Basic Math Examples

$- 2 \frac{5}{6} \cdot 1 \frac{3}{5}$

Step 1

Convert $2 \frac{5}{6}$ to an improper fraction.

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Step 1.1

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

$- (2 + \frac{5}{6}) \cdot 1 \frac{3}{5}$

Step 1.2

Add $2$ and $\frac{5}{6}$ .

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Step 1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$- (2 \cdot \frac{6}{6} + \frac{5}{6}) \cdot 1 \frac{3}{5}$

Step 1.2.2

Combine $2$ and $\frac{6}{6}$ .

$- (\frac{2 \cdot 6}{6} + \frac{5}{6}) \cdot 1 \frac{3}{5}$

Step 1.2.3

Combine the numerators over the common denominator.

$- \frac{2 \cdot 6 + 5}{6} \cdot 1 \frac{3}{5}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $6$ .

$- \frac{12 + 5}{6} \cdot 1 \frac{3}{5}$

Step 1.2.4.2

Add $12$ and $5$ .

$- \frac{17}{6} \cdot 1 \frac{3}{5}$

Step 2

Convert $1 \frac{3}{5}$ to an improper fraction.

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Step 2.1

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

$- \frac{17}{6} \cdot (1 + \frac{3}{5})$

Step 2.2

Add $1$ and $\frac{3}{5}$ .

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Step 2.2.1

Write $1$ as a fraction with a common denominator.

$- \frac{17}{6} \cdot (\frac{5}{5} + \frac{3}{5})$

Step 2.2.2

Combine the numerators over the common denominator.

$- \frac{17}{6} \cdot \frac{5 + 3}{5}$

Step 2.2.3

Add $5$ and $3$ .

$- \frac{17}{6} \cdot \frac{8}{5}$

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Move the leading negative in $- \frac{17}{6}$ into the numerator.

$\frac{- 17}{6} \cdot \frac{8}{5}$

Step 3.2

Factor $2$ out of $6$ .

$\frac{- 17}{2 (3)} \cdot \frac{8}{5}$

Step 3.3

Factor $2$ out of $8$ .

$\frac{- 17}{2 \cdot 3} \cdot \frac{2 \cdot 4}{5}$

Step 3.4

Cancel the common factor.

$\frac{- 17}{2 \cdot 3} \cdot \frac{2 \cdot 4}{5}$

Step 3.5

Rewrite the expression.

$\frac{- 17}{3} \cdot \frac{4}{5}$

Step 4

Multiply $\frac{- 17}{3}$ by $\frac{4}{5}$ .

$\frac{- 17 \cdot 4}{3 \cdot 5}$

Step 5

Simplify the expression.

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Step 5.1

Multiply $- 17$ by $4$ .

$\frac{- 68}{3 \cdot 5}$

Step 5.2

Multiply $3$ by $5$ .

$\frac{- 68}{15}$

Step 5.3

Move the negative in front of the fraction.

$- \frac{68}{15}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{68}{15}$

Decimal Form:

$- 4.5\overline{3}$

Mixed Number Form:

$- 4 \frac{8}{15}$