Basic Math Examples

(- 2 \frac{1}{2}, - 3)

$(- 2 \frac{1}{2}, - 3)$ ,

(1, - 3)

$(1, - 3)$

Step 1

Convert

2 \frac{1}{2}

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

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Step 1.1

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

(- (2 + \frac{1}{2}), - 3) - (1, - 3)

$(- (2 + \frac{1}{2}), - 3) - (1, - 3)$

Step 1.2

Add

2

$2$ and

\frac{1}{2}

$\frac{1}{2}$ .

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Step 1.2.1

To write

2

$2$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

(- (2 \cdot \frac{2}{2} + \frac{1}{2}), - 3) - (1, - 3)

$(- (2 \cdot \frac{2}{2} + \frac{1}{2}), - 3) - (1, - 3)$

Step 1.2.2

Combine

2

$2$ and

\frac{2}{2}

$\frac{2}{2}$ .

(- (\frac{2 \cdot 2}{2} + \frac{1}{2}), - 3) - (1, - 3)

$(- (\frac{2 \cdot 2}{2} + \frac{1}{2}), - 3) - (1, - 3)$

Step 1.2.3

Combine the numerators over the common denominator.

(- \frac{2 \cdot 2 + 1}{2}, - 3) - (1, - 3)

$(- \frac{2 \cdot 2 + 1}{2}, - 3) - (1, - 3)$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

2

$2$ by

2

$2$ .

(- \frac{4 + 1}{2}, - 3) - (1, - 3)

$(- \frac{4 + 1}{2}, - 3) - (1, - 3)$

Step 1.2.4.2

Add

4

$4$ and

1

$1$ .

(- \frac{5}{2}, - 3) - (1, - 3)

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

(- \frac{5}{2}, - 3) - (1, - 3)

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

(- \frac{5}{2}, - 3) - (1, - 3)

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

(- \frac{5}{2}, - 3) - (1, - 3)

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

Step 2

Use the distance formula to determine the distance between the two points.

Distance = \sqrt{{(x_{2} - x_{1})}_{2}^{2} + {(y_{2} - y_{1})}_{2}^{2}}

$Distance = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$

Step 3

Substitute the actual values of the points into the distance formula.

\sqrt{{(1 - (- \frac{5}{2}))}^{2} + {((- 3) - (- 3))}^{2}}

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

Step 4

Simplify.

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Step 4.1

Multiply

- (- \frac{5}{2})

$- (- \frac{5}{2})$ .

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Step 4.1.1

Multiply

- 1

$- 1$ by

- 1

$- 1$ .

\sqrt{{(1 + 1 (\frac{5}{2}))}^{2} + {((- 3) - (- 3))}^{2}}

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

Step 4.1.2

Multiply

\frac{5}{2}

$\frac{5}{2}$ by

1

$1$ .

\sqrt{{(1 + \frac{5}{2})}^{2} + {((- 3) - (- 3))}^{2}}

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

\sqrt{{(1 + \frac{5}{2})}^{2} + {((- 3) - (- 3))}^{2}}

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

Step 4.2

Write

1

$1$ as a fraction with a common denominator.

\sqrt{{(\frac{2}{2} + \frac{5}{2})}^{2} + {((- 3) - (- 3))}^{2}}

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

Step 4.3

Combine the numerators over the common denominator.

\sqrt{{(\frac{2 + 5}{2})}^{2} + {((- 3) - (- 3))}^{2}}

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

Step 4.4

Add

2

$2$ and

5

$5$ .

\sqrt{{(\frac{7}{2})}^{2} + {((- 3) - (- 3))}^{2}}

$\sqrt{{(\frac{7}{2})}^{2} + {((- 3) - (- 3))}^{2}}$

Step 4.5

Apply the product rule to

\frac{7}{2}

$\frac{7}{2}$ .

\sqrt{\frac{7^{2}}{2^{2}} + {((- 3) - (- 3))}^{2}}

$\sqrt{\frac{7^{2}}{2^{2}} + {((- 3) - (- 3))}^{2}}$

Step 4.6

Raise

$7$ to the power of

$2$ .

$\sqrt{\frac{49}{2^{2}} + {((- 3) - (- 3))}^{2}}$

Step 4.7

Raise

$2$ to the power of

$2$ .

$\sqrt{\frac{49}{4} + {((- 3) - (- 3))}^{2}}$

Step 4.8

Multiply

$- 1$ by

$- 3$ .

$\sqrt{\frac{49}{4} + {(- 3 + 3)}^{2}}$

Step 4.9

Add

$- 3$ and

$3$ .

$\sqrt{\frac{49}{4} + 0^{2}}$

Step 4.10

Raising

$0$ to any positive power yields

$0$ .

$\sqrt{\frac{49}{4} + 0}$

Step 4.11

Add

$\frac{49}{4}$ and

$0$ .

$\sqrt{\frac{49}{4}}$

Step 4.12

Rewrite

$\sqrt{\frac{49}{4}}$ as

$\frac{\sqrt{49}}{\sqrt{4}}$ .

$\frac{\sqrt{49}}{\sqrt{4}}$

Step 4.13

Simplify the numerator.

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Step 4.13.1

Rewrite

$49$ as

$7^{2}$ .

$\frac{\sqrt{7^{2}}}{\sqrt{4}}$

Step 4.13.2

Pull terms out from under the radical, assuming positive real numbers.

$\frac{7}{\sqrt{4}}$

Step 4.14

Simplify the denominator.

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Step 4.14.1

Rewrite

$4$ as

$2^{2}$ .

$\frac{7}{\sqrt{2^{2}}}$

Step 4.14.2

Pull terms out from under the radical, assuming positive real numbers.

$\frac{7}{2}$

Step 5