Evaluate (22/7-2/3)÷2

$(\frac{22}{7} - \frac{2}{3}) \div 2$

Step 1

Rewrite the division as a fraction.

$\frac{\frac{22}{7} - \frac{2}{3}}{2}$

Step 2

Simplify the numerator.

To write $\frac{22}{7}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{\frac{22}{7} \cdot \frac{3}{3} - \frac{2}{3}}{2}$

To write $- \frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{\frac{22}{7} \cdot \frac{3}{3} - \frac{2}{3} \cdot \frac{7}{7}}{2}$

Write each expression with a common denominator of $21$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{22}{7}$ by $\frac{3}{3}$ .

$\frac{\frac{22 \cdot 3}{7 \cdot 3} - \frac{2}{3} \cdot \frac{7}{7}}{2}$

Multiply $7$ by $3$ .

$\frac{\frac{22 \cdot 3}{21} - \frac{2}{3} \cdot \frac{7}{7}}{2}$

Multiply $\frac{2}{3}$ by $\frac{7}{7}$ .

$\frac{\frac{22 \cdot 3}{21} - \frac{2 \cdot 7}{3 \cdot 7}}{2}$

Multiply $3$ by $7$ .

$\frac{\frac{22 \cdot 3}{21} - \frac{2 \cdot 7}{21}}{2}$

Combine the numerators over the common denominator.

$\frac{\frac{22 \cdot 3 - 2 \cdot 7}{21}}{2}$

Simplify the numerator.

Multiply $22$ by $3$ .

$\frac{\frac{66 - 2 \cdot 7}{21}}{2}$

Multiply $- 2$ by $7$ .

$\frac{\frac{66 - 14}{21}}{2}$

Subtract $14$ from $66$ .

$\frac{\frac{52}{21}}{2}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{52}{21} \cdot \frac{1}{2}$

Step 4

Cancel the common factor of $2$ .

Factor $2$ out of $52$ .

$\frac{2 (26)}{21} \cdot \frac{1}{2}$

Cancel the common factor.

$\frac{2 \cdot 26}{21} \cdot \frac{1}{2}$

Rewrite the expression.

$\frac{26}{21}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{26}{21}$

Decimal Form:

$1.\overline{238095}$

Mixed Number Form:

$1 \frac{5}{21}$

Evaluate (22/7-2/3)÷2

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