Algebra Examples

$\frac{p}{1 \frac{6}{7}} = - 4.4$

Step 1

Simplify the left side.

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Step 1.1

Simplify $\frac{p}{1 \frac{6}{7}}$ .

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Step 1.1.1

Convert $1 \frac{6}{7}$ to an improper fraction.

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Step 1.1.1.1

A mixed number is an addition of its whole and fractional parts.

$\frac{p}{1 + \frac{6}{7}} = - 4.4$

Step 1.1.1.2

Add $1$ and $\frac{6}{7}$ .

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Step 1.1.1.2.1

Write $1$ as a fraction with a common denominator.

$\frac{p}{\frac{7}{7} + \frac{6}{7}} = - 4.4$

Step 1.1.1.2.2

Combine the numerators over the common denominator.

$\frac{p}{\frac{7 + 6}{7}} = - 4.4$

Step 1.1.1.2.3

Add $7$ and $6$ .

$\frac{p}{\frac{13}{7}} = - 4.4$

Step 1.1.2

Multiply the numerator by the reciprocal of the denominator.

$p \frac{7}{13} = - 4.4$

Step 1.1.3

Combine $p$ and $\frac{7}{13}$ .

$\frac{p \cdot 7}{13} = - 4.4$

Step 1.1.4

Move $7$ to the left of $p$ .

$\frac{7 p}{13} = - 4.4$

Step 2

Multiply both sides of the equation by $\frac{13}{7}$ .

$\frac{13}{7} \cdot \frac{7 p}{13} = \frac{13}{7} \cdot - 4.4$

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 $\frac{13}{7} \cdot \frac{7 p}{13}$ .

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Step 3.1.1.1

Cancel the common factor of $13$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{13}{7} \cdot \frac{7 p}{13} = \frac{13}{7} \cdot - 4.4$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{7} (7 p) = \frac{13}{7} \cdot - 4.4$

Step 3.1.1.2

Cancel the common factor of $7$ .

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Step 3.1.1.2.1

Factor $7$ out of $7 p$ .

$\frac{1}{7} (7 (p)) = \frac{13}{7} \cdot - 4.4$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{7} (7 p) = \frac{13}{7} \cdot - 4.4$

Step 3.1.1.2.3

Rewrite the expression.

$p = \frac{13}{7} \cdot - 4.4$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{13}{7} \cdot - 4.4$ .

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Step 3.2.1.1

Multiply $\frac{13}{7} \cdot - 4.4$ .

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Step 3.2.1.1.1

Combine $\frac{13}{7}$ and $- 4.4$ .

$p = \frac{13 \cdot - 4.4}{7}$

Step 3.2.1.1.2

Multiply $13$ by $- 4.4$ .

$p = \frac{- 57.2}{7}$

Step 3.2.1.2

Divide $- 57.2$ by $7$ .

$p = - 8.1\overline{714285}$