Basic Math Examples

$(\frac{7}{12} \div \frac{21}{5}) - (\frac{7}{12} \cdot \frac{21}{5})$

Step 1

Simplify each term.

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Step 1.1

To divide by a fraction, multiply by its reciprocal.

$\frac{7}{12} \cdot \frac{5}{21} - (\frac{7}{12} \cdot \frac{21}{5})$

Step 1.2

Cancel the common factor of $7$ .

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Step 1.2.1

Factor $7$ out of $21$ .

$\frac{7}{12} \cdot \frac{5}{7 (3)} - (\frac{7}{12} \cdot \frac{21}{5})$

Step 1.2.2

Cancel the common factor.

$\frac{7}{12} \cdot \frac{5}{7 \cdot 3} - (\frac{7}{12} \cdot \frac{21}{5})$

Step 1.2.3

Rewrite the expression.

$\frac{1}{12} \cdot \frac{5}{3} - (\frac{7}{12} \cdot \frac{21}{5})$

Step 1.3

Multiply $\frac{1}{12}$ by $\frac{5}{3}$ .

$\frac{5}{12 \cdot 3} - (\frac{7}{12} \cdot \frac{21}{5})$

Step 1.4

Multiply $12$ by $3$ .

$\frac{5}{36} - (\frac{7}{12} \cdot \frac{21}{5})$

Step 1.5

Cancel the common factor of $3$ .

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Step 1.5.1

Factor $3$ out of $12$ .

$\frac{5}{36} - (\frac{7}{3 (4)} \cdot \frac{21}{5})$

Step 1.5.2

Factor $3$ out of $21$ .

$\frac{5}{36} - (\frac{7}{3 \cdot 4} \cdot \frac{3 \cdot 7}{5})$

Step 1.5.3

Cancel the common factor.

$\frac{5}{36} - (\frac{7}{3 \cdot 4} \cdot \frac{3 \cdot 7}{5})$

Step 1.5.4

Rewrite the expression.

$\frac{5}{36} - (\frac{7}{4} \cdot \frac{7}{5})$

Step 1.6

Multiply $\frac{7}{4}$ by $\frac{7}{5}$ .

$\frac{5}{36} - \frac{7 \cdot 7}{4 \cdot 5}$

Step 1.7

Multiply $7$ by $7$ .

$\frac{5}{36} - \frac{49}{4 \cdot 5}$

Step 1.8

Multiply $4$ by $5$ .

$\frac{5}{36} - \frac{49}{20}$

Step 2

To write $\frac{5}{36}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{5}{36} \cdot \frac{5}{5} - \frac{49}{20}$

Step 3

To write $- \frac{49}{20}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{5}{36} \cdot \frac{5}{5} - \frac{49}{20} \cdot \frac{9}{9}$

Step 4

Write each expression with a common denominator of $180$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{5}{36}$ by $\frac{5}{5}$ .

$\frac{5 \cdot 5}{36 \cdot 5} - \frac{49}{20} \cdot \frac{9}{9}$

Step 4.2

Multiply $36$ by $5$ .

$\frac{5 \cdot 5}{180} - \frac{49}{20} \cdot \frac{9}{9}$

Step 4.3

Multiply $\frac{49}{20}$ by $\frac{9}{9}$ .

$\frac{5 \cdot 5}{180} - \frac{49 \cdot 9}{20 \cdot 9}$

Step 4.4

Multiply $20$ by $9$ .

$\frac{5 \cdot 5}{180} - \frac{49 \cdot 9}{180}$

Step 5

Combine the numerators over the common denominator.

$\frac{5 \cdot 5 - 49 \cdot 9}{180}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $5$ by $5$ .

$\frac{25 - 49 \cdot 9}{180}$

Step 6.2

Multiply $- 49$ by $9$ .

$\frac{25 - 441}{180}$

Step 6.3

Subtract $441$ from $25$ .

$\frac{- 416}{180}$

Step 7

Cancel the common factor of $- 416$ and $180$ .

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Step 7.1

Factor $4$ out of $- 416$ .

$\frac{4 (- 104)}{180}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $4$ out of $180$ .

$\frac{4 \cdot - 104}{4 \cdot 45}$

Step 7.2.2

Cancel the common factor.

$\frac{4 \cdot - 104}{4 \cdot 45}$

Step 7.2.3

Rewrite the expression.

$\frac{- 104}{45}$

Step 8

Move the negative in front of the fraction.

$- \frac{104}{45}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$- \frac{104}{45}$

Decimal Form:

$- 2.3\overline{1}$

Mixed Number Form:

$- 2 \frac{14}{45}$