Basic Math Examples

\frac{3}{5} - \frac{2}{3} - (- \frac{8}{15})

$\frac{3}{5} - \frac{2}{3} - (- \frac{8}{15})$

Step 1

Multiply

- (- \frac{8}{15})

$- (- \frac{8}{15})$ .

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Step 1.1

Multiply

- 1

$- 1$ by

- 1

$- 1$ .

\frac{3}{5} - \frac{2}{3} + 1 (\frac{8}{15})

$\frac{3}{5} - \frac{2}{3} + 1 (\frac{8}{15})$

Step 1.2

Multiply

\frac{8}{15}

$\frac{8}{15}$ by

1

$1$ .

\frac{3}{5} - \frac{2}{3} + \frac{8}{15}

$\frac{3}{5} - \frac{2}{3} + \frac{8}{15}$

\frac{3}{5} - \frac{2}{3} + \frac{8}{15}

$\frac{3}{5} - \frac{2}{3} + \frac{8}{15}$

Step 2

Find the common denominator.

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Step 2.1

Multiply

\frac{3}{5}

$\frac{3}{5}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{3}{5} \cdot \frac{3}{3} - \frac{2}{3} + \frac{8}{15}

$\frac{3}{5} \cdot \frac{3}{3} - \frac{2}{3} + \frac{8}{15}$

Step 2.2

Multiply

\frac{3}{5}

$\frac{3}{5}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{3 \cdot 3}{5 \cdot 3} - \frac{2}{3} + \frac{8}{15}

$\frac{3 \cdot 3}{5 \cdot 3} - \frac{2}{3} + \frac{8}{15}$

Step 2.3

Multiply

\frac{2}{3}

$\frac{2}{3}$ by

\frac{5}{5}

$\frac{5}{5}$ .

\frac{3 \cdot 3}{5 \cdot 3} - (\frac{2}{3} \cdot \frac{5}{5}) + \frac{8}{15}

$\frac{3 \cdot 3}{5 \cdot 3} - (\frac{2}{3} \cdot \frac{5}{5}) + \frac{8}{15}$

Step 2.4

Multiply

\frac{2}{3}

$\frac{2}{3}$ by

\frac{5}{5}

$\frac{5}{5}$ .

\frac{3 \cdot 3}{5 \cdot 3} - \frac{2 \cdot 5}{3 \cdot 5} + \frac{8}{15}

$\frac{3 \cdot 3}{5 \cdot 3} - \frac{2 \cdot 5}{3 \cdot 5} + \frac{8}{15}$

Step 2.5

Reorder the factors of

5 \cdot 3

$5 \cdot 3$ .

\frac{3 \cdot 3}{3 \cdot 5} - \frac{2 \cdot 5}{3 \cdot 5} + \frac{8}{15}

$\frac{3 \cdot 3}{3 \cdot 5} - \frac{2 \cdot 5}{3 \cdot 5} + \frac{8}{15}$

Step 2.6

Multiply

3

$3$ by

5

$5$ .

\frac{3 \cdot 3}{15} - \frac{2 \cdot 5}{3 \cdot 5} + \frac{8}{15}

$\frac{3 \cdot 3}{15} - \frac{2 \cdot 5}{3 \cdot 5} + \frac{8}{15}$

Step 2.7

Multiply

3

$3$ by

5

$5$ .

\frac{3 \cdot 3}{15} - \frac{2 \cdot 5}{15} + \frac{8}{15}

$\frac{3 \cdot 3}{15} - \frac{2 \cdot 5}{15} + \frac{8}{15}$

\frac{3 \cdot 3}{15} - \frac{2 \cdot 5}{15} + \frac{8}{15}

$\frac{3 \cdot 3}{15} - \frac{2 \cdot 5}{15} + \frac{8}{15}$

Step 3

Combine the numerators over the common denominator.

\frac{3 \cdot 3 - 2 \cdot 5 + 8}{15}

$\frac{3 \cdot 3 - 2 \cdot 5 + 8}{15}$

Step 4

Simplify each term.

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Step 4.1

Multiply

3

$3$ by

3

$3$ .

\frac{9 - 2 \cdot 5 + 8}{15}

$\frac{9 - 2 \cdot 5 + 8}{15}$

Step 4.2

Multiply

- 2

$- 2$ by

5

$5$ .

\frac{9 - 10 + 8}{15}

$\frac{9 - 10 + 8}{15}$

\frac{9 - 10 + 8}{15}

$\frac{9 - 10 + 8}{15}$

Step 5

Simplify by adding and subtracting.

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Step 5.1

Subtract

10

$10$ from

9

$9$ .

\frac{- 1 + 8}{15}

$\frac{- 1 + 8}{15}$

Step 5.2

Add

- 1

$- 1$ and

8

$8$ .

\frac{7}{15}

$\frac{7}{15}$

\frac{7}{15}

$\frac{7}{15}$

Step 6

The result can be shown in multiple forms.

Exact Form:

\frac{7}{15}

$\frac{7}{15}$

Decimal Form:

0.4\overline{6}

$0.4\overline{6}$