Algebra Examples

$(0, \frac{1}{2})$ , $(0, \frac{3}{4})$

Step 1

Use the midpoint formula to find the midpoint of the line segment.

$(\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})$

Step 2

Substitute in the values for $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ .

$(\frac{0 + 0}{2}, \frac{\frac{1}{2} + \frac{3}{4}}{2})$

Step 3

Cancel the common factor of $0 + 0$ and $2$ .

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Step 3.1

Factor $2$ out of $0$ .

$(\frac{2 (0) + 0}{2}, \frac{\frac{1}{2} + \frac{3}{4}}{2})$

Step 3.2

Factor $2$ out of $0$ .

$(\frac{2 \cdot 0 + 2 \cdot 0}{2}, \frac{\frac{1}{2} + \frac{3}{4}}{2})$

Step 3.3

Factor $2$ out of $2 \cdot 0 + 2 \cdot 0$ .

$(\frac{2 \cdot (0 + 0)}{2}, \frac{\frac{1}{2} + \frac{3}{4}}{2})$

Step 3.4

Cancel the common factors.

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Step 3.4.1

Factor $2$ out of $2$ .

$(\frac{2 \cdot (0 + 0)}{2 (1)}, \frac{\frac{1}{2} + \frac{3}{4}}{2})$

Step 3.4.2

Cancel the common factor.

$(\frac{2 \cdot (0 + 0)}{2 \cdot 1}, \frac{\frac{1}{2} + \frac{3}{4}}{2})$

Step 3.4.3

Rewrite the expression.

$(\frac{0 + 0}{1}, \frac{\frac{1}{2} + \frac{3}{4}}{2})$

Step 3.4.4

Divide $0 + 0$ by $1$ .

$(0 + 0, \frac{\frac{1}{2} + \frac{3}{4}}{2})$

Step 4

Add $0$ and $0$ .

$(0, \frac{\frac{1}{2} + \frac{3}{4}}{2})$

Step 5

Simplify the numerator.

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Step 5.1

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$(0, \frac{\frac{1}{2} \cdot \frac{2}{2} + \frac{3}{4}}{2})$

Step 5.2

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.2.1

Multiply $\frac{1}{2}$ by $\frac{2}{2}$ .

$(0, \frac{\frac{2}{2 \cdot 2} + \frac{3}{4}}{2})$

Step 5.2.2

Multiply $2$ by $2$ .

$(0, \frac{\frac{2}{4} + \frac{3}{4}}{2})$

Step 5.3

Combine the numerators over the common denominator.

$(0, \frac{\frac{2 + 3}{4}}{2})$

Step 5.4

Add $2$ and $3$ .

$(0, \frac{\frac{5}{4}}{2})$

Step 6

Multiply the numerator by the reciprocal of the denominator.

$(0, \frac{5}{4} \cdot \frac{1}{2})$

Step 7

Multiply $\frac{5}{4} \cdot \frac{1}{2}$ .

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Step 7.1

Multiply $\frac{5}{4}$ by $\frac{1}{2}$ .

$(0, \frac{5}{4 \cdot 2})$

Step 7.2

Multiply $4$ by $2$ .

$(0, \frac{5}{8})$

Step 8