Basic Math Examples

$- \frac{1}{3} + - \frac{8}{5} \div 5 + (- 4) (3 + \frac{- 11}{5}) + 3 \div \frac{2}{3} + (2 - 3)$

Step 1

Remove parentheses.

$- \frac{1}{3} + - \frac{8}{5} \div 5 + (- 4) (3 + \frac{- 11}{5}) + 3 \div \frac{2}{3} + 2 - 3$

Step 2

Simplify each term.

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Step 2.1

Rewrite the division as a fraction.

$- \frac{1}{3} + \frac{- \frac{8}{5}}{5} + (- 4) (3 + \frac{- 11}{5}) + 3 \div \frac{2}{3} + 2 - 3$

Step 2.2

Multiply the numerator by the reciprocal of the denominator.

$- \frac{1}{3} - \frac{8}{5} \cdot \frac{1}{5} + (- 4) (3 + \frac{- 11}{5}) + 3 \div \frac{2}{3} + 2 - 3$

Step 2.3

Multiply $- \frac{8}{5} \cdot \frac{1}{5}$ .

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Step 2.3.1

Multiply $\frac{1}{5}$ by $\frac{8}{5}$ .

$- \frac{1}{3} - \frac{8}{5 \cdot 5} + (- 4) (3 + \frac{- 11}{5}) + 3 \div \frac{2}{3} + 2 - 3$

Step 2.3.2

Multiply $5$ by $5$ .

$- \frac{1}{3} - \frac{8}{25} + (- 4) (3 + \frac{- 11}{5}) + 3 \div \frac{2}{3} + 2 - 3$

Step 2.4

Move the negative in front of the fraction.

$- \frac{1}{3} - \frac{8}{25} - 4 (3 - \frac{11}{5}) + 3 \div \frac{2}{3} + 2 - 3$

Step 2.5

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

$- \frac{1}{3} - \frac{8}{25} - 4 (3 \cdot \frac{5}{5} - \frac{11}{5}) + 3 \div \frac{2}{3} + 2 - 3$

Step 2.6

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

$- \frac{1}{3} - \frac{8}{25} - 4 (\frac{3 \cdot 5}{5} - \frac{11}{5}) + 3 \div \frac{2}{3} + 2 - 3$

Step 2.7

Combine the numerators over the common denominator.

$- \frac{1}{3} - \frac{8}{25} - 4 \frac{3 \cdot 5 - 11}{5} + 3 \div \frac{2}{3} + 2 - 3$

Step 2.8

Simplify the numerator.

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Step 2.8.1

Multiply $3$ by $5$ .

$- \frac{1}{3} - \frac{8}{25} - 4 \frac{15 - 11}{5} + 3 \div \frac{2}{3} + 2 - 3$

Step 2.8.2

Subtract $11$ from $15$ .

$- \frac{1}{3} - \frac{8}{25} - 4 (\frac{4}{5}) + 3 \div \frac{2}{3} + 2 - 3$

Step 2.9

Multiply $- 4 (\frac{4}{5})$ .

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Step 2.9.1

Combine $- 4$ and $\frac{4}{5}$ .

$- \frac{1}{3} - \frac{8}{25} + \frac{- 4 \cdot 4}{5} + 3 \div \frac{2}{3} + 2 - 3$

Step 2.9.2

Multiply $- 4$ by $4$ .

$- \frac{1}{3} - \frac{8}{25} + \frac{- 16}{5} + 3 \div \frac{2}{3} + 2 - 3$

Step 2.10

Move the negative in front of the fraction.

$- \frac{1}{3} - \frac{8}{25} - \frac{16}{5} + 3 \div \frac{2}{3} + 2 - 3$

Step 2.11

To divide by a fraction, multiply by its reciprocal.

$- \frac{1}{3} - \frac{8}{25} - \frac{16}{5} + 3 (\frac{3}{2}) + 2 - 3$

Step 2.12

Multiply $3 (\frac{3}{2})$ .

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Step 2.12.1

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

$- \frac{1}{3} - \frac{8}{25} - \frac{16}{5} + \frac{3 \cdot 3}{2} + 2 - 3$

Step 2.12.2

Multiply $3$ by $3$ .

