Basic Math Examples

$\frac{\frac{11}{15} - \frac{7}{5}}{\frac{4}{11}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$(\frac{11}{15} - \frac{7}{5}) \frac{11}{4}$

Step 2

To write $- \frac{7}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$(\frac{11}{15} - \frac{7}{5} \cdot \frac{3}{3}) \frac{11}{4}$

Step 3

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

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

$(\frac{11}{15} - \frac{7 \cdot 3}{5 \cdot 3}) \frac{11}{4}$

Step 3.2

Multiply $5$ by $3$ .

$(\frac{11}{15} - \frac{7 \cdot 3}{15}) \frac{11}{4}$

Step 4

Combine the numerators over the common denominator.

$\frac{11 - 7 \cdot 3}{15} \cdot \frac{11}{4}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $- 7$ by $3$ .

$\frac{11 - 21}{15} \cdot \frac{11}{4}$

Step 5.2

Subtract $21$ from $11$ .

$\frac{- 10}{15} \cdot \frac{11}{4}$

Step 6

Cancel the common factor of $2$ .

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Step 6.1

Factor $2$ out of $- 10$ .

$\frac{2 (- 5)}{15} \cdot \frac{11}{4}$

Step 6.2

Factor $2$ out of $4$ .

$\frac{2 \cdot - 5}{15} \cdot \frac{11}{2 \cdot 2}$

Step 6.3

Cancel the common factor.

$\frac{2 \cdot - 5}{15} \cdot \frac{11}{2 \cdot 2}$

Step 6.4

Rewrite the expression.

$\frac{- 5}{15} \cdot \frac{11}{2}$

Step 7

Multiply $\frac{- 5}{15}$ by $\frac{11}{2}$ .

$\frac{- 5 \cdot 11}{15 \cdot 2}$

Step 8

Multiply.

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Step 8.1

Multiply $- 5$ by $11$ .

$\frac{- 55}{15 \cdot 2}$

Step 8.2

Multiply $15$ by $2$ .

$\frac{- 55}{30}$

Step 9

Cancel the common factor of $- 55$ and $30$ .

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Step 9.1

Factor $5$ out of $- 55$ .

$\frac{5 (- 11)}{30}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $5$ out of $30$ .

$\frac{5 \cdot - 11}{5 \cdot 6}$

Step 9.2.2

Cancel the common factor.

$\frac{5 \cdot - 11}{5 \cdot 6}$

Step 9.2.3

Rewrite the expression.

$\frac{- 11}{6}$

Step 10

Move the negative in front of the fraction.

$- \frac{11}{6}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$- \frac{11}{6}$

Decimal Form:

$- 1.8\overline{3}$

Mixed Number Form:

$- 1 \frac{5}{6}$