Basic Math Examples

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

Step 1

Convert $1 \frac{4}{5}$ to an improper fraction.

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Step 1.1

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

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

Step 1.2

Add $1$ and $\frac{4}{5}$ .

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Step 1.2.1

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

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

Step 1.2.2

Combine the numerators over the common denominator.

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

Step 1.2.3

Add $5$ and $4$ .

$- \frac{9}{5} {(- 2 \frac{1}{2})}^{2}$

Step 2

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

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Step 2.1

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

$- \frac{9}{5} {(- (2 + \frac{1}{2}))}^{2}$

Step 2.2

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

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Step 2.2.1

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

$- \frac{9}{5} {(- (2 \cdot \frac{2}{2} + \frac{1}{2}))}^{2}$

Step 2.2.2

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

$- \frac{9}{5} {(- (\frac{2 \cdot 2}{2} + \frac{1}{2}))}^{2}$

Step 2.2.3

Combine the numerators over the common denominator.

$- \frac{9}{5} {(- \frac{2 \cdot 2 + 1}{2})}^{2}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $2$ by $2$ .

$- \frac{9}{5} {(- \frac{4 + 1}{2})}^{2}$

Step 2.2.4.2

Add $4$ and $1$ .

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

Step 3

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

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Step 3.1

Apply the product rule to $- \frac{5}{2}$ .

$- \frac{9}{5} ({(- 1)}^{2} {(\frac{5}{2})}^{2})$

Step 3.2

Apply the product rule to $\frac{5}{2}$ .

$- \frac{9}{5} ({(- 1)}^{2} \frac{5^{2}}{2^{2}})$

Step 4

Multiply $- 1$ by ${(- 1)}^{2}$ by adding the exponents.

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Step 4.1

Move ${(- 1)}^{2}$ .

${(- 1)}^{2} \cdot - 1 \frac{9}{5} \frac{5^{2}}{2^{2}}$

Step 4.2

Multiply ${(- 1)}^{2}$ by $- 1$ .

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Step 4.2.1

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

${(- 1)}^{2} \cdot {(- 1)}^{1} \frac{9}{5} \frac{5^{2}}{2^{2}}$

Step 4.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(- 1)}^{2 + 1} \frac{9}{5} \frac{5^{2}}{2^{2}}$

Step 4.3

Add $2$ and $1$ .

${(- 1)}^{3} \frac{9}{5} \frac{5^{2}}{2^{2}}$

Step 5

Evaluate the exponents.

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Step 5.1

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

${(- 1)}^{3} \frac{9}{5} \frac{25}{2^{2}}$

Step 5.2

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

${(- 1)}^{3} \frac{9}{5} \frac{25}{4}$

Step 5.3

Raise $- 1$ to the power of $3$ .

$- \frac{9}{5} \cdot \frac{25}{4}$

Step 6

Cancel the common factor of $5$ .

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Step 6.1

Move the leading negative in $- \frac{9}{5}$ into the numerator.

$\frac{- 9}{5} \cdot \frac{25}{4}$

Step 6.2

Factor $5$ out of $25$ .

$\frac{- 9}{5} \cdot \frac{5 (5)}{4}$

Step 6.3

Cancel the common factor.

$\frac{- 9}{5} \cdot \frac{5 \cdot 5}{4}$

Step 6.4

Rewrite the expression.

$- 9 (\frac{5}{4})$

Step 7

Combine $- 9$ and $\frac{5}{4}$ .

$\frac{- 9 \cdot 5}{4}$

Step 8

Simplify the expression.

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Step 8.1

Multiply $- 9$ by $5$ .

$\frac{- 45}{4}$

Step 8.2

Move the negative in front of the fraction.

$- \frac{45}{4}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$- \frac{45}{4}$

Decimal Form:

$- 11.25$

Mixed Number Form:

$- 11 \frac{1}{4}$