Evaluate 5 1/9-1/12*2/3

$5 \frac{1}{9} - \frac{1}{12} \cdot \frac{2}{3}$

Step 1

Convert $5 \frac{1}{9}$ to an improper fraction.

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

$5 + \frac{1}{9} - \frac{1}{12} \cdot \frac{2}{3}$

Add $5$ and $\frac{1}{9}$ .

To write $5$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$5 \cdot \frac{9}{9} + \frac{1}{9} - \frac{1}{12} \cdot \frac{2}{3}$

Combine $5$ and $\frac{9}{9}$ .

$\frac{5 \cdot 9}{9} + \frac{1}{9} - \frac{1}{12} \cdot \frac{2}{3}$

Combine the numerators over the common denominator.

$\frac{5 \cdot 9 + 1}{9} - \frac{1}{12} \cdot \frac{2}{3}$

Simplify the numerator.

Multiply $5$ by $9$ .

$\frac{45 + 1}{9} - \frac{1}{12} \cdot \frac{2}{3}$

Add $45$ and $1$ .

$\frac{46}{9} - \frac{1}{12} \cdot \frac{2}{3}$

Step 2

Simplify each term.

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{12}$ into the numerator.

$\frac{46}{9} + \frac{- 1}{12} \cdot \frac{2}{3}$

Factor $2$ out of $12$ .

$\frac{46}{9} + \frac{- 1}{2 (6)} \cdot \frac{2}{3}$

Cancel the common factor.

$\frac{46}{9} + \frac{- 1}{2 \cdot 6} \cdot \frac{2}{3}$

Rewrite the expression.

$\frac{46}{9} + \frac{- 1}{6} \cdot \frac{1}{3}$

Multiply $\frac{- 1}{6}$ by $\frac{1}{3}$ .

$\frac{46}{9} + \frac{- 1}{6 \cdot 3}$

Multiply $6$ by $3$ .

$\frac{46}{9} + \frac{- 1}{18}$

Move the negative in front of the fraction.

$\frac{46}{9} - \frac{1}{18}$

Step 3

To write $\frac{46}{9}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{46}{9} \cdot \frac{2}{2} - \frac{1}{18}$

Step 4

Write each expression with a common denominator of $18$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{46}{9}$ by $\frac{2}{2}$ .

$\frac{46 \cdot 2}{9 \cdot 2} - \frac{1}{18}$

Multiply $9$ by $2$ .

$\frac{46 \cdot 2}{18} - \frac{1}{18}$

Step 5

Combine the numerators over the common denominator.

$\frac{46 \cdot 2 - 1}{18}$

Step 6

Simplify the numerator.

Multiply $46$ by $2$ .

$\frac{92 - 1}{18}$

Subtract $1$ from $92$ .

$\frac{91}{18}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{91}{18}$

Decimal Form:

$5.0\overline{5}$

Mixed Number Form:

$5 \frac{1}{18}$

Evaluate 5 1/9-1/12*2/3

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