Basic Math Examples

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

Step 1

Convert $4 \frac{5}{9}$ to an improper fraction.

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Step 1.1

A mixed number is an addition of its whole and fractional parts.

$- (4 + \frac{5}{9}) \div ((- \frac{7}{8}) - \frac{3}{4})$

Step 1.2

Add $4$ and $\frac{5}{9}$ .

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Step 1.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

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

Step 1.2.2

Combine $4$ and $\frac{9}{9}$ .

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $4$ by $9$ .

$- \frac{36 + 5}{9} \div ((- \frac{7}{8}) - \frac{3}{4})$

Step 1.2.4.2

Add $36$ and $5$ .

$- \frac{41}{9} \div ((- \frac{7}{8}) - \frac{3}{4})$

Step 2

Rewrite the division as a fraction.

$\frac{- \frac{41}{9}}{(- \frac{7}{8}) - \frac{3}{4}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$- \frac{41}{9} \cdot \frac{1}{- \frac{7}{8} - \frac{3}{4}}$

Step 4

Simplify the denominator.

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Step 4.1

To write $- \frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{41}{9} \cdot \frac{1}{- \frac{7}{8} - \frac{3}{4} \cdot \frac{2}{2}}$

Step 4.2

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.2.1

Multiply $\frac{3}{4}$ by $\frac{2}{2}$ .

$- \frac{41}{9} \cdot \frac{1}{- \frac{7}{8} - \frac{3 \cdot 2}{4 \cdot 2}}$

Step 4.2.2

Multiply $4$ by $2$ .

$- \frac{41}{9} \cdot \frac{1}{- \frac{7}{8} - \frac{3 \cdot 2}{8}}$

Step 4.3

Combine the numerators over the common denominator.

$- \frac{41}{9} \cdot \frac{1}{\frac{- 7 - 3 \cdot 2}{8}}$

Step 4.4

Simplify the numerator.

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Step 4.4.1

Multiply $- 3$ by $2$ .

$- \frac{41}{9} \cdot \frac{1}{\frac{- 7 - 6}{8}}$

Step 4.4.2

Subtract $6$ from $- 7$ .

$- \frac{41}{9} \cdot \frac{1}{\frac{- 13}{8}}$

Step 4.5

Move the negative in front of the fraction.

$- \frac{41}{9} \cdot \frac{1}{- \frac{13}{8}}$

Step 5

Cancel the common factor of $1$ and $- 1$ .

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Step 5.1

Rewrite $1$ as $- 1 (- 1)$ .

$- \frac{41}{9} \cdot \frac{- 1 (- 1)}{- \frac{13}{8}}$

Step 5.2

Move the negative in front of the fraction.

$- \frac{41}{9} (- \frac{1}{\frac{13}{8}})$

Step 6

Multiply the numerator by the reciprocal of the denominator.

$- \frac{41}{9} (- (1 (\frac{8}{13})))$

Step 7

Multiply $\frac{8}{13}$ by $1$ .

$- \frac{41}{9} (- \frac{8}{13})$

Step 8

Multiply $- \frac{41}{9} (- \frac{8}{13})$ .

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Step 8.1

Multiply $- 1$ by $- 1$ .

$1 (\frac{41}{9}) \frac{8}{13}$

Step 8.2

Multiply $\frac{41}{9}$ by $1$ .

$\frac{41}{9} \cdot \frac{8}{13}$

Step 8.3

Multiply $\frac{41}{9}$ by $\frac{8}{13}$ .

$\frac{41 \cdot 8}{9 \cdot 13}$

Step 8.4

Multiply $41$ by $8$ .

$\frac{328}{9 \cdot 13}$

Step 8.5

Multiply $9$ by $13$ .

$\frac{328}{117}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{328}{117}$

Decimal Form:

$2.80341880 \dots$

Mixed Number Form:

$2 \frac{94}{117}$