Basic Math Examples

\frac{2 s}{5} - \frac{s}{3} = 3

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

Step 1

Simplify

\frac{2 s}{5} - \frac{s}{3}

$\frac{2 s}{5} - \frac{s}{3}$ .

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Step 1.1

To write

\frac{2 s}{5}

$\frac{2 s}{5}$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{2 s}{5} \cdot \frac{3}{3} - \frac{s}{3} = 3

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

Step 1.2

To write

- \frac{s}{3}

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

\frac{5}{5}

$\frac{5}{5}$ .

\frac{2 s}{5} \cdot \frac{3}{3} - \frac{s}{3} \cdot \frac{5}{5} = 3

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

Step 1.3

Write each expression with a common denominator of

15

$15$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 1.3.1

Multiply

\frac{2 s}{5}

$\frac{2 s}{5}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{2 s \cdot 3}{5 \cdot 3} - \frac{s}{3} \cdot \frac{5}{5} = 3

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

Step 1.3.2

Multiply

5

$5$ by

3

$3$ .

\frac{2 s \cdot 3}{15} - \frac{s}{3} \cdot \frac{5}{5} = 3

$\frac{2 s \cdot 3}{15} - \frac{s}{3} \cdot \frac{5}{5} = 3$

Step 1.3.3

Multiply

\frac{s}{3}

$\frac{s}{3}$ by

\frac{5}{5}

$\frac{5}{5}$ .

\frac{2 s \cdot 3}{15} - \frac{s \cdot 5}{3 \cdot 5} = 3

$\frac{2 s \cdot 3}{15} - \frac{s \cdot 5}{3 \cdot 5} = 3$

Step 1.3.4

Multiply

3

$3$ by

5

$5$ .

\frac{2 s \cdot 3}{15} - \frac{s \cdot 5}{15} = 3

$\frac{2 s \cdot 3}{15} - \frac{s \cdot 5}{15} = 3$

\frac{2 s \cdot 3}{15} - \frac{s \cdot 5}{15} = 3

$\frac{2 s \cdot 3}{15} - \frac{s \cdot 5}{15} = 3$

Step 1.4

Combine the numerators over the common denominator.

\frac{2 s \cdot 3 - s \cdot 5}{15} = 3

$\frac{2 s \cdot 3 - s \cdot 5}{15} = 3$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Factor

s

$s$ out of

2 s \cdot 3 - s \cdot 5

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

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Step 1.5.1.1

Factor

s

$s$ out of

2 s \cdot 3

$2 s \cdot 3$ .

\frac{s (2 \cdot 3) - s \cdot 5}{15} = 3

$\frac{s (2 \cdot 3) - s \cdot 5}{15} = 3$

Step 1.5.1.2

Factor

s

$s$ out of

- s \cdot 5

$- s \cdot 5$ .

\frac{s (2 \cdot 3) + s (- 1 \cdot 5)}{15} = 3

$\frac{s (2 \cdot 3) + s (- 1 \cdot 5)}{15} = 3$

Step 1.5.1.3

Factor

s

$s$ out of

s (2 \cdot 3) + s (- 1 \cdot 5)

$s (2 \cdot 3) + s (- 1 \cdot 5)$ .

\frac{s (2 \cdot 3 - 1 \cdot 5)}{15} = 3

$\frac{s (2 \cdot 3 - 1 \cdot 5)}{15} = 3$

\frac{s (2 \cdot 3 - 1 \cdot 5)}{15} = 3

$\frac{s (2 \cdot 3 - 1 \cdot 5)}{15} = 3$

Step 1.5.2

Multiply

2

$2$ by

3

$3$ .

\frac{s (6 - 1 \cdot 5)}{15} = 3

$\frac{s (6 - 1 \cdot 5)}{15} = 3$

Step 1.5.3

Multiply

- 1

$- 1$ by

5

$5$ .

\frac{s (6 - 5)}{15} = 3

$\frac{s (6 - 5)}{15} = 3$

Step 1.5.4

Subtract

5

$5$ from

6

$6$ .

\frac{s \cdot 1}{15} = 3

$\frac{s \cdot 1}{15} = 3$

\frac{s \cdot 1}{15} = 3

$\frac{s \cdot 1}{15} = 3$

Step 1.6

Multiply

s

$s$ by

1

$1$ .

\frac{s}{15} = 3

$\frac{s}{15} = 3$

\frac{s}{15} = 3

$\frac{s}{15} = 3$

Step 2

Multiply both sides of the equation by

15

$15$ .

15 \frac{s}{15} = 15 \cdot 3

$15 \frac{s}{15} = 15 \cdot 3$

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

Cancel the common factor of

15

$15$ .

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Step 3.1.1.1

Cancel the common factor.

$15 \frac{s}{15} = 15 \cdot 3$

Step 3.1.1.2

Rewrite the expression.

$s = 15 \cdot 3$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply

$15$ by

$3$ .

$s = 45$