Basic Math Examples

- (- \frac{25}{42} - \frac{2}{7}) - \frac{5}{3}

$- (- \frac{25}{42} - \frac{2}{7}) - \frac{5}{3}$

Step 1

Simplify each term.

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Step 1.1

To write

- \frac{2}{7}

$- \frac{2}{7}$ as a fraction with a common denominator, multiply by

\frac{6}{6}

$\frac{6}{6}$ .

- (- \frac{25}{42} - \frac{2}{7} \cdot \frac{6}{6}) - \frac{5}{3}

$- (- \frac{25}{42} - \frac{2}{7} \cdot \frac{6}{6}) - \frac{5}{3}$

Step 1.2

Write each expression with a common denominator of

42

$42$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 1.2.1

Multiply

\frac{2}{7}

$\frac{2}{7}$ by

\frac{6}{6}

$\frac{6}{6}$ .

- (- \frac{25}{42} - \frac{2 \cdot 6}{7 \cdot 6}) - \frac{5}{3}

$- (- \frac{25}{42} - \frac{2 \cdot 6}{7 \cdot 6}) - \frac{5}{3}$

Step 1.2.2

Multiply

7

$7$ by

6

$6$ .

- (- \frac{25}{42} - \frac{2 \cdot 6}{42}) - \frac{5}{3}

$- (- \frac{25}{42} - \frac{2 \cdot 6}{42}) - \frac{5}{3}$

- (- \frac{25}{42} - \frac{2 \cdot 6}{42}) - \frac{5}{3}

$- (- \frac{25}{42} - \frac{2 \cdot 6}{42}) - \frac{5}{3}$

Step 1.3

Combine the numerators over the common denominator.

- \frac{- 25 - 2 \cdot 6}{42} - \frac{5}{3}

$- \frac{- 25 - 2 \cdot 6}{42} - \frac{5}{3}$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Multiply

- 2

$- 2$ by

6

$6$ .

- \frac{- 25 - 12}{42} - \frac{5}{3}

$- \frac{- 25 - 12}{42} - \frac{5}{3}$

Step 1.4.2

Subtract

$12$ from

$- 25$ .

$- \frac{- 37}{42} - \frac{5}{3}$

Step 1.5

Move the negative in front of the fraction.

$- - \frac{37}{42} - \frac{5}{3}$

Step 1.6

Multiply

$- - \frac{37}{42}$ .

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Step 1.6.1

Multiply

$- 1$ by

$- 1$ .

$1 (\frac{37}{42}) - \frac{5}{3}$

Step 1.6.2

Multiply

$\frac{37}{42}$ by

$1$ .

$\frac{37}{42} - \frac{5}{3}$

Step 2

To write

$- \frac{5}{3}$ as a fraction with a common denominator, multiply by

$\frac{14}{14}$ .

$\frac{37}{42} - \frac{5}{3} \cdot \frac{14}{14}$

Step 3

Write each expression with a common denominator of

$42$ , by multiplying each by an appropriate factor of

$1$ .

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Step 3.1

Multiply

$\frac{5}{3}$ by

$\frac{14}{14}$ .

$\frac{37}{42} - \frac{5 \cdot 14}{3 \cdot 14}$

Step 3.2

Multiply

$3$ by

$14$ .

$\frac{37}{42} - \frac{5 \cdot 14}{42}$

Step 4

Combine the numerators over the common denominator.

$\frac{37 - 5 \cdot 14}{42}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply

$- 5$ by

$14$ .

$\frac{37 - 70}{42}$

Step 5.2

Subtract

$70$ from

$37$ .

$\frac{- 33}{42}$

Step 6

Cancel the common factor of

$- 33$ and

$42$ .

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Step 6.1

Factor

$3$ out of

$- 33$ .

$\frac{3 (- 11)}{42}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor

$3$ out of

$42$ .

$\frac{3 \cdot - 11}{3 \cdot 14}$

Step 6.2.2

Cancel the common factor.

$\frac{3 \cdot - 11}{3 \cdot 14}$

Step 6.2.3

Rewrite the expression.

$\frac{- 11}{14}$

Step 7

Move the negative in front of the fraction.

$- \frac{11}{14}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{11}{14}$

Decimal Form:

$- 0.7\overline{857142}$