Basic Math Examples

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

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

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

$- 1 \cdot - 1 = 1$

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

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

Step 2

Convert

4 \frac{1}{2}

$4 \frac{1}{2}$ 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}

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

Step 2.2

Add

4

$4$ and

\frac{1}{2}

$\frac{1}{2}$ .

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Step 2.2.1

To write

4

$4$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

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

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

Step 2.2.2

Combine

4

$4$ and

\frac{2}{2}

$\frac{2}{2}$ .

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

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

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

4

$4$ by

2

$2$ .

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

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

Step 2.2.4.2

Add

8

$8$ and

1

$1$ .

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

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

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

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

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

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

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

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

Step 3

Convert

5 \frac{2}{5}

$5 \frac{2}{5}$ 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}

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

Step 3.2

Add

5

$5$ and

\frac{2}{5}

$\frac{2}{5}$ .

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Step 3.2.1

To write

5

$5$ as a fraction with a common denominator, multiply by

\frac{5}{5}

$\frac{5}{5}$ .

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

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

Step 3.2.2

Combine

5

$5$ and

\frac{5}{5}

$\frac{5}{5}$ .

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

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

Step 3.2.3

Combine the numerators over the common denominator.

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

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

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply

5

$5$ by

5

$5$ .

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

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

Step 3.2.4.2

Add

25

$25$ and

2

$2$ .

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

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

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

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

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

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

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

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

Step 5

Cancel the common factor of

9

$9$ .

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Step 5.1

Move the leading negative in

- \frac{5}{27}

$- \frac{5}{27}$ into the numerator.

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

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

Step 5.2

Factor

9

$9$ out of

27

$27$ .

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

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

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:

$0.69\overline{4}$