$- \frac{1}{3} - \frac{8}{25} - \frac{16}{5} + \frac{9}{2} + 2 - 3$

Step 3

Find the common denominator.

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Step 3.1

Multiply $\frac{1}{3}$ by $\frac{50}{50}$ .

$- (\frac{1}{3} \cdot \frac{50}{50}) - \frac{8}{25} - \frac{16}{5} + \frac{9}{2} + 2 - 3$

Step 3.2

Multiply $\frac{1}{3}$ by $\frac{50}{50}$ .

$- \frac{50}{3 \cdot 50} - \frac{8}{25} - \frac{16}{5} + \frac{9}{2} + 2 - 3$

Step 3.3

Multiply $\frac{8}{25}$ by $\frac{6}{6}$ .

$- \frac{50}{3 \cdot 50} - (\frac{8}{25} \cdot \frac{6}{6}) - \frac{16}{5} + \frac{9}{2} + 2 - 3$

Step 3.4

Multiply $\frac{8}{25}$ by $\frac{6}{6}$ .

$- \frac{50}{3 \cdot 50} - \frac{8 \cdot 6}{25 \cdot 6} - \frac{16}{5} + \frac{9}{2} + 2 - 3$

Step 3.5

Multiply $\frac{16}{5}$ by $\frac{30}{30}$ .

$- \frac{50}{3 \cdot 50} - \frac{8 \cdot 6}{25 \cdot 6} - (\frac{16}{5} \cdot \frac{30}{30}) + \frac{9}{2} + 2 - 3$

Step 3.6

Multiply $\frac{16}{5}$ by $\frac{30}{30}$ .

$- \frac{50}{3 \cdot 50} - \frac{8 \cdot 6}{25 \cdot 6} - \frac{16 \cdot 30}{5 \cdot 30} + \frac{9}{2} + 2 - 3$

Step 3.7

Multiply $\frac{9}{2}$ by $\frac{75}{75}$ .

$- \frac{50}{3 \cdot 50} - \frac{8 \cdot 6}{25 \cdot 6} - \frac{16 \cdot 30}{5 \cdot 30} + \frac{9}{2} \cdot \frac{75}{75} + 2 - 3$

Step 3.8

Multiply $\frac{9}{2}$ by $\frac{75}{75}$ .

$- \frac{50}{3 \cdot 50} - \frac{8 \cdot 6}{25 \cdot 6} - \frac{16 \cdot 30}{5 \cdot 30} + \frac{9 \cdot 75}{2 \cdot 75} + 2 - 3$

Step 3.9

Write $2$ as a fraction with denominator $1$ .

$- \frac{50}{3 \cdot 50} - \frac{8 \cdot 6}{25 \cdot 6} - \frac{16 \cdot 30}{5 \cdot 30} + \frac{9 \cdot 75}{2 \cdot 75} + \frac{2}{1} - 3$

Step 3.10

Multiply $\frac{2}{1}$ by $\frac{150}{150}$ .

$- \frac{50}{3 \cdot 50} - \frac{8 \cdot 6}{25 \cdot 6} - \frac{16 \cdot 30}{5 \cdot 30} + \frac{9 \cdot 75}{2 \cdot 75} + \frac{2}{1} \cdot \frac{150}{150} - 3$

Step 3.11

Multiply $\frac{2}{1}$ by $\frac{150}{150}$ .

$- \frac{50}{3 \cdot 50} - \frac{8 \cdot 6}{25 \cdot 6} - \frac{16 \cdot 30}{5 \cdot 30} + \frac{9 \cdot 75}{2 \cdot 75} + \frac{2 \cdot 150}{150} - 3$

Step 3.12

Write $- 3$ as a fraction with denominator $1$ .

$- \frac{50}{3 \cdot 50} - \frac{8 \cdot 6}{25 \cdot 6} - \frac{16 \cdot 30}{5 \cdot 30} + \frac{9 \cdot 75}{2 \cdot 75} + \frac{2 \cdot 150}{150} + \frac{- 3}{1}$

Step 3.13

Multiply $\frac{- 3}{1}$ by $\frac{150}{150}$ .

