Basic Math Examples

\frac{5}{3} s = \frac{15}{3} + \frac{3}{2} s - \frac{1}{4}

$\frac{5}{3} s = \frac{15}{3} + \frac{3}{2} s - \frac{1}{4}$

Step 1

Simplify

\frac{5}{3} s

$\frac{5}{3} s$ .

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Step 1.1

Rewrite.

0 + 0 + \frac{5}{3} s = \frac{15}{3} + \frac{3}{2} s - \frac{1}{4}

$0 + 0 + \frac{5}{3} s = \frac{15}{3} + \frac{3}{2} s - \frac{1}{4}$

Step 1.2

Simplify by adding zeros.

\frac{5}{3} s = \frac{15}{3} + \frac{3}{2} s - \frac{1}{4}

$\frac{5}{3} s = \frac{15}{3} + \frac{3}{2} s - \frac{1}{4}$

Step 1.3

Combine

\frac{5}{3}

$\frac{5}{3}$ and

s

$s$ .

\frac{5 s}{3} = \frac{15}{3} + \frac{3}{2} s - \frac{1}{4}

$\frac{5 s}{3} = \frac{15}{3} + \frac{3}{2} s - \frac{1}{4}$

\frac{5 s}{3} = \frac{15}{3} + \frac{3}{2} s - \frac{1}{4}

$\frac{5 s}{3} = \frac{15}{3} + \frac{3}{2} s - \frac{1}{4}$

Step 2

Simplify

\frac{15}{3} + \frac{3}{2} s - \frac{1}{4}

$\frac{15}{3} + \frac{3}{2} s - \frac{1}{4}$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Divide

15

$15$ by

3

$3$ .

\frac{5 s}{3} = 5 + \frac{3}{2} s - \frac{1}{4}

$\frac{5 s}{3} = 5 + \frac{3}{2} s - \frac{1}{4}$

Step 2.1.2

Combine

\frac{3}{2}

$\frac{3}{2}$ and

s

$s$ .

\frac{5 s}{3} = 5 + \frac{3 s}{2} - \frac{1}{4}

$\frac{5 s}{3} = 5 + \frac{3 s}{2} - \frac{1}{4}$

\frac{5 s}{3} = 5 + \frac{3 s}{2} - \frac{1}{4}

$\frac{5 s}{3} = 5 + \frac{3 s}{2} - \frac{1}{4}$

Step 2.2

To write

$5$ as a fraction with a common denominator, multiply by

$\frac{4}{4}$ .

$\frac{5 s}{3} = \frac{3 s}{2} + 5 \cdot \frac{4}{4} - \frac{1}{4}$

Step 2.3

Combine

$5$ and

$\frac{4}{4}$ .

$\frac{5 s}{3} = \frac{3 s}{2} + \frac{5 \cdot 4}{4} - \frac{1}{4}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{5 s}{3} = \frac{3 s}{2} + \frac{5 \cdot 4 - 1}{4}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply

$5$ by

$4$ .

$\frac{5 s}{3} = \frac{3 s}{2} + \frac{20 - 1}{4}$

Step 2.5.2

Subtract

$1$ from

$20$ .

$\frac{5 s}{3} = \frac{3 s}{2} + \frac{19}{4}$

Step 3

Move all terms containing

$s$ to the left side of the equation.

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Step 3.1

Subtract

$\frac{3 s}{2}$ from both sides of the equation.

$\frac{5 s}{3} - \frac{3 s}{2} = \frac{19}{4}$

Step 3.2

To write

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

$\frac{2}{2}$ .

$\frac{5 s}{3} \cdot \frac{2}{2} - \frac{3 s}{2} = \frac{19}{4}$

Step 3.3

To write

$- \frac{3 s}{2}$ as a fraction with a common denominator, multiply by

$\frac{3}{3}$ .

$\frac{5 s}{3} \cdot \frac{2}{2} - \frac{3 s}{2} \cdot \frac{3}{3} = \frac{19}{4}$

Step 3.4

Write each expression with a common denominator of

$6$ , by multiplying each by an appropriate factor of

$1$ .

