Basic Math Examples

$\frac{57}{17} - \frac{153}{221} + (- \frac{5}{12} - \frac{7}{442})$

Step 1

Remove parentheses.

$\frac{57}{17} - \frac{153}{221} - \frac{5}{12} - \frac{7}{442}$

Step 2

Find the common denominator.

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Step 2.1

Multiply $\frac{57}{17}$ by $\frac{156}{156}$ .

$\frac{57}{17} \cdot \frac{156}{156} - \frac{153}{221} - \frac{5}{12} - \frac{7}{442}$

Step 2.2

Multiply $\frac{57}{17}$ by $\frac{156}{156}$ .

$\frac{57 \cdot 156}{17 \cdot 156} - \frac{153}{221} - \frac{5}{12} - \frac{7}{442}$

Step 2.3

Multiply $\frac{153}{221}$ by $\frac{12}{12}$ .

$\frac{57 \cdot 156}{17 \cdot 156} - (\frac{153}{221} \cdot \frac{12}{12}) - \frac{5}{12} - \frac{7}{442}$

Step 2.4

Multiply $\frac{153}{221}$ by $\frac{12}{12}$ .

$\frac{57 \cdot 156}{17 \cdot 156} - \frac{153 \cdot 12}{221 \cdot 12} - \frac{5}{12} - \frac{7}{442}$

Step 2.5

Multiply $\frac{5}{12}$ by $\frac{221}{221}$ .

$\frac{57 \cdot 156}{17 \cdot 156} - \frac{153 \cdot 12}{221 \cdot 12} - (\frac{5}{12} \cdot \frac{221}{221}) - \frac{7}{442}$

Step 2.6

Multiply $\frac{5}{12}$ by $\frac{221}{221}$ .

$\frac{57 \cdot 156}{17 \cdot 156} - \frac{153 \cdot 12}{221 \cdot 12} - \frac{5 \cdot 221}{12 \cdot 221} - \frac{7}{442}$

Step 2.7

Multiply $\frac{7}{442}$ by $\frac{6}{6}$ .

$\frac{57 \cdot 156}{17 \cdot 156} - \frac{153 \cdot 12}{221 \cdot 12} - \frac{5 \cdot 221}{12 \cdot 221} - (\frac{7}{442} \cdot \frac{6}{6})$

Step 2.8

Multiply $\frac{7}{442}$ by $\frac{6}{6}$ .

$\frac{57 \cdot 156}{17 \cdot 156} - \frac{153 \cdot 12}{221 \cdot 12} - \frac{5 \cdot 221}{12 \cdot 221} - \frac{7 \cdot 6}{442 \cdot 6}$

Step 2.9

Multiply $17$ by $156$ .

$\frac{57 \cdot 156}{2652} - \frac{153 \cdot 12}{221 \cdot 12} - \frac{5 \cdot 221}{12 \cdot 221} - \frac{7 \cdot 6}{442 \cdot 6}$

Step 2.10

Reorder the factors of $221 \cdot 12$ .

$\frac{57 \cdot 156}{2652} - \frac{153 \cdot 12}{12 \cdot 221} - \frac{5 \cdot 221}{12 \cdot 221} - \frac{7 \cdot 6}{442 \cdot 6}$

Step 2.11

Multiply $12$ by $221$ .

$\frac{57 \cdot 156}{2652} - \frac{153 \cdot 12}{2652} - \frac{5 \cdot 221}{12 \cdot 221} - \frac{7 \cdot 6}{442 \cdot 6}$

Step 2.12

Multiply $12$ by $221$ .

$\frac{57 \cdot 156}{2652} - \frac{153 \cdot 12}{2652} - \frac{5 \cdot 221}{2652} - \frac{7 \cdot 6}{442 \cdot 6}$

Step 2.13

Reorder the factors of $442 \cdot 6$ .

$\frac{57 \cdot 156}{2652} - \frac{153 \cdot 12}{2652} - \frac{5 \cdot 221}{2652} - \frac{7 \cdot 6}{6 \cdot 442}$

Step 2.14

Multiply $6$ by $442$ .

$\frac{57 \cdot 156}{2652} - \frac{153 \cdot 12}{2652} - \frac{5 \cdot 221}{2652} - \frac{7 \cdot 6}{2652}$

Step 3

Combine the numerators over the common denominator.

$\frac{57 \cdot 156 - 153 \cdot 12 - 5 \cdot 221 - 7 \cdot 6}{2652}$

Step 4

Simplify each term.

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Step 4.1

Multiply $57$ by $156$ .

$\frac{8892 - 153 \cdot 12 - 5 \cdot 221 - 7 \cdot 6}{2652}$

Step 4.2

Multiply $- 153$ by $12$ .

$\frac{8892 - 1836 - 5 \cdot 221 - 7 \cdot 6}{2652}$

Step 4.3

Multiply $- 5$ by $221$ .

$\frac{8892 - 1836 - 1105 - 7 \cdot 6}{2652}$

Step 4.4

Multiply $- 7$ by $6$ .

$\frac{8892 - 1836 - 1105 - 42}{2652}$

Step 5

Simplify by subtracting numbers.

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Step 5.1

Subtract $1836$ from $8892$ .

$\frac{7056 - 1105 - 42}{2652}$

Step 5.2

Subtract $1105$ from $7056$ .

$\frac{5951 - 42}{2652}$

Step 5.3

Subtract $42$ from $5951$ .

$\frac{5909}{2652}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{5909}{2652}$

Decimal Form:

$2.22812971 \dots$

Mixed Number Form:

$2 \frac{605}{2652}$