Basic Math Examples

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

Step 1

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

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Step 1.1

Rewrite.

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

Step 1.2

Simplify by adding zeros.

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

Step 1.3

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

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

Step 2

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

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Step 2.1

Simplify each term.

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Step 2.1.1

Divide $15$ by $3$ .

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

Step 2.1.2

Combine $\frac{3}{2}$ and $s$ .

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

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:

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