Basic Math Examples

$(\frac{1}{5}) \cdot 8 \frac{1}{3} - 3 \frac{3}{4} \div (- 1 \frac{17}{28})$

Step 1

Convert $8 \frac{1}{3}$ to an improper fraction.

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Step 1.1

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

$\frac{1}{5} \cdot (8 + \frac{1}{3}) - 3 \frac{3}{4} \div (- 1 \frac{17}{28})$

Step 1.2

Add $8$ and $\frac{1}{3}$ .

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Step 1.2.1

To write $8$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{1}{5} \cdot (8 \cdot \frac{3}{3} + \frac{1}{3}) - 3 \frac{3}{4} \div (- 1 \frac{17}{28})$

Step 1.2.2

Combine $8$ and $\frac{3}{3}$ .

$\frac{1}{5} \cdot (\frac{8 \cdot 3}{3} + \frac{1}{3}) - 3 \frac{3}{4} \div (- 1 \frac{17}{28})$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{1}{5} \cdot \frac{8 \cdot 3 + 1}{3} - 3 \frac{3}{4} \div (- 1 \frac{17}{28})$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $8$ by $3$ .

$\frac{1}{5} \cdot \frac{24 + 1}{3} - 3 \frac{3}{4} \div (- 1 \frac{17}{28})$

Step 1.2.4.2

Add $24$ and $1$ .

$\frac{1}{5} \cdot \frac{25}{3} - 3 \frac{3}{4} \div (- 1 \frac{17}{28})$

Step 2

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

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Step 2.1

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

$\frac{1}{5} \cdot \frac{25}{3} - (3 + \frac{3}{4}) \div (- 1 \frac{17}{28})$

Step 2.2

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

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Step 2.2.1

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

$\frac{1}{5} \cdot \frac{25}{3} - (3 \cdot \frac{4}{4} + \frac{3}{4}) \div (- 1 \frac{17}{28})$

Step 2.2.2

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

$\frac{1}{5} \cdot \frac{25}{3} - (\frac{3 \cdot 4}{4} + \frac{3}{4}) \div (- 1 \frac{17}{28})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{1}{5} \cdot \frac{25}{3} - \frac{3 \cdot 4 + 3}{4} \div (- 1 \frac{17}{28})$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $3$ by $4$ .

$\frac{1}{5} \cdot \frac{25}{3} - \frac{12 + 3}{4} \div (- 1 \frac{17}{28})$

Step 2.2.4.2

Add $12$ and $3$ .

$\frac{1}{5} \cdot \frac{25}{3} - \frac{15}{4} \div (- 1 \frac{17}{28})$

Step 3

Convert $1 \frac{17}{28}$ to an improper fraction.

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Step 3.1

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

$\frac{1}{5} \cdot \frac{25}{3} - \frac{15}{4} \div (- (1 + \frac{17}{28}))$

Step 3.2

Add $1$ and $\frac{17}{28}$ .

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Step 3.2.1

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

$\frac{1}{5} \cdot \frac{25}{3} - \frac{15}{4} \div (- (\frac{28}{28} + \frac{17}{28}))$

Step 3.2.2

Combine the numerators over the common denominator.

$\frac{1}{5} \cdot \frac{25}{3} - \frac{15}{4} \div (- \frac{28 + 17}{28})$

Step 3.2.3

Add $28$ and $17$ .

$\frac{1}{5} \cdot \frac{25}{3} - \frac{15}{4} \div (- \frac{45}{28})$

Step 4

Simplify each term.

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Step 4.1

Cancel the common factor of $5$ .

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Step 4.1.1

Factor $5$ out of $25$ .

$\frac{1}{5} \cdot \frac{5 (5)}{3} - \frac{15}{4} \div (- \frac{45}{28})$

Step 4.1.2

Cancel the common factor.

$\frac{1}{5} \cdot \frac{5 \cdot 5}{3} - \frac{15}{4} \div (- \frac{45}{28})$

Step 4.1.3

Rewrite the expression.

$\frac{5}{3} - \frac{15}{4} \div (- \frac{45}{28})$

Step 4.2

To divide by a fraction, multiply by its reciprocal.

$\frac{5}{3} - (\frac{15}{4} (- \frac{28}{45}))$

Step 4.3

Cancel the common factor of $15$ .

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Step 4.3.1

Move the leading negative in $- \frac{28}{45}$ into the numerator.

$\frac{5}{3} - (\frac{15}{4} \cdot \frac{- 28}{45})$

Step 4.3.2

Factor $15$ out of $45$ .

$\frac{5}{3} - (\frac{15}{4} \cdot \frac{- 28}{15 (3)})$

Step 4.3.3

Cancel the common factor.

$\frac{5}{3} - (\frac{15}{4} \cdot \frac{- 28}{15 \cdot 3})$

Step 4.3.4

Rewrite the expression.

$\frac{5}{3} - (\frac{1}{4} \cdot \frac{- 28}{3})$

Step 4.4

Cancel the common factor of $4$ .

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Step 4.4.1

Factor $4$ out of $- 28$ .

$\frac{5}{3} - (\frac{1}{4} \cdot \frac{4 (- 7)}{3})$

Step 4.4.2

Cancel the common factor.

$\frac{5}{3} - (\frac{1}{4} \cdot \frac{4 \cdot - 7}{3})$

Step 4.4.3

Rewrite the expression.

$\frac{5}{3} - \frac{- 7}{3}$

Step 4.5

Move the negative in front of the fraction.

$\frac{5}{3} - - \frac{7}{3}$

Step 4.6

Multiply $- - \frac{7}{3}$ .

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Step 4.6.1

Multiply $- 1$ by $- 1$ .

$\frac{5}{3} + 1 (\frac{7}{3})$

Step 4.6.2

Multiply $\frac{7}{3}$ by $1$ .

$\frac{5}{3} + \frac{7}{3}$

Step 5

Combine fractions.

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Step 5.1

Combine the numerators over the common denominator.

$\frac{5 + 7}{3}$

Step 5.2

Simplify the expression.

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Step 5.2.1

Add $5$ and $7$ .

$\frac{12}{3}$

Step 5.2.2

Divide $12$ by $3$ .

$4$