Basic Math Examples

$(\frac{3}{4} - \frac{8}{10}) \div (\frac{3}{4} + \frac{8}{10})$

Step 1

Rewrite the division as a fraction.

$\frac{\frac{3}{4} - \frac{8}{10}}{\frac{3}{4} + \frac{8}{10}}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Cancel the common factor of $8$ and $10$ .

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Step 2.1.1

Factor $2$ out of $8$ .

$\frac{\frac{3}{4} - \frac{2 (4)}{10}}{\frac{3}{4} + \frac{8}{10}}$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $2$ out of $10$ .

$\frac{\frac{3}{4} - \frac{2 \cdot 4}{2 \cdot 5}}{\frac{3}{4} + \frac{8}{10}}$

Step 2.1.2.2

Cancel the common factor.

$\frac{\frac{3}{4} - \frac{2 \cdot 4}{2 \cdot 5}}{\frac{3}{4} + \frac{8}{10}}$

Step 2.1.2.3

Rewrite the expression.

$\frac{\frac{3}{4} - \frac{4}{5}}{\frac{3}{4} + \frac{8}{10}}$

Step 2.2

Cancel the common factor of $8$ and $10$ .

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Step 2.2.1

Factor $2$ out of $8$ .

$\frac{\frac{3}{4} - \frac{4}{5}}{\frac{3}{4} + \frac{2 (4)}{10}}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $2$ out of $10$ .

$\frac{\frac{3}{4} - \frac{4}{5}}{\frac{3}{4} + \frac{2 \cdot 4}{2 \cdot 5}}$

Step 2.2.2.2

Cancel the common factor.

$\frac{\frac{3}{4} - \frac{4}{5}}{\frac{3}{4} + \frac{2 \cdot 4}{2 \cdot 5}}$

Step 2.2.2.3

Rewrite the expression.

$\frac{\frac{3}{4} - \frac{4}{5}}{\frac{3}{4} + \frac{4}{5}}$

Step 3

Multiply the numerator and denominator of the fraction by $20$ .

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Step 3.1

Multiply $\frac{\frac{3}{4} - \frac{4}{5}}{\frac{3}{4} + \frac{4}{5}}$ by $\frac{20}{20}$ .

$\frac{20}{20} \cdot \frac{\frac{3}{4} - \frac{4}{5}}{\frac{3}{4} + \frac{4}{5}}$

Step 3.2

Combine.

$\frac{20 (\frac{3}{4} - \frac{4}{5})}{20 (\frac{3}{4} + \frac{4}{5})}$

Step 4

Apply the distributive property.

$\frac{20 (\frac{3}{4}) + 20 (- \frac{4}{5})}{20 (\frac{3}{4}) + 20 (\frac{4}{5})}$

Step 5

Simplify by cancelling.

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Step 5.1

Cancel the common factor of $4$ .

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Step 5.1.1

Factor $4$ out of $20$ .

$\frac{4 (5) \frac{3}{4} + 20 (- \frac{4}{5})}{20 (\frac{3}{4}) + 20 (\frac{4}{5})}$

Step 5.1.2

Cancel the common factor.

$\frac{4 \cdot 5 \frac{3}{4} + 20 (- \frac{4}{5})}{20 (\frac{3}{4}) + 20 (\frac{4}{5})}$

Step 5.1.3

Rewrite the expression.

$\frac{5 \cdot 3 + 20 (- \frac{4}{5})}{20 (\frac{3}{4}) + 20 (\frac{4}{5})}$

Step 5.2

Multiply $5$ by $3$ .

$\frac{15 + 20 (- \frac{4}{5})}{20 (\frac{3}{4}) + 20 (\frac{4}{5})}$

Step 5.3

Cancel the common factor of $5$ .

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Step 5.3.1

Move the leading negative in $- \frac{4}{5}$ into the numerator.

$\frac{15 + 20 (\frac{- 4}{5})}{20 (\frac{3}{4}) + 20 (\frac{4}{5})}$

Step 5.3.2

Factor $5$ out of $20$ .

$\frac{15 + 5 (4) \frac{- 4}{5}}{20 (\frac{3}{4}) + 20 (\frac{4}{5})}$

Step 5.3.3

Cancel the common factor.

$\frac{15 + 5 \cdot 4 \frac{- 4}{5}}{20 (\frac{3}{4}) + 20 (\frac{4}{5})}$

Step 5.3.4

Rewrite the expression.

$\frac{15 + 4 \cdot - 4}{20 (\frac{3}{4}) + 20 (\frac{4}{5})}$

Step 5.4

Multiply $4$ by $- 4$ .

$\frac{15 - 16}{20 (\frac{3}{4}) + 20 (\frac{4}{5})}$

Step 5.5

Cancel the common factor of $4$ .

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Step 5.5.1

Factor $4$ out of $20$ .

$\frac{15 - 16}{4 (5) \frac{3}{4} + 20 (\frac{4}{5})}$

Step 5.5.2

Cancel the common factor.

$\frac{15 - 16}{4 \cdot 5 \frac{3}{4} + 20 (\frac{4}{5})}$

Step 5.5.3

Rewrite the expression.

$\frac{15 - 16}{5 \cdot 3 + 20 (\frac{4}{5})}$

Step 5.6

Multiply $5$ by $3$ .

$\frac{15 - 16}{15 + 20 (\frac{4}{5})}$

Step 5.7

Cancel the common factor of $5$ .

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Step 5.7.1

Factor $5$ out of $20$ .

$\frac{15 - 16}{15 + 5 (4) \frac{4}{5}}$

Step 5.7.2

Cancel the common factor.

$\frac{15 - 16}{15 + 5 \cdot 4 \frac{4}{5}}$

Step 5.7.3

Rewrite the expression.

$\frac{15 - 16}{15 + 4 \cdot 4}$

Step 5.8

Multiply $4$ by $4$ .

$\frac{15 - 16}{15 + 16}$

Step 6

Simplify the expression.

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Step 6.1

Subtract $16$ from $15$ .

$\frac{- 1}{15 + 16}$

Step 6.2

Add $15$ and $16$ .

$\frac{- 1}{31}$

Step 6.3

Move the negative in front of the fraction.

$- \frac{1}{31}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{31}$

Decimal Form:

$- 0.03225806 \dots$