Basic Math Examples

$\frac{\frac{1}{3} - \frac{2}{5} \cdot \frac{15}{8} + \frac{7}{12}}{\frac{1}{5} - \frac{7}{2}}$

Step 1

Multiply the numerator and denominator of the fraction by $60$ .

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Step 1.1

Multiply $\frac{\frac{1}{3} - \frac{2}{5} \cdot \frac{15}{8} + \frac{7}{12}}{\frac{1}{5} - \frac{7}{2}}$ by $\frac{60}{60}$ .

$\frac{60}{60} \cdot \frac{\frac{1}{3} - \frac{2}{5} \cdot \frac{15}{8} + \frac{7}{12}}{\frac{1}{5} - \frac{7}{2}}$

Step 1.2

Combine.

$\frac{60 (\frac{1}{3} - \frac{2}{5} \cdot \frac{15}{8} + \frac{7}{12})}{60 (\frac{1}{5} - \frac{7}{2})}$

Step 2

Apply the distributive property.

$\frac{60 (\frac{1}{3}) + 60 (- \frac{2}{5} \cdot \frac{15}{8}) + 60 (\frac{7}{12})}{60 (\frac{1}{5}) + 60 (- \frac{7}{2})}$

Step 3

Simplify by cancelling.

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Step 3.1

Cancel the common factor of $3$ .

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Step 3.1.1

Factor $3$ out of $60$ .

$\frac{3 (20) \frac{1}{3} + 60 (- \frac{2}{5} \cdot \frac{15}{8}) + 60 (\frac{7}{12})}{60 (\frac{1}{5}) + 60 (- \frac{7}{2})}$

Step 3.1.2

Cancel the common factor.

$\frac{3 \cdot 20 \frac{1}{3} + 60 (- \frac{2}{5} \cdot \frac{15}{8}) + 60 (\frac{7}{12})}{60 (\frac{1}{5}) + 60 (- \frac{7}{2})}$

Step 3.1.3

Rewrite the expression.

$\frac{20 + 60 (- \frac{2}{5} \cdot \frac{15}{8}) + 60 (\frac{7}{12})}{60 (\frac{1}{5}) + 60 (- \frac{7}{2})}$

Step 3.2

Cancel the common factor of $12$ .

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Step 3.2.1

Factor $12$ out of $60$ .

$\frac{20 + 60 (- \frac{2}{5} \cdot \frac{15}{8}) + 12 (5) \frac{7}{12}}{60 (\frac{1}{5}) + 60 (- \frac{7}{2})}$

Step 3.2.2

Cancel the common factor.

$\frac{20 + 60 (- \frac{2}{5} \cdot \frac{15}{8}) + 12 \cdot 5 \frac{7}{12}}{60 (\frac{1}{5}) + 60 (- \frac{7}{2})}$

Step 3.2.3

Rewrite the expression.

$\frac{20 + 60 (- \frac{2}{5} \cdot \frac{15}{8}) + 5 \cdot 7}{60 (\frac{1}{5}) + 60 (- \frac{7}{2})}$

Step 3.3

Multiply $5$ by $7$ .

$\frac{20 + 60 (- \frac{2}{5} \cdot \frac{15}{8}) + 35}{60 (\frac{1}{5}) + 60 (- \frac{7}{2})}$

Step 3.4

Cancel the common factor of $5$ .

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Step 3.4.1

Factor $5$ out of $60$ .

$\frac{20 + 60 (- \frac{2}{5} \cdot \frac{15}{8}) + 35}{5 (12) \frac{1}{5} + 60 (- \frac{7}{2})}$

Step 3.4.2

Cancel the common factor.

$\frac{20 + 60 (- \frac{2}{5} \cdot \frac{15}{8}) + 35}{5 \cdot 12 \frac{1}{5} + 60 (- \frac{7}{2})}$

Step 3.4.3

Rewrite the expression.

$\frac{20 + 60 (- \frac{2}{5} \cdot \frac{15}{8}) + 35}{12 + 60 (- \frac{7}{2})}$

Step 3.5

Cancel the common factor of $2$ .

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Step 3.5.1

Move the leading negative in $- \frac{7}{2}$ into the numerator.

$\frac{20 + 60 (- \frac{2}{5} \cdot \frac{15}{8}) + 35}{12 + 60 (\frac{- 7}{2})}$

Step 3.5.2

Factor $2$ out of $60$ .

