Basic Math Examples

$(- 3 \frac{1}{4}) + 8 \frac{1}{9} \cdot (- 4 \frac{5}{6})$

Step 1

Convert $3 \frac{1}{4}$ to an improper fraction.

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Step 1.1

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

$- (3 + \frac{1}{4}) + 8 \frac{1}{9} \cdot (- 4 \frac{5}{6})$

Step 1.2

Add $3$ and $\frac{1}{4}$ .

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Step 1.2.1

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

$- (3 \cdot \frac{4}{4} + \frac{1}{4}) + 8 \frac{1}{9} \cdot (- 4 \frac{5}{6})$

Step 1.2.2

Combine $3$ and $\frac{4}{4}$ .

$- (\frac{3 \cdot 4}{4} + \frac{1}{4}) + 8 \frac{1}{9} \cdot (- 4 \frac{5}{6})$

Step 1.2.3

Combine the numerators over the common denominator.

$- \frac{3 \cdot 4 + 1}{4} + 8 \frac{1}{9} \cdot (- 4 \frac{5}{6})$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $3$ by $4$ .

$- \frac{12 + 1}{4} + 8 \frac{1}{9} \cdot (- 4 \frac{5}{6})$

Step 1.2.4.2

Add $12$ and $1$ .

$- \frac{13}{4} + 8 \frac{1}{9} \cdot (- 4 \frac{5}{6})$

Step 2

Convert $8 \frac{1}{9}$ to an improper fraction.

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Step 2.1

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

$- \frac{13}{4} + (8 + \frac{1}{9}) \cdot (- 4 \frac{5}{6})$

Step 2.2

Add $8$ and $\frac{1}{9}$ .

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Step 2.2.1

To write $8$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$- \frac{13}{4} + (8 \cdot \frac{9}{9} + \frac{1}{9}) \cdot (- 4 \frac{5}{6})$

Step 2.2.2

Combine $8$ and $\frac{9}{9}$ .

$- \frac{13}{4} + (\frac{8 \cdot 9}{9} + \frac{1}{9}) \cdot (- 4 \frac{5}{6})$

Step 2.2.3

Combine the numerators over the common denominator.

$- \frac{13}{4} + \frac{8 \cdot 9 + 1}{9} \cdot (- 4 \frac{5}{6})$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $8$ by $9$ .

$- \frac{13}{4} + \frac{72 + 1}{9} \cdot (- 4 \frac{5}{6})$

Step 2.2.4.2

Add $72$ and $1$ .

$- \frac{13}{4} + \frac{73}{9} \cdot (- 4 \frac{5}{6})$

Step 3

Convert $4 \frac{5}{6}$ to an improper fraction.

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Step 3.1

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

$- \frac{13}{4} + \frac{73}{9} \cdot (- (4 + \frac{5}{6}))$

Step 3.2

Add $4$ and $\frac{5}{6}$ .

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Step 3.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$- \frac{13}{4} + \frac{73}{9} \cdot (- (4 \cdot \frac{6}{6} + \frac{5}{6}))$

Step 3.2.2

Combine $4$ and $\frac{6}{6}$ .

$- \frac{13}{4} + \frac{73}{9} \cdot (- (\frac{4 \cdot 6}{6} + \frac{5}{6}))$

Step 3.2.3

Combine the numerators over the common denominator.

$- \frac{13}{4} + \frac{73}{9} \cdot (- \frac{4 \cdot 6 + 5}{6})$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $4$ by $6$ .

$- \frac{13}{4} + \frac{73}{9} \cdot (- \frac{24 + 5}{6})$

Step 3.2.4.2

Add $24$ and $5$ .

$- \frac{13}{4} + \frac{73}{9} \cdot (- \frac{29}{6})$

Step 4

Multiply $\frac{73}{9} (- \frac{29}{6})$ .

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Step 4.1

Multiply $\frac{73}{9}$ by $\frac{29}{6}$ .

$- \frac{13}{4} - \frac{73 \cdot 29}{9 \cdot 6}$

Step 4.2

Multiply $73$ by $29$ .

$- \frac{13}{4} - \frac{2117}{9 \cdot 6}$

Step 4.3

Multiply $9$ by $6$ .

$- \frac{13}{4} - \frac{2117}{54}$

Step 5

To write $- \frac{13}{4}$ as a fraction with a common denominator, multiply by $\frac{27}{27}$ .

$- \frac{13}{4} \cdot \frac{27}{27} - \frac{2117}{54}$

Step 6

To write $- \frac{2117}{54}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{13}{4} \cdot \frac{27}{27} - \frac{2117}{54} \cdot \frac{2}{2}$

Step 7

Write each expression with a common denominator of $108$ , by multiplying each by an appropriate factor of $1$ .

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Step 7.1

Multiply $\frac{13}{4}$ by $\frac{27}{27}$ .

$- \frac{13 \cdot 27}{4 \cdot 27} - \frac{2117}{54} \cdot \frac{2}{2}$

Step 7.2

Multiply $4$ by $27$ .

$- \frac{13 \cdot 27}{108} - \frac{2117}{54} \cdot \frac{2}{2}$

Step 7.3

Multiply $\frac{2117}{54}$ by $\frac{2}{2}$ .

$- \frac{13 \cdot 27}{108} - \frac{2117 \cdot 2}{54 \cdot 2}$

Step 7.4

Multiply $54$ by $2$ .

$- \frac{13 \cdot 27}{108} - \frac{2117 \cdot 2}{108}$

Step 8

Combine the numerators over the common denominator.

$\frac{- 13 \cdot 27 - 2117 \cdot 2}{108}$

Step 9

Simplify the numerator.

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Step 9.1

Multiply $- 13$ by $27$ .

$\frac{- 351 - 2117 \cdot 2}{108}$

Step 9.2

Multiply $- 2117$ by $2$ .

$\frac{- 351 - 4234}{108}$

Step 9.3

Subtract $4234$ from $- 351$ .

$\frac{- 4585}{108}$

Step 10

Move the negative in front of the fraction.

$- \frac{4585}{108}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$- \frac{4585}{108}$

Decimal Form:

$- 42.45\overline{370}$

Mixed Number Form:

$- 42 \frac{49}{108}$