Basic Math Examples

(- \frac{7}{4} - \frac{6}{7}) - (- \frac{5}{4} - 7)

$(- \frac{7}{4} - \frac{6}{7}) - (- \frac{5}{4} - 7)$

Step 1

Find the common denominator.

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Step 1.1

Multiply

\frac{7}{4}

$\frac{7}{4}$ by

\frac{7}{7}

$\frac{7}{7}$ .

- (\frac{7}{4} \cdot \frac{7}{7}) - \frac{6}{7} - (- \frac{5}{4} - 7)

$- (\frac{7}{4} \cdot \frac{7}{7}) - \frac{6}{7} - (- \frac{5}{4} - 7)$

Step 1.2

Multiply

\frac{7}{4}

$\frac{7}{4}$ by

\frac{7}{7}

$\frac{7}{7}$ .

- \frac{7 \cdot 7}{4 \cdot 7} - \frac{6}{7} - (- \frac{5}{4} - 7)

$- \frac{7 \cdot 7}{4 \cdot 7} - \frac{6}{7} - (- \frac{5}{4} - 7)$

Step 1.3

Multiply

\frac{6}{7}

$\frac{6}{7}$ by

\frac{4}{4}

$\frac{4}{4}$ .

- \frac{7 \cdot 7}{4 \cdot 7} - (\frac{6}{7} \cdot \frac{4}{4}) - (- \frac{5}{4} - 7)

$- \frac{7 \cdot 7}{4 \cdot 7} - (\frac{6}{7} \cdot \frac{4}{4}) - (- \frac{5}{4} - 7)$

Step 1.4

Multiply

\frac{6}{7}

$\frac{6}{7}$ by

\frac{4}{4}

$\frac{4}{4}$ .

- \frac{7 \cdot 7}{4 \cdot 7} - \frac{6 \cdot 4}{7 \cdot 4} - (- \frac{5}{4} - 7)

$- \frac{7 \cdot 7}{4 \cdot 7} - \frac{6 \cdot 4}{7 \cdot 4} - (- \frac{5}{4} - 7)$

Step 1.5

Write

- (- \frac{5}{4} - 7)

$- (- \frac{5}{4} - 7)$ as a fraction with denominator

1

$1$ .

- \frac{7 \cdot 7}{4 \cdot 7} - \frac{6 \cdot 4}{7 \cdot 4} + \frac{- (- \frac{5}{4} - 7)}{1}

$- \frac{7 \cdot 7}{4 \cdot 7} - \frac{6 \cdot 4}{7 \cdot 4} + \frac{- (- \frac{5}{4} - 7)}{1}$

Step 1.6

Multiply

\frac{- (- \frac{5}{4} - 7)}{1}

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

\frac{28}{28}

$\frac{28}{28}$ .

- \frac{7 \cdot 7}{4 \cdot 7} - \frac{6 \cdot 4}{7 \cdot 4} + \frac{- (- \frac{5}{4} - 7)}{1} \cdot \frac{28}{28}

$- \frac{7 \cdot 7}{4 \cdot 7} - \frac{6 \cdot 4}{7 \cdot 4} + \frac{- (- \frac{5}{4} - 7)}{1} \cdot \frac{28}{28}$

Step 1.7

Multiply

\frac{- (- \frac{5}{4} - 7)}{1}

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

\frac{28}{28}

$\frac{28}{28}$ .

- \frac{7 \cdot 7}{4 \cdot 7} - \frac{6 \cdot 4}{7 \cdot 4} + \frac{- (- \frac{5}{4} - 7) \cdot 28}{28}

$- \frac{7 \cdot 7}{4 \cdot 7} - \frac{6 \cdot 4}{7 \cdot 4} + \frac{- (- \frac{5}{4} - 7) \cdot 28}{28}$

Step 1.8

Multiply

4

$4$ by

7

$7$ .

- \frac{7 \cdot 7}{28} - \frac{6 \cdot 4}{7 \cdot 4} + \frac{- (- \frac{5}{4} - 7) \cdot 28}{28}

$- \frac{7 \cdot 7}{28} - \frac{6 \cdot 4}{7 \cdot 4} + \frac{- (- \frac{5}{4} - 7) \cdot 28}{28}$

Step 1.9

Reorder the factors of

7 \cdot 4

$7 \cdot 4$ .