$\frac{20 + 60 (- \frac{2}{5} \cdot \frac{15}{8}) + 35}{12 + 2 (30) \frac{- 7}{2}}$

Step 3.5.3

Cancel the common factor.

$\frac{20 + 60 (- \frac{2}{5} \cdot \frac{15}{8}) + 35}{12 + 2 \cdot 30 \frac{- 7}{2}}$

Step 3.5.4

Rewrite the expression.

$\frac{20 + 60 (- \frac{2}{5} \cdot \frac{15}{8}) + 35}{12 + 30 \cdot - 7}$

Step 3.6

Multiply $30$ by $- 7$ .

$\frac{20 + 60 (- \frac{2}{5} \cdot \frac{15}{8}) + 35}{12 - 210}$

Step 4

Simplify the numerator.

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Step 4.1

Cancel the common factor of $2$ .

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Step 4.1.1

Move the leading negative in $- \frac{2}{5}$ into the numerator.

$\frac{20 + 60 (\frac{- 2}{5} \cdot \frac{15}{8}) + 35}{12 - 210}$

Step 4.1.2

Factor $2$ out of $- 2$ .

$\frac{20 + 60 (\frac{2 (- 1)}{5} \cdot \frac{15}{8}) + 35}{12 - 210}$

Step 4.1.3

Factor $2$ out of $8$ .

$\frac{20 + 60 (\frac{2 \cdot - 1}{5} \cdot \frac{15}{2 \cdot 4}) + 35}{12 - 210}$

Step 4.1.4

Cancel the common factor.

$\frac{20 + 60 (\frac{2 \cdot - 1}{5} \cdot \frac{15}{2 \cdot 4}) + 35}{12 - 210}$

Step 4.1.5

Rewrite the expression.

$\frac{20 + 60 (\frac{- 1}{5} \cdot \frac{15}{4}) + 35}{12 - 210}$

Step 4.2

Cancel the common factor of $5$ .

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Step 4.2.1

Factor $5$ out of $15$ .

$\frac{20 + 60 (\frac{- 1}{5} \cdot \frac{5 (3)}{4}) + 35}{12 - 210}$

Step 4.2.2

Cancel the common factor.

$\frac{20 + 60 (\frac{- 1}{5} \cdot \frac{5 \cdot 3}{4}) + 35}{12 - 210}$

Step 4.2.3

Rewrite the expression.

$\frac{20 + 60 (- 1 \cdot \frac{3}{4}) + 35}{12 - 210}$

Step 4.3

Rewrite $- 1 (\frac{3}{4})$ as $- (\frac{3}{4})$ .

$\frac{20 + 60 (- (\frac{3}{4})) + 35}{12 - 210}$

Step 4.4

Cancel the common factor of $4$ .

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Step 4.4.1

Move the leading negative in $- (\frac{3}{4})$ into the numerator.

$\frac{20 + 60 (\frac{- 3}{4}) + 35}{12 - 210}$

Step 4.4.2

Factor $4$ out of $60$ .

$\frac{20 + 4 (15) \frac{- 3}{4} + 35}{12 - 210}$

Step 4.4.3

Cancel the common factor.

$\frac{20 + 4 \cdot 15 \frac{- 3}{4} + 35}{12 - 210}$

Step 4.4.4

Rewrite the expression.

$\frac{20 + 15 \cdot - 3 + 35}{12 - 210}$

Step 4.5

Multiply $15$ by $- 3$ .

$\frac{20 - 45 + 35}{12 - 210}$

Step 4.6

Subtract $45$ from $20$ .

$\frac{- 25 + 35}{12 - 210}$

Step 4.7

Add $- 25$ and $35$ .

$\frac{10}{12 - 210}$

Step 5

Reduce the expression by cancelling the common factors.

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Step 5.1

Subtract $210$ from $12$ .

$\frac{10}{- 198}$

Step 5.2

Cancel the common factor of $10$ and $- 198$ .

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Step 5.2.1

Factor $2$ out of $10$ .

$\frac{2 (5)}{- 198}$

Step 5.2.2

Cancel the common factors.

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Step 5.2.2.1

Factor $2$ out of $- 198$ .

$\frac{2 \cdot 5}{2 \cdot - 99}$

Step 5.2.2.2

Cancel the common factor.

$\frac{2 \cdot 5}{2 \cdot - 99}$

Step 5.2.2.3

Rewrite the expression.

$\frac{5}{- 99}$

Step 5.3

Move the negative in front of the fraction.

$- \frac{5}{99}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{5}{99}$

Decimal Form:

$- 0.\overline{05}$