Basic Math Examples

$(- 3.4 + 1.45) \div (0.3 - {(- \frac{1}{2})}^{2})$

Step 1

Rewrite the division as a fraction.

$\frac{- 3.4 + 1.45}{0.3 - {(- \frac{1}{2})}^{2}}$

Step 2

Add $- 3.4$ and $1.45$ .

$\frac{- 1.95}{0.3 - {(- \frac{1}{2})}^{2}}$

Step 3

Simplify the denominator.

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Step 3.1

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

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Step 3.1.1

Apply the product rule to $- \frac{1}{2}$ .

$\frac{- 1.95}{0.3 - ({(- 1)}^{2} {(\frac{1}{2})}^{2})}$

Step 3.1.2

Apply the product rule to $\frac{1}{2}$ .

$\frac{- 1.95}{0.3 - ({(- 1)}^{2} \frac{1^{2}}{2^{2}})}$

Step 3.2

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

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Step 3.2.1

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

$\frac{- 1.95}{0.3 + {(- 1)}^{2} \cdot - 1 \frac{1^{2}}{2^{2}}}$

Step 3.2.2

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

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Step 3.2.2.1

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

$\frac{- 1.95}{0.3 + {(- 1)}^{2} \cdot {(- 1)}^{1} \frac{1^{2}}{2^{2}}}$

Step 3.2.2.2

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

$\frac{- 1.95}{0.3 + {(- 1)}^{2 + 1} \frac{1^{2}}{2^{2}}}$

Step 3.2.3

Add $2$ and $1$ .

$\frac{- 1.95}{0.3 + {(- 1)}^{3} \frac{1^{2}}{2^{2}}}$

Step 3.3

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

$\frac{- 1.95}{0.3 - \frac{1^{2}}{2^{2}}}$

Step 3.4

One to any power is one.

$\frac{- 1.95}{0.3 - \frac{1}{2^{2}}}$

Step 3.5

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

$\frac{- 1.95}{0.3 - \frac{1}{4}}$

Step 3.6

To write $0.3$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{- 1.95}{0.3 \cdot \frac{4}{4} - \frac{1}{4}}$

Step 3.7

Combine $0.3$ and $\frac{4}{4}$ .

$\frac{- 1.95}{\frac{0.3 \cdot 4}{4} - \frac{1}{4}}$

Step 3.8

Combine the numerators over the common denominator.

$\frac{- 1.95}{\frac{0.3 \cdot 4 - 1}{4}}$

Step 3.9

Rewrite $\frac{0.3 \cdot 4 - 1}{4}$ in a factored form.

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Step 3.9.1

Multiply $0.3$ by $4$ .

$\frac{- 1.95}{\frac{1.2 - 1}{4}}$

Step 3.9.2

Subtract $1$ from $1.2$ .

$\frac{- 1.95}{\frac{0.2}{4}}$

Step 3.9.3

Divide $0.2$ by $4$ .

$\frac{- 1.95}{0.05}$

Step 4

Divide $- 1.95$ by $0.05$ .

$- 39$