- \frac{7 \cdot 7}{28} - \frac{6 \cdot 4}{4 \cdot 7} + \frac{- (- \frac{5}{4} - 7) \cdot 28}{28}

$- \frac{7 \cdot 7}{28} - \frac{6 \cdot 4}{4 \cdot 7} + \frac{- (- \frac{5}{4} - 7) \cdot 28}{28}$

Step 1.10

Multiply

4

$4$ by

7

$7$ .

- \frac{7 \cdot 7}{28} - \frac{6 \cdot 4}{28} + \frac{- (- \frac{5}{4} - 7) \cdot 28}{28}

$- \frac{7 \cdot 7}{28} - \frac{6 \cdot 4}{28} + \frac{- (- \frac{5}{4} - 7) \cdot 28}{28}$

- \frac{7 \cdot 7}{28} - \frac{6 \cdot 4}{28} + \frac{- (- \frac{5}{4} - 7) \cdot 28}{28}

$- \frac{7 \cdot 7}{28} - \frac{6 \cdot 4}{28} + \frac{- (- \frac{5}{4} - 7) \cdot 28}{28}$

Step 2

Combine the numerators over the common denominator.

\frac{- 7 \cdot 7 - 6 \cdot 4 - (- \frac{5}{4} - 7) \cdot 28}{28}

$\frac{- 7 \cdot 7 - 6 \cdot 4 - (- \frac{5}{4} - 7) \cdot 28}{28}$

Step 3

Simplify each term.

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Step 3.1

Multiply

- 7

$- 7$ by

7

$7$ .

\frac{- 49 - 6 \cdot 4 - (- \frac{5}{4} - 7) \cdot 28}{28}

$\frac{- 49 - 6 \cdot 4 - (- \frac{5}{4} - 7) \cdot 28}{28}$

Step 3.2

Multiply

$- 6$ by

$4$ .

$\frac{- 49 - 24 - (- \frac{5}{4} - 7) \cdot 28}{28}$

Step 3.3

To write

$- 7$ as a fraction with a common denominator, multiply by

$\frac{4}{4}$ .

$\frac{- 49 - 24 - (- \frac{5}{4} - 7 \cdot \frac{4}{4}) \cdot 28}{28}$

Step 3.4

Combine

$- 7$ and

$\frac{4}{4}$ .

$\frac{- 49 - 24 - (- \frac{5}{4} + \frac{- 7 \cdot 4}{4}) \cdot 28}{28}$

Step 3.5

Combine the numerators over the common denominator.

$\frac{- 49 - 24 - \frac{- 5 - 7 \cdot 4}{4} \cdot 28}{28}$

Step 3.6

Simplify the numerator.

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Step 3.6.1

Multiply

$- 7$ by

$4$ .

$\frac{- 49 - 24 - \frac{- 5 - 28}{4} \cdot 28}{28}$

Step 3.6.2

Subtract

$28$ from

$- 5$ .

$\frac{- 49 - 24 - \frac{- 33}{4} \cdot 28}{28}$

Step 3.7

Cancel the common factor of

$4$ .

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Step 3.7.1

Move the leading negative in

$- \frac{- 33}{4}$ into the numerator.

$\frac{- 49 - 24 + \frac{33}{4} \cdot 28}{28}$

Step 3.7.2

Factor

$4$ out of

$28$ .

$\frac{- 49 - 24 + \frac{33}{4} \cdot (4 (7))}{28}$

Step 3.7.3

Cancel the common factor.

$\frac{- 49 - 24 + \frac{33}{4} \cdot (4 \cdot 7)}{28}$

Step 3.7.4

Rewrite the expression.

$\frac{- 49 - 24 + 33 \cdot 7}{28}$

Step 3.8

Multiply

$33$ by

$7$ .

$\frac{- 49 - 24 + 231}{28}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Subtract

$24$ from

$- 49$ .

$\frac{- 73 + 231}{28}$

Step 4.2

Add

$- 73$ and

$231$ .

$\frac{158}{28}$

Step 4.3

Cancel the common factor of

$158$ and

$28$ .

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Step 4.3.1

Factor

$2$ out of

$158$ .

$\frac{2 (79)}{28}$

Step 4.3.2

Cancel the common factors.

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Step 4.3.2.1

Factor

$2$ out of

$28$ .

$\frac{2 \cdot 79}{2 \cdot 14}$

Step 4.3.2.2

Cancel the common factor.

$\frac{2 \cdot 79}{2 \cdot 14}$

Step 4.3.2.3

Rewrite the expression.

$\frac{79}{14}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{79}{14}$

Decimal Form:

$5.64285714 \dots$

Mixed Number Form:

$5 \frac{9}{14}$