Basic Math Examples

$- \frac{5}{40} = \frac{6}{m}$

Step 1

Rewrite the equation as $\frac{6}{m} = - \frac{5}{40}$ .

$\frac{6}{m} = - \frac{5}{40}$

Step 2

Cancel the common factor of $5$ and $40$ .

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Step 2.1

Factor $5$ out of $5$ .

$\frac{6}{m} = - \frac{5 (1)}{40}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $5$ out of $40$ .

$\frac{6}{m} = - \frac{5 \cdot 1}{5 \cdot 8}$

Step 2.2.2

Cancel the common factor.

$\frac{6}{m} = - \frac{5 \cdot 1}{5 \cdot 8}$

Step 2.2.3

Rewrite the expression.

$\frac{6}{m} = - \frac{1}{8}$

Step 3

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

$6 \cdot 8 = m \cdot - 1$

Step 4

Solve the equation for $m$ .

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Step 4.1

Rewrite the equation as $m \cdot - 1 = 6 \cdot 8$ .

$m \cdot - 1 = 6 \cdot 8$

Step 4.2

Divide each term in $m \cdot - 1 = 6 \cdot 8$ by $- 1$ and simplify.

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Step 4.2.1

Divide each term in $m \cdot - 1 = 6 \cdot 8$ by $- 1$ .

$\frac{m \cdot - 1}{- 1} = \frac{6 \cdot 8}{- 1}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Move the negative one from the denominator of $\frac{m \cdot - 1}{- 1}$ .

$- 1 \cdot (m \cdot - 1) = \frac{6 \cdot 8}{- 1}$

Step 4.2.2.2

Rewrite $- 1 \cdot (m \cdot - 1)$ as $- (m \cdot - 1)$ .

$- (m \cdot - 1) = \frac{6 \cdot 8}{- 1}$

Step 4.2.2.3

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

$- (- 1 \cdot m) = \frac{6 \cdot 8}{- 1}$

Step 4.2.2.4

Rewrite $- 1 m$ as $- m$ .

$- - m = \frac{6 \cdot 8}{- 1}$

Step 4.2.2.5

Multiply $- - m$ .

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Step 4.2.2.5.1

Multiply $- 1$ by $- 1$ .

$1 m = \frac{6 \cdot 8}{- 1}$

Step 4.2.2.5.2

Multiply $m$ by $1$ .

$m = \frac{6 \cdot 8}{- 1}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Move the negative one from the denominator of $\frac{6 \cdot 8}{- 1}$ .

$m = - 1 \cdot (6 \cdot 8)$

Step 4.2.3.2

Rewrite $- 1 \cdot (6 \cdot 8)$ as $- (6 \cdot 8)$ .

$m = - (6 \cdot 8)$

Step 4.2.3.3

Multiply $- (6 \cdot 8)$ .

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Step 4.2.3.3.1

Multiply $6$ by $8$ .

$m = - 1 \cdot 48$

Step 4.2.3.3.2

Multiply $- 1$ by $48$ .

$m = - 48$