Basic Math Examples

$(2 \frac{3}{6} + \frac{1}{3}) \cdot (\frac{3}{5} - 1) \div 0.2$

Step 1

Convert $2 \frac{3}{6}$ to an improper fraction.

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Step 1.1

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

$(2 + \frac{3}{6} + \frac{1}{3}) \cdot (\frac{3}{5} - 1) \div 0.2$

Step 1.2

Add $2$ and $\frac{3}{6}$ .

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Step 1.2.1

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

$(2 \cdot \frac{6}{6} + \frac{3}{6} + \frac{1}{3}) \cdot (\frac{3}{5} - 1) \div 0.2$

Step 1.2.2

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

$(\frac{2 \cdot 6}{6} + \frac{3}{6} + \frac{1}{3}) \cdot (\frac{3}{5} - 1) \div 0.2$

Step 1.2.3

Combine the numerators over the common denominator.

$(\frac{2 \cdot 6 + 3}{6} + \frac{1}{3}) \cdot (\frac{3}{5} - 1) \div 0.2$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $6$ .

$(\frac{12 + 3}{6} + \frac{1}{3}) \cdot (\frac{3}{5} - 1) \div 0.2$

Step 1.2.4.2

Add $12$ and $3$ .

$(\frac{15}{6} + \frac{1}{3}) \cdot (\frac{3}{5} - 1) \div 0.2$

Step 2

Rewrite the division as a fraction.

$\frac{(\frac{15}{6} + \frac{1}{3}) \cdot (\frac{3}{5} - 1)}{0.2}$

Step 3

Cancel the common factor of $15$ and $6$ .

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Step 3.1

Factor $3$ out of $15$ .

$\frac{(\frac{3 (5)}{6} + \frac{1}{3}) \cdot (\frac{3}{5} - 1)}{0.2}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $3$ out of $6$ .

$\frac{(\frac{3 \cdot 5}{3 \cdot 2} + \frac{1}{3}) \cdot (\frac{3}{5} - 1)}{0.2}$

Step 3.2.2

Cancel the common factor.

$\frac{(\frac{3 \cdot 5}{3 \cdot 2} + \frac{1}{3}) \cdot (\frac{3}{5} - 1)}{0.2}$

Step 3.2.3

Rewrite the expression.

$\frac{(\frac{5}{2} + \frac{1}{3}) \cdot (\frac{3}{5} - 1)}{0.2}$

Step 4

Simplify the numerator.

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Step 4.1

To write $\frac{5}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{(\frac{5}{2} \cdot \frac{3}{3} + \frac{1}{3}) (\frac{3}{5} - 1)}{0.2}$

Step 4.2

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{(\frac{5}{2} \cdot \frac{3}{3} + \frac{1}{3} \cdot \frac{2}{2}) (\frac{3}{5} - 1)}{0.2}$

Step 4.3

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.3.1

Multiply $\frac{5}{2}$ by $\frac{3}{3}$ .

$\frac{(\frac{5 \cdot 3}{2 \cdot 3} + \frac{1}{3} \cdot \frac{2}{2}) (\frac{3}{5} - 1)}{0.2}$

Step 4.3.2

Multiply $2$ by $3$ .

$\frac{(\frac{5 \cdot 3}{6} + \frac{1}{3} \cdot \frac{2}{2}) (\frac{3}{5} - 1)}{0.2}$

Step 4.3.3

Multiply $\frac{1}{3}$ by $\frac{2}{2}$ .

$\frac{(\frac{5 \cdot 3}{6} + \frac{2}{3 \cdot 2}) (\frac{3}{5} - 1)}{0.2}$

Step 4.3.4

Multiply $3$ by $2$ .

$\frac{(\frac{5 \cdot 3}{6} + \frac{2}{6}) (\frac{3}{5} - 1)}{0.2}$

Step 4.4

Combine the numerators over the common denominator.

