Basic Math Examples

$(- \frac{3}{5} - (- 3)) \div \frac{6}{5} + (- \frac{9}{4}) \cdot (- \frac{8}{3} - 1)$

Step 1

Multiply $- 1$ by $- 3$ .

$(- \frac{3}{5} + 3) \div \frac{6}{5} + (- \frac{9}{4}) \cdot (- \frac{8}{3} - 1)$

Step 2

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

$(- \frac{3}{5} + 3 \cdot \frac{5}{5}) \div \frac{6}{5} + (- \frac{9}{4}) \cdot (- \frac{8}{3} - 1)$

Step 3

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

$(- \frac{3}{5} + \frac{3 \cdot 5}{5}) \div \frac{6}{5} + (- \frac{9}{4}) \cdot (- \frac{8}{3} - 1)$

Step 4

Combine the numerators over the common denominator.

$\frac{- 3 + 3 \cdot 5}{5} \div \frac{6}{5} + (- \frac{9}{4}) \cdot (- \frac{8}{3} - 1)$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $3$ by $5$ .

$\frac{- 3 + 15}{5} \div \frac{6}{5} + (- \frac{9}{4}) \cdot (- \frac{8}{3} - 1)$

Step 5.2

Add $- 3$ and $15$ .

$\frac{12}{5} \div \frac{6}{5} + (- \frac{9}{4}) \cdot (- \frac{8}{3} - 1)$

Step 6

Simplify each term.

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Step 6.1

To divide by a fraction, multiply by its reciprocal.

$\frac{12}{5} \cdot \frac{5}{6} + (- \frac{9}{4}) \cdot (- \frac{8}{3} - 1)$

Step 6.2

Cancel the common factor of $6$ .

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Step 6.2.1

Factor $6$ out of $12$ .

$\frac{6 (2)}{5} \cdot \frac{5}{6} + (- \frac{9}{4}) \cdot (- \frac{8}{3} - 1)$

Step 6.2.2

Cancel the common factor.

$\frac{6 \cdot 2}{5} \cdot \frac{5}{6} + (- \frac{9}{4}) \cdot (- \frac{8}{3} - 1)$

Step 6.2.3

Rewrite the expression.

$\frac{2}{5} \cdot 5 + (- \frac{9}{4}) \cdot (- \frac{8}{3} - 1)$

Step 6.3

Cancel the common factor of $5$ .

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Step 6.3.1

Cancel the common factor.

$\frac{2}{5} \cdot 5 + (- \frac{9}{4}) \cdot (- \frac{8}{3} - 1)$

Step 6.3.2

Rewrite the expression.

$2 + (- \frac{9}{4}) \cdot (- \frac{8}{3} - 1)$

Step 6.4

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$2 - \frac{9}{4} \cdot (- \frac{8}{3} - 1 \cdot \frac{3}{3})$

Step 6.5

Combine $- 1$ and $\frac{3}{3}$ .

$2 - \frac{9}{4} \cdot (- \frac{8}{3} + \frac{- 1 \cdot 3}{3})$

Step 6.6

Combine the numerators over the common denominator.

$2 - \frac{9}{4} \cdot \frac{- 8 - 1 \cdot 3}{3}$

Step 6.7

Simplify the numerator.

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Step 6.7.1

Multiply $- 1$ by $3$ .

$2 - \frac{9}{4} \cdot \frac{- 8 - 3}{3}$

Step 6.7.2

Subtract $3$ from $- 8$ .

$2 - \frac{9}{4} \cdot \frac{- 11}{3}$

Step 6.8

Cancel the common factor of $3$ .

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Step 6.8.1

Move the leading negative in $- \frac{9}{4}$ into the numerator.

$2 + \frac{- 9}{4} \cdot \frac{- 11}{3}$

Step 6.8.2

Factor $3$ out of $- 9$ .

$2 + \frac{3 (- 3)}{4} \cdot \frac{- 11}{3}$

Step 6.8.3

Cancel the common factor.

$2 + \frac{3 \cdot - 3}{4} \cdot \frac{- 11}{3}$

Step 6.8.4

Rewrite the expression.

$2 + \frac{- 3}{4} \cdot - 11$

Step 6.9

Combine $\frac{- 3}{4}$ and $- 11$ .

$2 + \frac{- 3 \cdot - 11}{4}$

Step 6.10

Multiply $- 3$ by $- 11$ .

$2 + \frac{33}{4}$

Step 7

To write $2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$2 \cdot \frac{4}{4} + \frac{33}{4}$

Step 8

Combine $2$ and $\frac{4}{4}$ .

$\frac{2 \cdot 4}{4} + \frac{33}{4}$

Step 9

Combine the numerators over the common denominator.

$\frac{2 \cdot 4 + 33}{4}$

Step 10

Simplify the numerator.

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Step 10.1

Multiply $2$ by $4$ .

$\frac{8 + 33}{4}$

Step 10.2

Add $8$ and $33$ .

$\frac{41}{4}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$\frac{41}{4}$

Decimal Form:

$10.25$

Mixed Number Form:

$10 \frac{1}{4}$