$- \frac{50}{3 \cdot 50} - \frac{8 \cdot 6}{25 \cdot 6} - \frac{16 \cdot 30}{5 \cdot 30} + \frac{9 \cdot 75}{2 \cdot 75} + \frac{2 \cdot 150}{150} + \frac{- 3}{1} \cdot \frac{150}{150}$

Step 3.14

Multiply $\frac{- 3}{1}$ by $\frac{150}{150}$ .

$- \frac{50}{3 \cdot 50} - \frac{8 \cdot 6}{25 \cdot 6} - \frac{16 \cdot 30}{5 \cdot 30} + \frac{9 \cdot 75}{2 \cdot 75} + \frac{2 \cdot 150}{150} + \frac{- 3 \cdot 150}{150}$

Step 3.15

Multiply $3$ by $50$ .

$- \frac{50}{150} - \frac{8 \cdot 6}{25 \cdot 6} - \frac{16 \cdot 30}{5 \cdot 30} + \frac{9 \cdot 75}{2 \cdot 75} + \frac{2 \cdot 150}{150} + \frac{- 3 \cdot 150}{150}$

Step 3.16

Reorder the factors of $25 \cdot 6$ .

$- \frac{50}{150} - \frac{8 \cdot 6}{6 \cdot 25} - \frac{16 \cdot 30}{5 \cdot 30} + \frac{9 \cdot 75}{2 \cdot 75} + \frac{2 \cdot 150}{150} + \frac{- 3 \cdot 150}{150}$

Step 3.17

Multiply $6$ by $25$ .

$- \frac{50}{150} - \frac{8 \cdot 6}{150} - \frac{16 \cdot 30}{5 \cdot 30} + \frac{9 \cdot 75}{2 \cdot 75} + \frac{2 \cdot 150}{150} + \frac{- 3 \cdot 150}{150}$

Step 3.18

Multiply $5$ by $30$ .

$- \frac{50}{150} - \frac{8 \cdot 6}{150} - \frac{16 \cdot 30}{150} + \frac{9 \cdot 75}{2 \cdot 75} + \frac{2 \cdot 150}{150} + \frac{- 3 \cdot 150}{150}$

Step 3.19

Multiply $2$ by $75$ .

$- \frac{50}{150} - \frac{8 \cdot 6}{150} - \frac{16 \cdot 30}{150} + \frac{9 \cdot 75}{150} + \frac{2 \cdot 150}{150} + \frac{- 3 \cdot 150}{150}$

Step 4

Combine the numerators over the common denominator.

$\frac{- 50 - 8 \cdot 6 - 16 \cdot 30 + 9 \cdot 75 + 2 \cdot 150 - 3 \cdot 150}{150}$

Step 5

Simplify each term.

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Step 5.1

Multiply $- 8$ by $6$ .

$\frac{- 50 - 48 - 16 \cdot 30 + 9 \cdot 75 + 2 \cdot 150 - 3 \cdot 150}{150}$

Step 5.2

Multiply $- 16$ by $30$ .

$\frac{- 50 - 48 - 480 + 9 \cdot 75 + 2 \cdot 150 - 3 \cdot 150}{150}$

Step 5.3

Multiply $9$ by $75$ .

$\frac{- 50 - 48 - 480 + 675 + 2 \cdot 150 - 3 \cdot 150}{150}$

Step 5.4

Multiply $2$ by $150$ .

$\frac{- 50 - 48 - 480 + 675 + 300 - 3 \cdot 150}{150}$

Step 5.5

Multiply $- 3$ by $150$ .

$\frac{- 50 - 48 - 480 + 675 + 300 - 450}{150}$

Step 6

Simplify the expression.

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Step 6.1

Subtract $48$ from $- 50$ .

$\frac{- 98 - 480 + 675 + 300 - 450}{150}$

Step 6.2

Subtract $480$ from $- 98$ .

$\frac{- 578 + 675 + 300 - 450}{150}$

Step 6.3

Add $- 578$ and $675$ .

$\frac{97 + 300 - 450}{150}$

Step 6.4

Add $97$ and $300$ .

$\frac{397 - 450}{150}$

Step 6.5

Subtract $450$ from $397$ .

$\frac{- 53}{150}$

Step 6.6

Move the negative in front of the fraction.

$- \frac{53}{150}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{53}{150}$

Decimal Form:

$- 0.35\overline{3}$