Evaluate 3/11-5/7

$\frac{3}{11} - \frac{5}{7}$

Step 1

To write $\frac{3}{11}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{3}{11} \cdot \frac{7}{7} - \frac{5}{7}$

Step 2

To write $- \frac{5}{7}$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$\frac{3}{11} \cdot \frac{7}{7} - \frac{5}{7} \cdot \frac{11}{11}$

Step 3

Write each expression with a common denominator of $77$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3}{11}$ by $\frac{7}{7}$ .

$\frac{3 \cdot 7}{11 \cdot 7} - \frac{5}{7} \cdot \frac{11}{11}$

Multiply $11$ by $7$ .

$\frac{3 \cdot 7}{77} - \frac{5}{7} \cdot \frac{11}{11}$

Multiply $\frac{5}{7}$ by $\frac{11}{11}$ .

$\frac{3 \cdot 7}{77} - \frac{5 \cdot 11}{7 \cdot 11}$

Multiply $7$ by $11$ .

$\frac{3 \cdot 7}{77} - \frac{5 \cdot 11}{77}$

Step 4

Combine the numerators over the common denominator.

$\frac{3 \cdot 7 - 5 \cdot 11}{77}$

Step 5

Simplify the numerator.

Multiply $3$ by $7$ .

$\frac{21 - 5 \cdot 11}{77}$

Multiply $- 5$ by $11$ .

$\frac{21 - 55}{77}$

Subtract $55$ from $21$ .

$\frac{- 34}{77}$

Step 6

Move the negative in front of the fraction.

$- \frac{34}{77}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{34}{77}$

Decimal Form:

$- 0.\overline{441558}$