Basic Math Examples

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

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

Step 1

Rewrite the division as a fraction.

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

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

Step 2

Add

- 3.4

$- 3.4$ and

1.45

$1.45$ .

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

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

Step 3

Simplify the denominator.

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Step 3.1

Use the power rule

{(a b)}^{n} = a^{n} b^{n}

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

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Step 3.1.1

Apply the product rule to

- \frac{1}{2}

$- \frac{1}{2}$ .

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

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

Step 3.1.2

Apply the product rule to

\frac{1}{2}

$\frac{1}{2}$ .

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

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

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

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

Step 3.2

Multiply

- 1

$- 1$ by

{(- 1)}^{2}

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

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Step 3.2.1

Move

{(- 1)}^{2}

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

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

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

Step 3.2.2

Multiply

{(- 1)}^{2}

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

- 1

$- 1$ .

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Step 3.2.2.1

Raise

- 1

$- 1$ to the power of

1

$1$ .

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

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

Step 3.2.2.2

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

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

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

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

Step 3.2.3

Add

2

$2$ and

1

$1$ .

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

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

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

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

Step 3.3

Raise

- 1

$- 1$ to the power of

3

$3$ .

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

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

Step 3.4

One to any power is one.

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

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

Step 3.5

Raise

2

$2$ to the power of

2

$2$ .

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

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

Step 3.6

To write

0.3

$0.3$ as a fraction with a common denominator, multiply by

\frac{4}{4}

$\frac{4}{4}$ .

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

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

Step 3.7

Combine

0.3

$0.3$ and

\frac{4}{4}

$\frac{4}{4}$ .

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

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

Step 3.9

Rewrite

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

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

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Step 3.9.1

Multiply

0.3

$0.3$ by

4

$4$ .

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

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

Step 3.9.2

Subtract

1

$1$ from

1.2

$1.2$ .

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

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

Step 3.9.3

Divide

0.2

$0.2$ by

4

$4$ .

\frac{- 1.95}{0.05}

$\frac{- 1.95}{0.05}$

\frac{- 1.95}{0.05}

$\frac{- 1.95}{0.05}$

\frac{- 1.95}{0.05}

$\frac{- 1.95}{0.05}$

Step 4

Divide

- 1.95

$- 1.95$ by

0.05

$0.05$ .

- 39

$- 39$