Basic Math Examples

$(- \frac{3}{4} \cdot \frac{2}{3} - \frac{5}{6}) (\frac{2}{7} \cdot (- \frac{14}{8}))$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $3$ .

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Step 1.1.1

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

$(\frac{- 3}{4} \cdot \frac{2}{3} - \frac{5}{6}) (\frac{2}{7} \cdot (- \frac{14}{8}))$

Step 1.1.2

Factor $3$ out of $- 3$ .

$(\frac{3 (- 1)}{4} \cdot \frac{2}{3} - \frac{5}{6}) (\frac{2}{7} \cdot (- \frac{14}{8}))$

Step 1.1.3

Cancel the common factor.

$(\frac{3 \cdot - 1}{4} \cdot \frac{2}{3} - \frac{5}{6}) (\frac{2}{7} \cdot (- \frac{14}{8}))$

Step 1.1.4

Rewrite the expression.

$(\frac{- 1}{4} \cdot 2 - \frac{5}{6}) (\frac{2}{7} \cdot (- \frac{14}{8}))$

Step 1.2

Cancel the common factor of $2$ .

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Step 1.2.1

Factor $2$ out of $4$ .

$(\frac{- 1}{2 (2)} \cdot 2 - \frac{5}{6}) (\frac{2}{7} \cdot (- \frac{14}{8}))$

Step 1.2.2

Cancel the common factor.

$(\frac{- 1}{2 \cdot 2} \cdot 2 - \frac{5}{6}) (\frac{2}{7} \cdot (- \frac{14}{8}))$

Step 1.2.3

Rewrite the expression.

$(\frac{- 1}{2} - \frac{5}{6}) (\frac{2}{7} \cdot (- \frac{14}{8}))$

Step 1.3

Move the negative in front of the fraction.

$(- \frac{1}{2} - \frac{5}{6}) (\frac{2}{7} \cdot (- \frac{14}{8}))$

Step 2

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

$(- \frac{1}{2} \cdot \frac{3}{3} - \frac{5}{6}) (\frac{2}{7} \cdot (- \frac{14}{8}))$

Step 3

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

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Step 3.1

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

$(- \frac{3}{2 \cdot 3} - \frac{5}{6}) (\frac{2}{7} \cdot (- \frac{14}{8}))$

Step 3.2

Multiply $2$ by $3$ .

$(- \frac{3}{6} - \frac{5}{6}) (\frac{2}{7} \cdot (- \frac{14}{8}))$

Step 4

Simplify the expression.

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Step 4.1

Combine the numerators over the common denominator.

$\frac{- 3 - 5}{6} (\frac{2}{7} \cdot (- \frac{14}{8}))$

Step 4.2

Subtract $5$ from $- 3$ .

$\frac{- 8}{6} (\frac{2}{7} \cdot (- \frac{14}{8}))$

Step 5

Cancel the common factor of $- 8$ and $6$ .

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Step 5.1

Factor $2$ out of $- 8$ .

$\frac{2 (- 4)}{6} (\frac{2}{7} \cdot (- \frac{14}{8}))$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $2$ out of $6$ .

$\frac{2 \cdot - 4}{2 \cdot 3} (\frac{2}{7} \cdot (- \frac{14}{8}))$

Step 5.2.2

Cancel the common factor.

$\frac{2 \cdot - 4}{2 \cdot 3} (\frac{2}{7} \cdot (- \frac{14}{8}))$

Step 5.2.3

Rewrite the expression.

$\frac{- 4}{3} (\frac{2}{7} \cdot (- \frac{14}{8}))$

Step 6

Move the negative in front of the fraction.

$- \frac{4}{3} (\frac{2}{7} \cdot (- \frac{14}{8}))$

Step 7

Cancel the common factor of $2$ .

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Step 7.1

Move the leading negative in $- \frac{14}{8}$ into the numerator.

$- \frac{4}{3} (\frac{2}{7} \cdot \frac{- 14}{8})$

Step 7.2

Factor $2$ out of $8$ .

$- \frac{4}{3} (\frac{2}{7} \cdot \frac{- 14}{2 (4)})$

Step 7.3

Cancel the common factor.

$- \frac{4}{3} (\frac{2}{7} \cdot \frac{- 14}{2 \cdot 4})$

Step 7.4

Rewrite the expression.

$- \frac{4}{3} (\frac{1}{7} \cdot \frac{- 14}{4})$

Step 8

Cancel the common factor of $7$ .

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Step 8.1

Factor $7$ out of $- 14$ .

$- \frac{4}{3} (\frac{1}{7} \cdot \frac{7 (- 2)}{4})$

Step 8.2

Cancel the common factor.

$- \frac{4}{3} (\frac{1}{7} \cdot \frac{7 \cdot - 2}{4})$

Step 8.3

Rewrite the expression.

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

Step 9

Cancel the common factor of $4$ .

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Step 9.1

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

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

Step 9.2

Factor $4$ out of $- 4$ .

$\frac{4 (- 1)}{3} \cdot \frac{- 2}{4}$

Step 9.3

Cancel the common factor.

$\frac{4 \cdot - 1}{3} \cdot \frac{- 2}{4}$

Step 9.4

Rewrite the expression.

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

Step 10

Combine $\frac{- 1}{3}$ and $- 2$ .

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

Step 11

Multiply $- 1$ by $- 2$ .

$\frac{2}{3}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{3}$

Decimal Form:

$0.\overline{6}$