

$\frac{16}{m - 1} \cdot \frac{1}{\frac{80 + 16}{25}}$

Step 2.4.2

Add $80$ and $16$ .

$\frac{16}{m - 1} \cdot \frac{1}{\frac{96}{25}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{16}{m - 1} (1 (\frac{25}{96}))$

Step 4

Multiply $\frac{25}{96}$ by $1$ .

$\frac{16}{m - 1} \cdot \frac{25}{96}$

Step 5

Cancel the common factor of $16$ .

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Step 5.1

Factor $16$ out of $96$ .

$\frac{16}{m - 1} \cdot \frac{25}{16 (6)}$

Step 5.2

Cancel the common factor.

$\frac{16}{m - 1} \cdot \frac{25}{16 \cdot 6}$

Step 5.3

Rewrite the expression.

$\frac{1}{m - 1} \cdot \frac{25}{6}$

Step 6

Multiply $\frac{1}{m - 1}$ by $\frac{25}{6}$ .

$\frac{25}{(m - 1) \cdot 6}$

Step 7

Move $6$ to the left of $m - 1$ .

$\frac{25}{6 (m - 1)}$