Basic Math Examples

$\frac{\frac{5}{8} - \frac{1}{4}}{\frac{1}{8} + \frac{3}{4}}$

Step 1

Multiply the numerator and denominator of the fraction by $8$ .

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Step 1.1

Multiply $\frac{\frac{5}{8} - \frac{1}{4}}{\frac{1}{8} + \frac{3}{4}}$ by $\frac{8}{8}$ .

$\frac{8}{8} \cdot \frac{\frac{5}{8} - \frac{1}{4}}{\frac{1}{8} + \frac{3}{4}}$

Step 1.2

Combine.

$\frac{8 (\frac{5}{8} - \frac{1}{4})}{8 (\frac{1}{8} + \frac{3}{4})}$

Step 2

Apply the distributive property.

$\frac{8 (\frac{5}{8}) + 8 (- \frac{1}{4})}{8 (\frac{1}{8}) + 8 (\frac{3}{4})}$

Step 3

Simplify by cancelling.

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Step 3.1

Cancel the common factor of $8$ .

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Step 3.1.1

Cancel the common factor.

$\frac{8 (\frac{5}{8}) + 8 (- \frac{1}{4})}{8 (\frac{1}{8}) + 8 (\frac{3}{4})}$

Step 3.1.2

Rewrite the expression.

$\frac{5 + 8 (- \frac{1}{4})}{8 (\frac{1}{8}) + 8 (\frac{3}{4})}$

Step 3.2

Cancel the common factor of $4$ .

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Step 3.2.1

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$\frac{5 + 8 (\frac{- 1}{4})}{8 (\frac{1}{8}) + 8 (\frac{3}{4})}$

Step 3.2.2

Factor $4$ out of $8$ .

$\frac{5 + 4 (2) \frac{- 1}{4}}{8 (\frac{1}{8}) + 8 (\frac{3}{4})}$

Step 3.2.3

Cancel the common factor.

$\frac{5 + 4 \cdot 2 \frac{- 1}{4}}{8 (\frac{1}{8}) + 8 (\frac{3}{4})}$

Step 3.2.4

Rewrite the expression.

$\frac{5 + 2 \cdot - 1}{8 (\frac{1}{8}) + 8 (\frac{3}{4})}$

Step 3.3

Multiply $2$ by $- 1$ .

$\frac{5 - 2}{8 (\frac{1}{8}) + 8 (\frac{3}{4})}$

Step 3.4

Cancel the common factor of $8$ .

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Step 3.4.1

Cancel the common factor.

$\frac{5 - 2}{8 (\frac{1}{8}) + 8 (\frac{3}{4})}$

Step 3.4.2

Rewrite the expression.

$\frac{5 - 2}{1 + 8 (\frac{3}{4})}$

Step 3.5

Cancel the common factor of $4$ .

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Step 3.5.1

Factor $4$ out of $8$ .

$\frac{5 - 2}{1 + 4 (2) \frac{3}{4}}$

Step 3.5.2

Cancel the common factor.

$\frac{5 - 2}{1 + 4 \cdot 2 \frac{3}{4}}$

Step 3.5.3

Rewrite the expression.

$\frac{5 - 2}{1 + 2 \cdot 3}$

Step 3.6

Multiply $2$ by $3$ .

$\frac{5 - 2}{1 + 6}$

Step 4

Simplify by adding and subtracting.

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Step 4.1

Subtract $2$ from $5$ .

$\frac{3}{1 + 6}$

Step 4.2

Add $1$ and $6$ .

$\frac{3}{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{7}$

Decimal Form:

$0.\overline{428571}$