Basic Math Examples

$\frac{s}{3} + 4 s = \frac{1}{5}$

Step 1

Simplify $\frac{s}{3} + 4 s$ .

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Step 1.1

To write $4 s$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{s}{3} + 4 s \cdot \frac{3}{3} = \frac{1}{5}$

Step 1.2

Simplify terms.

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Step 1.2.1

Combine $4 s$ and $\frac{3}{3}$ .

$\frac{s}{3} + \frac{4 s \cdot 3}{3} = \frac{1}{5}$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{s + 4 s \cdot 3}{3} = \frac{1}{5}$

Step 1.3

Simplify the numerator.

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Step 1.3.1

Factor $s$ out of $s + 4 s \cdot 3$ .

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Step 1.3.1.1

Raise $s$ to the power of $1$ .

$\frac{s^{1} + 4 s \cdot 3}{3} = \frac{1}{5}$

Step 1.3.1.2

Factor $s$ out of $s^{1}$ .

$\frac{s \cdot 1 + 4 s \cdot 3}{3} = \frac{1}{5}$

Step 1.3.1.3

Factor $s$ out of $4 s \cdot 3$ .

$\frac{s \cdot 1 + s (4 \cdot 3)}{3} = \frac{1}{5}$

Step 1.3.1.4

Factor $s$ out of $s \cdot 1 + s (4 \cdot 3)$ .

$\frac{s (1 + 4 \cdot 3)}{3} = \frac{1}{5}$

Step 1.3.2

Multiply $4$ by $3$ .

$\frac{s (1 + 12)}{3} = \frac{1}{5}$

Step 1.3.3

Add $1$ and $12$ .

$\frac{s \cdot 13}{3} = \frac{1}{5}$

Step 1.4

Move $13$ to the left of $s$ .

$\frac{13 s}{3} = \frac{1}{5}$

Step 2

Multiply both sides of the equation by $\frac{3}{13}$ .

$\frac{3}{13} \cdot \frac{13 s}{3} = \frac{3}{13} \cdot \frac{1}{5}$

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 $\frac{3}{13} \cdot \frac{13 s}{3}$ .

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Step 3.1.1.1

Cancel the common factor of $3$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{3}{13} \cdot \frac{13 s}{3} = \frac{3}{13} \cdot \frac{1}{5}$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{13} (13 s) = \frac{3}{13} \cdot \frac{1}{5}$

Step 3.1.1.2

Cancel the common factor of $13$ .

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Step 3.1.1.2.1

Factor $13$ out of $13 s$ .

$\frac{1}{13} (13 (s)) = \frac{3}{13} \cdot \frac{1}{5}$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{13} (13 s) = \frac{3}{13} \cdot \frac{1}{5}$

Step 3.1.1.2.3

Rewrite the expression.

$s = \frac{3}{13} \cdot \frac{1}{5}$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $\frac{3}{13} \cdot \frac{1}{5}$ .

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Step 3.2.1.1

Multiply $\frac{3}{13}$ by $\frac{1}{5}$ .

$s = \frac{3}{13 \cdot 5}$

Step 3.2.1.2

Multiply $13$ by $5$ .

$s = \frac{3}{65}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$s = \frac{3}{65}$

Decimal Form:

$s = 0.0\overline{461538}$