Evaluate 5/34*22 2/3-2 1/9

$\frac{5}{34} \cdot 22 \frac{2}{3} - 2 \frac{1}{9}$

Step 1

Convert $22 \frac{2}{3}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$\frac{5}{34} \cdot (22 + \frac{2}{3}) - 2 \frac{1}{9}$

Add $22$ and $\frac{2}{3}$ .

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

$\frac{5}{34} \cdot (22 \cdot \frac{3}{3} + \frac{2}{3}) - 2 \frac{1}{9}$

Combine $22$ and $\frac{3}{3}$ .

$\frac{5}{34} \cdot (\frac{22 \cdot 3}{3} + \frac{2}{3}) - 2 \frac{1}{9}$

Combine the numerators over the common denominator.

$\frac{5}{34} \cdot \frac{22 \cdot 3 + 2}{3} - 2 \frac{1}{9}$

Simplify the numerator.

Multiply $22$ by $3$ .

$\frac{5}{34} \cdot \frac{66 + 2}{3} - 2 \frac{1}{9}$

Add $66$ and $2$ .

$\frac{5}{34} \cdot \frac{68}{3} - 2 \frac{1}{9}$

Step 2

Convert $2 \frac{1}{9}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$\frac{5}{34} \cdot \frac{68}{3} - (2 + \frac{1}{9})$

Add $2$ and $\frac{1}{9}$ .

To write $2$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{5}{34} \cdot \frac{68}{3} - (2 \cdot \frac{9}{9} + \frac{1}{9})$

Combine $2$ and $\frac{9}{9}$ .

$\frac{5}{34} \cdot \frac{68}{3} - (\frac{2 \cdot 9}{9} + \frac{1}{9})$

Combine the numerators over the common denominator.

$\frac{5}{34} \cdot \frac{68}{3} - \frac{2 \cdot 9 + 1}{9}$

Simplify the numerator.

Multiply $2$ by $9$ .

$\frac{5}{34} \cdot \frac{68}{3} - \frac{18 + 1}{9}$

Add $18$ and $1$ .

$\frac{5}{34} \cdot \frac{68}{3} - \frac{19}{9}$

Step 3

Simplify each term.

Cancel the common factor of $34$ .

Factor $34$ out of $68$ .

$\frac{5}{34} \cdot \frac{34 (2)}{3} - \frac{19}{9}$

Cancel the common factor.

$\frac{5}{34} \cdot \frac{34 \cdot 2}{3} - \frac{19}{9}$

Rewrite the expression.

$5 \cdot \frac{2}{3} - \frac{19}{9}$

Combine $5$ and $\frac{2}{3}$ .

$\frac{5 \cdot 2}{3} - \frac{19}{9}$

Multiply $5$ by $2$ .

$\frac{10}{3} - \frac{19}{9}$

Step 4

To write $\frac{10}{3}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{10}{3} \cdot \frac{3}{3} - \frac{19}{9}$

Step 5

Write each expression with a common denominator of $9$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{10}{3}$ by $\frac{3}{3}$ .

$\frac{10 \cdot 3}{3 \cdot 3} - \frac{19}{9}$

Multiply $3$ by $3$ .

$\frac{10 \cdot 3}{9} - \frac{19}{9}$

Step 6

Combine the numerators over the common denominator.

$\frac{10 \cdot 3 - 19}{9}$

Step 7

Simplify the numerator.

Multiply $10$ by $3$ .

$\frac{30 - 19}{9}$

Subtract $19$ from $30$ .

$\frac{11}{9}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{11}{9}$

Decimal Form:

$1.\overline{2}$

Mixed Number Form:

$1 \frac{2}{9}$

Evaluate 5/34*22 2/3-2 1/9

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