Basic Math Examples

$3 \frac{1}{5} \cdot p = - 16$

Step 1

Simplify the left side.

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Step 1.1

Simplify $3 \frac{1}{5} \cdot p$ .

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Step 1.1.1

Convert $3 \frac{1}{5}$ 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.

$(3 + \frac{1}{5}) \cdot p = - 16$

Step 1.1.1.2

Add $3$ and $\frac{1}{5}$ .

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Step 1.1.1.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$(3 \cdot \frac{5}{5} + \frac{1}{5}) \cdot p = - 16$

Step 1.1.1.2.2

Combine $3$ and $\frac{5}{5}$ .

$(\frac{3 \cdot 5}{5} + \frac{1}{5}) \cdot p = - 16$

Step 1.1.1.2.3

Combine the numerators over the common denominator.

$\frac{3 \cdot 5 + 1}{5} \cdot p = - 16$

Step 1.1.1.2.4

Simplify the numerator.

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Step 1.1.1.2.4.1

Multiply $3$ by $5$ .

$\frac{15 + 1}{5} \cdot p = - 16$

Step 1.1.1.2.4.2

Add $15$ and $1$ .

$\frac{16}{5} \cdot p = - 16$

Step 1.1.2

Combine $\frac{16}{5}$ and $p$ .

$\frac{16 p}{5} = - 16$

Step 2

Multiply both sides of the equation by $\frac{5}{16}$ .

$\frac{5}{16} \cdot \frac{16 p}{5} = \frac{5}{16} \cdot - 16$

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 $\frac{5}{16} \cdot \frac{16 p}{5}$ .

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Step 3.1.1.1

Cancel the common factor of $5$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{5}{16} \cdot \frac{16 p}{5} = \frac{5}{16} \cdot - 16$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{16} (16 p) = \frac{5}{16} \cdot - 16$

Step 3.1.1.2

Cancel the common factor of $16$ .

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Step 3.1.1.2.1

Factor $16$ out of $16 p$ .

$\frac{1}{16} (16 (p)) = \frac{5}{16} \cdot - 16$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{16} (16 p) = \frac{5}{16} \cdot - 16$

Step 3.1.1.2.3

Rewrite the expression.

$p = \frac{5}{16} \cdot - 16$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{5}{16} \cdot - 16$ .

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Step 3.2.1.1

Cancel the common factor of $16$ .

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Step 3.2.1.1.1

Factor $16$ out of $- 16$ .

$p = \frac{5}{16} \cdot (16 (- 1))$

Step 3.2.1.1.2

Cancel the common factor.

$p = \frac{5}{16} \cdot (16 \cdot - 1)$

Step 3.2.1.1.3

Rewrite the expression.

$p = 5 \cdot - 1$

Step 3.2.1.2

Multiply $5$ by $- 1$ .

$p = - 5$