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Step 3.4.1

Multiply

$\frac{5 s}{3}$ by

$\frac{2}{2}$ .

$\frac{5 s \cdot 2}{3 \cdot 2} - \frac{3 s}{2} \cdot \frac{3}{3} = \frac{19}{4}$

Step 3.4.2

Multiply

$3$ by

$2$ .

$\frac{5 s \cdot 2}{6} - \frac{3 s}{2} \cdot \frac{3}{3} = \frac{19}{4}$

Step 3.4.3

Multiply

$\frac{3 s}{2}$ by

$\frac{3}{3}$ .

$\frac{5 s \cdot 2}{6} - \frac{3 s \cdot 3}{2 \cdot 3} = \frac{19}{4}$

Step 3.4.4

Multiply

$2$ by

$3$ .

$\frac{5 s \cdot 2}{6} - \frac{3 s \cdot 3}{6} = \frac{19}{4}$

Step 3.5

Combine the numerators over the common denominator.

$\frac{5 s \cdot 2 - 3 s \cdot 3}{6} = \frac{19}{4}$

Step 3.6

Simplify the numerator.

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Step 3.6.1

Factor

$s$ out of

$5 s \cdot 2 - 3 s \cdot 3$ .

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Step 3.6.1.1

Factor

$s$ out of

$5 s \cdot 2$ .

$\frac{s (5 \cdot 2) - 3 s \cdot 3}{6} = \frac{19}{4}$

Step 3.6.1.2

Factor

$s$ out of

$- 3 s \cdot 3$ .

$\frac{s (5 \cdot 2) + s (- 3 \cdot 3)}{6} = \frac{19}{4}$

Step 3.6.1.3

Factor

$s$ out of

$s (5 \cdot 2) + s (- 3 \cdot 3)$ .

$\frac{s (5 \cdot 2 - 3 \cdot 3)}{6} = \frac{19}{4}$

Step 3.6.2

Multiply

$5$ by

$2$ .

$\frac{s (10 - 3 \cdot 3)}{6} = \frac{19}{4}$

Step 3.6.3

Multiply

$- 3$ by

$3$ .

$\frac{s (10 - 9)}{6} = \frac{19}{4}$

Step 3.6.4

Subtract

$9$ from

$10$ .

$\frac{s \cdot 1}{6} = \frac{19}{4}$

Step 3.7

Multiply

$s$ by

$1$ .

$\frac{s}{6} = \frac{19}{4}$

Step 4

Multiply both sides of the equation by

$6$ .

$6 \frac{s}{6} = 6 (\frac{19}{4})$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Cancel the common factor of

$6$ .

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Step 5.1.1.1

Cancel the common factor.

$6 \frac{s}{6} = 6 (\frac{19}{4})$

Step 5.1.1.2

Rewrite the expression.

$s = 6 (\frac{19}{4})$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify

$6 (\frac{19}{4})$ .

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Step 5.2.1.1

Cancel the common factor of

$2$ .

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Step 5.2.1.1.1

Factor

$2$ out of

$6$ .

$s = 2 (3) \frac{19}{4}$

Step 5.2.1.1.2

Factor

$2$ out of

$4$ .

$s = 2 \cdot 3 \frac{19}{2 \cdot 2}$

Step 5.2.1.1.3

Cancel the common factor.

$s = 2 \cdot 3 \frac{19}{2 \cdot 2}$

Step 5.2.1.1.4

Rewrite the expression.

$s = 3 (\frac{19}{2})$

Step 5.2.1.2

Combine

$3$ and

$\frac{19}{2}$ .

$s = \frac{3 \cdot 19}{2}$

Step 5.2.1.3

Multiply

$3$ by

$19$ .

$s = \frac{57}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$s = \frac{57}{2}$

Decimal Form:

$s = 28.5$

Mixed Number Form:

$s = 28 \frac{1}{2}$