Basic Math Examples

$s + \frac{1}{3} + 3 s - \frac{1}{2} = 2 s + \frac{1}{4}$

Step 1

Simplify $s + \frac{1}{3} + 3 s - \frac{1}{2}$ .

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Step 1.1

Add $s$ and $3 s$ .

$4 s + \frac{1}{3} - \frac{1}{2} = 2 s + \frac{1}{4}$

Step 1.2

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$4 s + \frac{1}{3} \cdot \frac{2}{2} - \frac{1}{2} = 2 s + \frac{1}{4}$

Step 1.3

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$4 s + \frac{1}{3} \cdot \frac{2}{2} - \frac{1}{2} \cdot \frac{3}{3} = 2 s + \frac{1}{4}$

Step 1.4

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{1}{3}$ by $\frac{2}{2}$ .

$4 s + \frac{2}{3 \cdot 2} - \frac{1}{2} \cdot \frac{3}{3} = 2 s + \frac{1}{4}$

Step 1.4.2

Multiply $3$ by $2$ .

$4 s + \frac{2}{6} - \frac{1}{2} \cdot \frac{3}{3} = 2 s + \frac{1}{4}$

Step 1.4.3

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

$4 s + \frac{2}{6} - \frac{3}{2 \cdot 3} = 2 s + \frac{1}{4}$

Step 1.4.4

Multiply $2$ by $3$ .

$4 s + \frac{2}{6} - \frac{3}{6} = 2 s + \frac{1}{4}$

Step 1.5

Combine the numerators over the common denominator.

$4 s + \frac{2 - 3}{6} = 2 s + \frac{1}{4}$

Step 1.6

Subtract $3$ from $2$ .

$4 s + \frac{- 1}{6} = 2 s + \frac{1}{4}$

Step 1.7

Move the negative in front of the fraction.

$4 s - \frac{1}{6} = 2 s + \frac{1}{4}$

Step 2

Move all terms containing $s$ to the left side of the equation.

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Step 2.1

Subtract $2 s$ from both sides of the equation.

$4 s - \frac{1}{6} - 2 s = \frac{1}{4}$

Step 2.2

Subtract $2 s$ from $4 s$ .

$2 s - \frac{1}{6} = \frac{1}{4}$

Step 3

Move all terms not containing $s$ to the right side of the equation.

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Step 3.1

Add $\frac{1}{6}$ to both sides of the equation.

$2 s = \frac{1}{4} + \frac{1}{6}$

Step 3.2

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$2 s = \frac{1}{4} \cdot \frac{3}{3} + \frac{1}{6}$

Step 3.3

To write $\frac{1}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$2 s = \frac{1}{4} \cdot \frac{3}{3} + \frac{1}{6} \cdot \frac{2}{2}$

Step 3.4

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.4.1

Multiply $\frac{1}{4}$ by $\frac{3}{3}$ .

$2 s = \frac{3}{4 \cdot 3} + \frac{1}{6} \cdot \frac{2}{2}$

Step 3.4.2

Multiply $4$ by $3$ .

$2 s = \frac{3}{12} + \frac{1}{6} \cdot \frac{2}{2}$

Step 3.4.3

Multiply $\frac{1}{6}$ by $\frac{2}{2}$ .

$2 s = \frac{3}{12} + \frac{2}{6 \cdot 2}$

Step 3.4.4

Multiply $6$ by $2$ .

$2 s = \frac{3}{12} + \frac{2}{12}$

Step 3.5

Combine the numerators over the common denominator.

$2 s = \frac{3 + 2}{12}$

Step 3.6

Add $3$ and $2$ .

$2 s = \frac{5}{12}$

Step 4

Divide each term in $2 s = \frac{5}{12}$ by $2$ and simplify.

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Step 4.1

Divide each term in $2 s = \frac{5}{12}$ by $2$ .

$\frac{2 s}{2} = \frac{\frac{5}{12}}{2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $2$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{2 s}{2} = \frac{\frac{5}{12}}{2}$

Step 4.2.1.2

Divide $s$ by $1$ .

$s = \frac{\frac{5}{12}}{2}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Multiply the numerator by the reciprocal of the denominator.

$s = \frac{5}{12} \cdot \frac{1}{2}$

Step 4.3.2

Multiply $\frac{5}{12} \cdot \frac{1}{2}$ .

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Step 4.3.2.1

Multiply $\frac{5}{12}$ by $\frac{1}{2}$ .

$s = \frac{5}{12 \cdot 2}$

Step 4.3.2.2

Multiply $12$ by $2$ .

$s = \frac{5}{24}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$s = \frac{5}{24}$

Decimal Form:

$s = 0.208\overline{3}$