Basic Math Examples

${(\frac{3}{8})}^{2} (- 64) + \frac{2}{3} \div (- \frac{4}{5})$

Step 1

Simplify each term.

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Step 1.1

Apply the product rule to $\frac{3}{8}$ .

$\frac{3^{2}}{8^{2}} \cdot - 64 + \frac{2}{3} \div (- \frac{4}{5})$

Step 1.2

Raise $3$ to the power of $2$ .

$\frac{9}{8^{2}} \cdot - 64 + \frac{2}{3} \div (- \frac{4}{5})$

Step 1.3

Raise $8$ to the power of $2$ .

$\frac{9}{64} \cdot - 64 + \frac{2}{3} \div (- \frac{4}{5})$

Step 1.4

Cancel the common factor of $64$ .

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Step 1.4.1

Factor $64$ out of $- 64$ .

$\frac{9}{64} \cdot (64 (- 1)) + \frac{2}{3} \div (- \frac{4}{5})$

Step 1.4.2

Cancel the common factor.

$\frac{9}{64} \cdot (64 \cdot - 1) + \frac{2}{3} \div (- \frac{4}{5})$

Step 1.4.3

Rewrite the expression.

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

Step 1.5

Multiply $9$ by $- 1$ .

$- 9 + \frac{2}{3} \div (- \frac{4}{5})$

Step 1.6

To divide by a fraction, multiply by its reciprocal.

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

Step 1.7

Cancel the common factor of $2$ .

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Step 1.7.1

Move the leading negative in $- \frac{5}{4}$ into the numerator.

$- 9 + \frac{2}{3} \cdot \frac{- 5}{4}$

Step 1.7.2

Factor $2$ out of $4$ .

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

Step 1.7.3

Cancel the common factor.

$- 9 + \frac{2}{3} \cdot \frac{- 5}{2 \cdot 2}$

Step 1.7.4

Rewrite the expression.

$- 9 + \frac{1}{3} \cdot \frac{- 5}{2}$

Step 1.8

Multiply $\frac{1}{3}$ by $\frac{- 5}{2}$ .

$- 9 + \frac{- 5}{3 \cdot 2}$

Step 1.9

Multiply $3$ by $2$ .

$- 9 + \frac{- 5}{6}$

Step 1.10

Move the negative in front of the fraction.

$- 9 - \frac{5}{6}$

Step 2

To write $- 9$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$- 9 \cdot \frac{6}{6} - \frac{5}{6}$

Step 3

Combine $- 9$ and $\frac{6}{6}$ .

$\frac{- 9 \cdot 6}{6} - \frac{5}{6}$

Step 4

Combine the numerators over the common denominator.

$\frac{- 9 \cdot 6 - 5}{6}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $- 9$ by $6$ .

$\frac{- 54 - 5}{6}$

Step 5.2

Subtract $5$ from $- 54$ .

$\frac{- 59}{6}$

Step 6

Move the negative in front of the fraction.

$- \frac{59}{6}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{59}{6}$

Decimal Form:

$- 9.8\overline{3}$

Mixed Number Form:

$- 9 \frac{5}{6}$