Basic Math Examples

$6 = \frac{4}{- 7} t$

Step 1

Rewrite the equation as $\frac{4}{- 7} t = 6$ .

$\frac{4}{- 7} t = 6$

Step 2

Multiply both sides of the equation by $\frac{- 7}{4}$ .

$\frac{- 7}{4} (\frac{4}{- 7} t) = \frac{- 7}{4} \cdot 6$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{- 7}{4} (\frac{4}{- 7} t)$ .

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Step 3.1.1.1

Simplify the expression.

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Step 3.1.1.1.1

Move the negative in front of the fraction.

$- \frac{7}{4} (\frac{4}{- 7} t) = \frac{- 7}{4} \cdot 6$

Step 3.1.1.1.2

Move the negative in front of the fraction.

$- \frac{7}{4} (- \frac{4}{7} t) = \frac{- 7}{4} \cdot 6$

Step 3.1.1.2

Combine $t$ and $\frac{4}{7}$ .

$- \frac{7}{4} (- \frac{t \cdot 4}{7}) = \frac{- 7}{4} \cdot 6$

Step 3.1.1.3

Cancel the common factor of $7$ .

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Step 3.1.1.3.1

Move the leading negative in $- \frac{7}{4}$ into the numerator.

$\frac{- 7}{4} (- \frac{t \cdot 4}{7}) = \frac{- 7}{4} \cdot 6$

Step 3.1.1.3.2

Move the leading negative in $- \frac{t \cdot 4}{7}$ into the numerator.

$\frac{- 7}{4} \cdot \frac{- t \cdot 4}{7} = \frac{- 7}{4} \cdot 6$

Step 3.1.1.3.3

Factor $7$ out of $- 7$ .

$\frac{7 (- 1)}{4} \cdot \frac{- t \cdot 4}{7} = \frac{- 7}{4} \cdot 6$

Step 3.1.1.3.4

Cancel the common factor.

$\frac{7 \cdot - 1}{4} \cdot \frac{- t \cdot 4}{7} = \frac{- 7}{4} \cdot 6$

Step 3.1.1.3.5

Rewrite the expression.

$\frac{- 1}{4} (- t \cdot 4) = \frac{- 7}{4} \cdot 6$

Step 3.1.1.4

Cancel the common factor of $4$ .

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Step 3.1.1.4.1

Factor $4$ out of $- t \cdot 4$ .

$\frac{- 1}{4} (4 \cdot (- t)) = \frac{- 7}{4} \cdot 6$

Step 3.1.1.4.2

Cancel the common factor.

$\frac{- 1}{4} (4 \cdot (- t)) = \frac{- 7}{4} \cdot 6$

Step 3.1.1.4.3

Rewrite the expression.

$- - t = \frac{- 7}{4} \cdot 6$

Step 3.1.1.5

Multiply.

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Step 3.1.1.5.1

Multiply $- 1$ by $- 1$ .

$1 t = \frac{- 7}{4} \cdot 6$

Step 3.1.1.5.2

Multiply $t$ by $1$ .

$t = \frac{- 7}{4} \cdot 6$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{- 7}{4} \cdot 6$ .

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Step 3.2.1.1

Cancel the common factor of $2$ .

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Step 3.2.1.1.1

Factor $2$ out of $4$ .

$t = \frac{- 7}{2 (2)} \cdot 6$

Step 3.2.1.1.2

Factor $2$ out of $6$ .

$t = \frac{- 7}{2 \cdot 2} \cdot (2 \cdot 3)$

Step 3.2.1.1.3

Cancel the common factor.

$t = \frac{- 7}{2 \cdot 2} \cdot (2 \cdot 3)$

Step 3.2.1.1.4

Rewrite the expression.

$t = \frac{- 7}{2} \cdot 3$

Step 3.2.1.2

Combine $\frac{- 7}{2}$ and $3$ .

$t = \frac{- 7 \cdot 3}{2}$

Step 3.2.1.3

Simplify the expression.

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Step 3.2.1.3.1

Multiply $- 7$ by $3$ .

$t = \frac{- 21}{2}$

Step 3.2.1.3.2

Move the negative in front of the fraction.

$t = - \frac{21}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$t = - \frac{21}{2}$

Decimal Form:

$t = - 10.5$

Mixed Number Form:

$t = - 10 \frac{1}{2}$