Basic Math Examples

${(- - 4 \frac{1}{2} \div (- 5 \frac{2}{5}))}^{2}$

Step 1

Replace all occurrences of $-$ $-$ with a single $+$ . Two consecutive minus signs have the same mathematical meaning as a single plus sign because $- 1 \cdot - 1 = 1$

${(4 \frac{1}{2} \div (- 5 \frac{2}{5}))}^{2}$

Step 2

Convert $4 \frac{1}{2}$ to an improper fraction.

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Step 2.1

A mixed number is an addition of its whole and fractional parts.

${((4 + \frac{1}{2}) \div (- 5 \frac{2}{5}))}^{2}$

Step 2.2

Add $4$ and $\frac{1}{2}$ .

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Step 2.2.1

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

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

Step 2.2.2

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

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

Step 2.2.3

Combine the numerators over the common denominator.

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

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $4$ by $2$ .

${(\frac{8 + 1}{2} \div (- 5 \frac{2}{5}))}^{2}$

Step 2.2.4.2

Add $8$ and $1$ .

${(\frac{9}{2} \div (- 5 \frac{2}{5}))}^{2}$

Step 3

Convert $5 \frac{2}{5}$ to an improper fraction.

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Step 3.1

A mixed number is an addition of its whole and fractional parts.

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

Step 3.2

Add $5$ and $\frac{2}{5}$ .

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Step 3.2.1

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

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

Step 3.2.2

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

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

Step 3.2.3

Combine the numerators over the common denominator.

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

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $5$ by $5$ .

${(\frac{9}{2} \div (- \frac{25 + 2}{5}))}^{2}$

Step 3.2.4.2

Add $25$ and $2$ .

${(\frac{9}{2} \div (- \frac{27}{5}))}^{2}$

Step 4

To divide by a fraction, multiply by its reciprocal.

${(\frac{9}{2} (- \frac{5}{27}))}^{2}$

Step 5

Cancel the common factor of $9$ .

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Step 5.1

Move the leading negative in $- \frac{5}{27}$ into the numerator.

${(\frac{9}{2} \cdot \frac{- 5}{27})}^{2}$

Step 5.2

Factor $9$ out of $27$ .

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

Step 5.3

Cancel the common factor.

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

Step 5.4

Rewrite the expression.

${(\frac{1}{2} \cdot \frac{- 5}{3})}^{2}$

Step 6

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

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

Step 7

Simplify the expression.

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Step 7.1

Multiply $2$ by $3$ .

${(\frac{- 5}{6})}^{2}$

Step 7.2

Move the negative in front of the fraction.

${(- \frac{5}{6})}^{2}$

Step 8

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 8.1

Apply the product rule to $- \frac{5}{6}$ .

${(- 1)}^{2} {(\frac{5}{6})}^{2}$

Step 8.2

Apply the product rule to $\frac{5}{6}$ .

${(- 1)}^{2} \frac{5^{2}}{6^{2}}$

Step 9

Raise $- 1$ to the power of $2$ .

$1 \frac{5^{2}}{6^{2}}$

Step 10

Multiply $\frac{5^{2}}{6^{2}}$ by $1$ .

$\frac{5^{2}}{6^{2}}$

Step 11

Raise $5$ to the power of $2$ .

$\frac{25}{6^{2}}$

Step 12

Raise $6$ to the power of $2$ .

$\frac{25}{36}$

Step 13

The result can be shown in multiple forms.

Exact Form:

$\frac{25}{36}$

Decimal Form:

$0.69\overline{4}$