$\frac{\frac{5 \cdot 3 + 2}{6} (\frac{3}{5} - 1)}{0.2}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $5$ by $3$ .

$\frac{\frac{15 + 2}{6} (\frac{3}{5} - 1)}{0.2}$

Step 4.5.2

Add $15$ and $2$ .

$\frac{\frac{17}{6} (\frac{3}{5} - 1)}{0.2}$

Step 4.6

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{\frac{17}{6} (\frac{3}{5} - 1 \cdot \frac{5}{5})}{0.2}$

Step 4.7

Combine $- 1$ and $\frac{5}{5}$ .

$\frac{\frac{17}{6} (\frac{3}{5} + \frac{- 1 \cdot 5}{5})}{0.2}$

Step 4.8

Combine the numerators over the common denominator.

$\frac{\frac{17}{6} \cdot \frac{3 - 1 \cdot 5}{5}}{0.2}$

Step 4.9

Simplify the numerator.

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Step 4.9.1

Multiply $- 1$ by $5$ .

$\frac{\frac{17}{6} \cdot \frac{3 - 5}{5}}{0.2}$

Step 4.9.2

Subtract $5$ from $3$ .

$\frac{\frac{17}{6} \cdot \frac{- 2}{5}}{0.2}$

Step 4.10

Move the negative in front of the fraction.

$\frac{\frac{17}{6} \cdot - 1 \frac{2}{5}}{0.2}$

Step 4.11

Combine exponents.

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Step 4.11.1

Factor out negative.

$\frac{- (\frac{17}{6} \cdot \frac{2}{5})}{0.2}$

Step 4.11.2

Multiply $\frac{17}{6}$ by $\frac{2}{5}$ .

$\frac{- \frac{17 \cdot 2}{6 \cdot 5}}{0.2}$

Step 4.11.3

Multiply $17$ by $2$ .

$\frac{- \frac{34}{6 \cdot 5}}{0.2}$

Step 4.11.4

Multiply $6$ by $5$ .

$\frac{- \frac{34}{30}}{0.2}$

Step 4.12

Cancel the common factor of $34$ and $30$ .

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Step 4.12.1

Factor $2$ out of $34$ .

$\frac{- \frac{2 (17)}{30}}{0.2}$

Step 4.12.2

Cancel the common factors.

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Step 4.12.2.1

Factor $2$ out of $30$ .

$\frac{- \frac{2 \cdot 17}{2 \cdot 15}}{0.2}$

Step 4.12.2.2

Cancel the common factor.

$\frac{- \frac{2 \cdot 17}{2 \cdot 15}}{0.2}$

Step 4.12.2.3

Rewrite the expression.

$\frac{- \frac{17}{15}}{0.2}$

Step 5

Multiply the numerator by the reciprocal of the denominator.

$- \frac{17}{15} \cdot \frac{1}{0.2}$

Step 6

Cancel the common factor of $0.2$ .

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Step 6.1

Move the leading negative in $- \frac{17}{15}$ into the numerator.

$\frac{- 17}{15} \cdot \frac{1}{0.2}$

Step 6.2

Factor $0.2$ out of $- 17$ .

$\frac{0.2 (- 85)}{15} \cdot \frac{1}{0.2}$

Step 6.3

Cancel the common factor.

$\frac{0.2 \cdot - 85}{15} \cdot \frac{1}{0.2}$

Step 6.4

Rewrite the expression.

$\frac{- 85}{15}$

Step 7

Cancel the common factor of $- 85$ and $15$ .

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Step 7.1

Factor $5$ out of $- 85$ .

$\frac{5 (- 17)}{15}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $5$ out of $15$ .

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

Step 7.2.2

Cancel the common factor.

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

Step 7.2.3

Rewrite the expression.

$\frac{- 17}{3}$

Step 8

Move the negative in front of the fraction.

$- \frac{17}{3}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$- \frac{17}{3}$

Decimal Form:

$- 5.\overline{6}$

Mixed Number Form:

$- 5 \frac{2}{3}$