Basic Math Examples

$(\frac{8}{3}, - \frac{4}{7})$ , $(- \frac{5}{9}, \frac{6}{5})$

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 $(x_{2}, y_{2})$ .

$(\frac{\frac{8}{3} - \frac{5}{9}}{2}, \frac{- \frac{4}{7} + \frac{6}{5}}{2})$

Step 3

Simplify the numerator.

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Step 3.1

To write $\frac{8}{3}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$(\frac{\frac{8}{3} \cdot \frac{3}{3} - \frac{5}{9}}{2}, \frac{- \frac{4}{7} + \frac{6}{5}}{2})$

Step 3.2

Write each expression with a common denominator of $9$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.2.1

Multiply $\frac{8}{3}$ by $\frac{3}{3}$ .

$(\frac{\frac{8 \cdot 3}{3 \cdot 3} - \frac{5}{9}}{2}, \frac{- \frac{4}{7} + \frac{6}{5}}{2})$

Step 3.2.2

Multiply $3$ by $3$ .

$(\frac{\frac{8 \cdot 3}{9} - \frac{5}{9}}{2}, \frac{- \frac{4}{7} + \frac{6}{5}}{2})$

Step 3.3

Combine the numerators over the common denominator.

$(\frac{\frac{8 \cdot 3 - 5}{9}}{2}, \frac{- \frac{4}{7} + \frac{6}{5}}{2})$

Step 3.4

Simplify the numerator.

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Step 3.4.1

Multiply $8$ by $3$ .

$(\frac{\frac{24 - 5}{9}}{2}, \frac{- \frac{4}{7} + \frac{6}{5}}{2})$

Step 3.4.2

Subtract $5$ from $24$ .

$(\frac{\frac{19}{9}}{2}, \frac{- \frac{4}{7} + \frac{6}{5}}{2})$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$(\frac{19}{9} \cdot \frac{1}{2}, \frac{- \frac{4}{7} + \frac{6}{5}}{2})$

Step 5

Multiply $\frac{19}{9} \cdot \frac{1}{2}$ .

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Step 5.1

Multiply $\frac{19}{9}$ by $\frac{1}{2}$ .

$(\frac{19}{9 \cdot 2}, \frac{- \frac{4}{7} + \frac{6}{5}}{2})$

Step 5.2

Multiply $9$ by $2$ .

$(\frac{19}{18}, \frac{- \frac{4}{7} + \frac{6}{5}}{2})$

Step 6

Simplify the numerator.

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Step 6.1

To write $- \frac{4}{7}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$(\frac{19}{18}, \frac{- \frac{4}{7} \cdot \frac{5}{5} + \frac{6}{5}}{2})$

Step 6.2

To write $\frac{6}{5}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$(\frac{19}{18}, \frac{- \frac{4}{7} \cdot \frac{5}{5} + \frac{6}{5} \cdot \frac{7}{7}}{2})$

Step 6.3

Write each expression with a common denominator of $35$ , by multiplying each by an appropriate factor of $1$ .

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Step 6.3.1

Multiply $\frac{4}{7}$ by $\frac{5}{5}$ .

$(\frac{19}{18}, \frac{- \frac{4 \cdot 5}{7 \cdot 5} + \frac{6}{5} \cdot \frac{7}{7}}{2})$

Step 6.3.2

Multiply $7$ by $5$ .

$(\frac{19}{18}, \frac{- \frac{4 \cdot 5}{35} + \frac{6}{5} \cdot \frac{7}{7}}{2})$

Step 6.3.3

Multiply $\frac{6}{5}$ by $\frac{7}{7}$ .

$(\frac{19}{18}, \frac{- \frac{4 \cdot 5}{35} + \frac{6 \cdot 7}{5 \cdot 7}}{2})$

Step 6.3.4

Multiply $5$ by $7$ .

$(\frac{19}{18}, \frac{- \frac{4 \cdot 5}{35} + \frac{6 \cdot 7}{35}}{2})$

Step 6.4

Combine the numerators over the common denominator.

$(\frac{19}{18}, \frac{\frac{- 4 \cdot 5 + 6 \cdot 7}{35}}{2})$

Step 6.5

Simplify the numerator.

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Step 6.5.1

Multiply $- 4$ by $5$ .

$(\frac{19}{18}, \frac{\frac{- 20 + 6 \cdot 7}{35}}{2})$

Step 6.5.2

Multiply $6$ by $7$ .

$(\frac{19}{18}, \frac{\frac{- 20 + 42}{35}}{2})$

Step 6.5.3

Add $- 20$ and $42$ .

$(\frac{19}{18}, \frac{\frac{22}{35}}{2})$

Step 7

Multiply the numerator by the reciprocal of the denominator.

$(\frac{19}{18}, \frac{22}{35} \cdot \frac{1}{2})$

Step 8

Cancel the common factor of $2$ .

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Step 8.1

Factor $2$ out of $22$ .

$(\frac{19}{18}, \frac{2 (11)}{35} \cdot \frac{1}{2})$

Step 8.2

Cancel the common factor.

$(\frac{19}{18}, \frac{2 \cdot 11}{35} \cdot \frac{1}{2})$

Step 8.3

Rewrite the expression.

$(\frac{19}{18}, \frac{11}{35})$

Step 9