Evaluate ((7/6)÷(14/5))-(7/6*14/5)

$(\frac{7}{6} \div \frac{14}{5}) - (\frac{7}{6} \cdot \frac{14}{5})$

Step 1

Simplify each term.

To divide by a fraction, multiply by its reciprocal.

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

Cancel the common factor of $7$ .

Factor $7$ out of $14$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $\frac{1}{6}$ by $\frac{5}{2}$ .

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

Multiply $6$ by $2$ .

$\frac{5}{12} - (\frac{7}{6} \cdot \frac{14}{5})$

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$\frac{5}{12} - (\frac{7}{2 (3)} \cdot \frac{14}{5})$

Factor $2$ out of $14$ .

$\frac{5}{12} - (\frac{7}{2 \cdot 3} \cdot \frac{2 \cdot 7}{5})$

Cancel the common factor.

$\frac{5}{12} - (\frac{7}{2 \cdot 3} \cdot \frac{2 \cdot 7}{5})$

Rewrite the expression.

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

Multiply $\frac{7}{3}$ by $\frac{7}{5}$ .

$\frac{5}{12} - \frac{7 \cdot 7}{3 \cdot 5}$

Multiply $7$ by $7$ .

$\frac{5}{12} - \frac{49}{3 \cdot 5}$

Multiply $3$ by $5$ .

$\frac{5}{12} - \frac{49}{15}$

Step 2

To write $\frac{5}{12}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{5}{12} \cdot \frac{5}{5} - \frac{49}{15}$

Step 3

To write $- \frac{49}{15}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{5}{12} \cdot \frac{5}{5} - \frac{49}{15} \cdot \frac{4}{4}$

Step 4

Write each expression with a common denominator of $60$ , by multiplying each by an appropriate factor of $1$ .

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

$\frac{5 \cdot 5}{12 \cdot 5} - \frac{49}{15} \cdot \frac{4}{4}$

Multiply $12$ by $5$ .

$\frac{5 \cdot 5}{60} - \frac{49}{15} \cdot \frac{4}{4}$

Multiply $\frac{49}{15}$ by $\frac{4}{4}$ .

$\frac{5 \cdot 5}{60} - \frac{49 \cdot 4}{15 \cdot 4}$

Multiply $15$ by $4$ .

$\frac{5 \cdot 5}{60} - \frac{49 \cdot 4}{60}$

Step 5

Combine the numerators over the common denominator.

$\frac{5 \cdot 5 - 49 \cdot 4}{60}$

Step 6

Simplify the numerator.

Multiply $5$ by $5$ .

$\frac{25 - 49 \cdot 4}{60}$

Multiply $- 49$ by $4$ .

$\frac{25 - 196}{60}$

Subtract $196$ from $25$ .

$\frac{- 171}{60}$

Step 7

Cancel the common factor of $- 171$ and $60$ .

Factor $3$ out of $- 171$ .

$\frac{3 (- 57)}{60}$

Cancel the common factors.

Factor $3$ out of $60$ .

$\frac{3 \cdot - 57}{3 \cdot 20}$

Cancel the common factor.

$\frac{3 \cdot - 57}{3 \cdot 20}$

Rewrite the expression.

$\frac{- 57}{20}$

Step 8

Move the negative in front of the fraction.

$- \frac{57}{20}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$- \frac{57}{20}$

Decimal Form:

$- 2.85$

Mixed Number Form:

$- 2 \frac{17}{20}$

Evaluate ((7/6)÷(14/5))-(7/6*14/5)

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