Algebra Examples

$\frac{p}{2 \frac{1}{7}} = - 5.3$

Step 1

Simplify the left side.

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Step 1.1

Simplify $\frac{p}{2 \frac{1}{7}}$ .

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Step 1.1.1

Convert $2 \frac{1}{7}$ 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.

$\frac{p}{2 + \frac{1}{7}} = - 5.3$

Step 1.1.1.2

Add $2$ and $\frac{1}{7}$ .

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Step 1.1.1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{p}{2 \cdot \frac{7}{7} + \frac{1}{7}} = - 5.3$

Step 1.1.1.2.2

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

$\frac{p}{\frac{2 \cdot 7}{7} + \frac{1}{7}} = - 5.3$

Step 1.1.1.2.3

Combine the numerators over the common denominator.

$\frac{p}{\frac{2 \cdot 7 + 1}{7}} = - 5.3$

Step 1.1.1.2.4

Simplify the numerator.

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Step 1.1.1.2.4.1

Multiply $2$ by $7$ .

$\frac{p}{\frac{14 + 1}{7}} = - 5.3$

Step 1.1.1.2.4.2

Add $14$ and $1$ .

$\frac{p}{\frac{15}{7}} = - 5.3$

Step 1.1.2

Multiply the numerator by the reciprocal of the denominator.

$p \frac{7}{15} = - 5.3$

Step 1.1.3

Combine $p$ and $\frac{7}{15}$ .

$\frac{p \cdot 7}{15} = - 5.3$

Step 1.1.4

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

$\frac{7 p}{15} = - 5.3$

Step 2

Multiply both sides of the equation by $\frac{15}{7}$ .

$\frac{15}{7} \cdot \frac{7 p}{15} = \frac{15}{7} \cdot - 5.3$

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 $\frac{15}{7} \cdot \frac{7 p}{15}$ .

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Step 3.1.1.1

Cancel the common factor of $15$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{15}{7} \cdot \frac{7 p}{15} = \frac{15}{7} \cdot - 5.3$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{7} (7 p) = \frac{15}{7} \cdot - 5.3$

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 $7 p$ .

$\frac{1}{7} (7 (p)) = \frac{15}{7} \cdot - 5.3$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{7} (7 p) = \frac{15}{7} \cdot - 5.3$

Step 3.1.1.2.3

Rewrite the expression.

$p = \frac{15}{7} \cdot - 5.3$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{15}{7} \cdot - 5.3$ .

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Step 3.2.1.1

Multiply $\frac{15}{7} \cdot - 5.3$ .

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Step 3.2.1.1.1

Combine $\frac{15}{7}$ and $- 5.3$ .

$p = \frac{15 \cdot - 5.3}{7}$

Step 3.2.1.1.2

Multiply $15$ by $- 5.3$ .

$p = \frac{- 79.5}{7}$

Step 3.2.1.2

Divide $- 79.5$ by $7$ .

$p = - 11.3\overline{571428}$