Basic Math Examples

$\frac{\frac{7}{4} + 2}{1 - \frac{8}{5}}$

Step 1

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

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Step 1.1

Multiply $\frac{\frac{7}{4} + 2}{1 - \frac{8}{5}}$ by $\frac{20}{20}$ .

$\frac{20}{20} \cdot \frac{\frac{7}{4} + 2}{1 - \frac{8}{5}}$

Step 1.2

Combine.

$\frac{20 (\frac{7}{4} + 2)}{20 (1 - \frac{8}{5})}$

Step 2

Apply the distributive property.

$\frac{20 (\frac{7}{4}) + 20 \cdot 2}{20 \cdot 1 + 20 (- \frac{8}{5})}$

Step 3

Simplify by cancelling.

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Step 3.1

Cancel the common factor of $4$ .

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Step 3.1.1

Factor $4$ out of $20$ .

$\frac{4 (5) \frac{7}{4} + 20 \cdot 2}{20 \cdot 1 + 20 (- \frac{8}{5})}$

Step 3.1.2

Cancel the common factor.

$\frac{4 \cdot 5 \frac{7}{4} + 20 \cdot 2}{20 \cdot 1 + 20 (- \frac{8}{5})}$

Step 3.1.3

Rewrite the expression.

$\frac{5 \cdot 7 + 20 \cdot 2}{20 \cdot 1 + 20 (- \frac{8}{5})}$

Step 3.2

Multiply $5$ by $7$ .

$\frac{35 + 20 \cdot 2}{20 \cdot 1 + 20 (- \frac{8}{5})}$

Step 3.3

Cancel the common factor of $5$ .

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Step 3.3.1

Move the leading negative in $- \frac{8}{5}$ into the numerator.

$\frac{35 + 20 \cdot 2}{20 \cdot 1 + 20 (\frac{- 8}{5})}$

Step 3.3.2

Factor $5$ out of $20$ .

$\frac{35 + 20 \cdot 2}{20 \cdot 1 + 5 (4) \frac{- 8}{5}}$

Step 3.3.3

Cancel the common factor.

$\frac{35 + 20 \cdot 2}{20 \cdot 1 + 5 \cdot 4 \frac{- 8}{5}}$

Step 3.3.4

Rewrite the expression.

$\frac{35 + 20 \cdot 2}{20 \cdot 1 + 4 \cdot - 8}$

Step 3.4

Multiply $4$ by $- 8$ .

$\frac{35 + 20 \cdot 2}{20 \cdot 1 - 32}$

Step 4

Simplify the numerator.

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Step 4.1

Multiply $20$ by $2$ .

$\frac{35 + 40}{20 \cdot 1 - 32}$

Step 4.2

Add $35$ and $40$ .

$\frac{75}{20 \cdot 1 - 32}$

Step 5

Simplify the denominator.

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Step 5.1

Multiply $20$ by $1$ .

$\frac{75}{20 - 32}$

Step 5.2

Subtract $32$ from $20$ .

$\frac{75}{- 12}$

Step 6

Reduce the expression by cancelling the common factors.

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Step 6.1

Cancel the common factor of $75$ and $- 12$ .

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Step 6.1.1

Factor $3$ out of $75$ .

$\frac{3 (25)}{- 12}$

Step 6.1.2

Cancel the common factors.

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Step 6.1.2.1

Factor $3$ out of $- 12$ .

$\frac{3 \cdot 25}{3 \cdot - 4}$

Step 6.1.2.2

Cancel the common factor.

$\frac{3 \cdot 25}{3 \cdot - 4}$

Step 6.1.2.3

Rewrite the expression.

$\frac{25}{- 4}$

Step 6.2

Move the negative in front of the fraction.

$- \frac{25}{4}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{25}{4}$

Decimal Form:

$- 6.25$

Mixed Number Form:

$- 6 \frac{1}{4}$