Evaluate (1/2-19/9+15/9)/(1/4+1/3+19/12)+3/9

$\frac{\frac{1}{2} - \frac{19}{9} + \frac{15}{9}}{\frac{1}{4} + \frac{1}{3} + \frac{19}{12}} + \frac{3}{9}$

Step 1

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{\frac{1}{2} \cdot \frac{9}{9} - \frac{19}{9} + \frac{15}{9}}{\frac{1}{4} + \frac{1}{3} + \frac{19}{12}} + \frac{3}{9}$

Step 2

To write $- \frac{19}{9}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{\frac{1}{2} \cdot \frac{9}{9} - \frac{19}{9} \cdot \frac{2}{2} + \frac{15}{9}}{\frac{1}{4} + \frac{1}{3} + \frac{19}{12}} + \frac{3}{9}$

Step 3

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

Multiply $\frac{1}{2}$ by $\frac{9}{9}$ .

$\frac{\frac{9}{2 \cdot 9} - \frac{19}{9} \cdot \frac{2}{2} + \frac{15}{9}}{\frac{1}{4} + \frac{1}{3} + \frac{19}{12}} + \frac{3}{9}$

Multiply $2$ by $9$ .

$\frac{\frac{9}{18} - \frac{19}{9} \cdot \frac{2}{2} + \frac{15}{9}}{\frac{1}{4} + \frac{1}{3} + \frac{19}{12}} + \frac{3}{9}$

Multiply $\frac{19}{9}$ by $\frac{2}{2}$ .

$\frac{\frac{9}{18} - \frac{19 \cdot 2}{9 \cdot 2} + \frac{15}{9}}{\frac{1}{4} + \frac{1}{3} + \frac{19}{12}} + \frac{3}{9}$

Multiply $9$ by $2$ .

$\frac{\frac{9}{18} - \frac{19 \cdot 2}{18} + \frac{15}{9}}{\frac{1}{4} + \frac{1}{3} + \frac{19}{12}} + \frac{3}{9}$

Step 4

Combine the numerators over the common denominator.

$\frac{\frac{9 - 19 \cdot 2}{18} + \frac{15}{9}}{\frac{1}{4} + \frac{1}{3} + \frac{19}{12}} + \frac{3}{9}$

Step 5

Simplify the numerator.

Multiply $- 19$ by $2$ .

$\frac{\frac{9 - 38}{18} + \frac{15}{9}}{\frac{1}{4} + \frac{1}{3} + \frac{19}{12}} + \frac{3}{9}$

Subtract $38$ from $9$ .

$\frac{\frac{- 29}{18} + \frac{15}{9}}{\frac{1}{4} + \frac{1}{3} + \frac{19}{12}} + \frac{3}{9}$

Step 6

To write $\frac{15}{9}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{\frac{- 29}{18} + \frac{15}{9} \cdot \frac{2}{2}}{\frac{1}{4} + \frac{1}{3} + \frac{19}{12}} + \frac{3}{9}$

Step 7

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

Multiply $\frac{15}{9}$ by $\frac{2}{2}$ .

$\frac{\frac{- 29}{18} + \frac{15 \cdot 2}{9 \cdot 2}}{\frac{1}{4} + \frac{1}{3} + \frac{19}{12}} + \frac{3}{9}$

Multiply $9$ by $2$ .

$\frac{\frac{- 29}{18} + \frac{15 \cdot 2}{18}}{\frac{1}{4} + \frac{1}{3} + \frac{19}{12}} + \frac{3}{9}$

Step 8

Combine the numerators over the common denominator.

$\frac{\frac{- 29 + 15 \cdot 2}{18}}{\frac{1}{4} + \frac{1}{3} + \frac{19}{12}} + \frac{3}{9}$

Step 9

Simplify the numerator.

Multiply $15$ by $2$ .

$\frac{\frac{- 29 + 30}{18}}{\frac{1}{4} + \frac{1}{3} + \frac{19}{12}} + \frac{3}{9}$

Add $- 29$ and $30$ .

$\frac{\frac{1}{18}}{\frac{1}{4} + \frac{1}{3} + \frac{19}{12}} + \frac{3}{9}$

Step 10

Simplify each term.

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{18} \cdot \frac{1}{\frac{1}{4} + \frac{1}{3} + \frac{19}{12}} + \frac{3}{9}$

Simplify the denominator.

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{1}{18} \cdot \frac{1}{\frac{1}{4} \cdot \frac{3}{3} + \frac{1}{3} + \frac{19}{12}} + \frac{3}{9}$

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{1}{18} \cdot \frac{1}{\frac{1}{4} \cdot \frac{3}{3} + \frac{1}{3} \cdot \frac{4}{4} + \frac{19}{12}} + \frac{3}{9}$

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{4}$ by $\frac{3}{3}$ .

$\frac{1}{18} \cdot \frac{1}{\frac{3}{4 \cdot 3} + \frac{1}{3} \cdot \frac{4}{4} + \frac{19}{12}} + \frac{3}{9}$

Multiply $4$ by $3$ .

$\frac{1}{18} \cdot \frac{1}{\frac{3}{12} + \frac{1}{3} \cdot \frac{4}{4} + \frac{19}{12}} + \frac{3}{9}$

Multiply $\frac{1}{3}$ by $\frac{4}{4}$ .

$\frac{1}{18} \cdot \frac{1}{\frac{3}{12} + \frac{4}{3 \cdot 4} + \frac{19}{12}} + \frac{3}{9}$

Multiply $3$ by $4$ .

$\frac{1}{18} \cdot \frac{1}{\frac{3}{12} + \frac{4}{12} + \frac{19}{12}} + \frac{3}{9}$

Combine the numerators over the common denominator.

$\frac{1}{18} \cdot \frac{1}{\frac{3 + 4}{12} + \frac{19}{12}} + \frac{3}{9}$

Add $3$ and $4$ .

$\frac{1}{18} \cdot \frac{1}{\frac{7}{12} + \frac{19}{12}} + \frac{3}{9}$

Combine the numerators over the common denominator.

$\frac{1}{18} \cdot \frac{1}{\frac{7 + 19}{12}} + \frac{3}{9}$

Add $7$ and $19$ .

$\frac{1}{18} \cdot \frac{1}{\frac{26}{12}} + \frac{3}{9}$

Cancel the common factor of $26$ and $12$ .

Factor $2$ out of $26$ .

$\frac{1}{18} \cdot \frac{1}{\frac{2 (13)}{12}} + \frac{3}{9}$

Cancel the common factors.

Factor $2$ out of $12$ .

$\frac{1}{18} \cdot \frac{1}{\frac{2 \cdot 13}{2 \cdot 6}} + \frac{3}{9}$

Cancel the common factor.

$\frac{1}{18} \cdot \frac{1}{\frac{2 \cdot 13}{2 \cdot 6}} + \frac{3}{9}$

Rewrite the expression.

$\frac{1}{18} \cdot \frac{1}{\frac{13}{6}} + \frac{3}{9}$

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{18} (1 (\frac{6}{13})) + \frac{3}{9}$

Multiply $\frac{6}{13}$ by $1$ .

$\frac{1}{18} \cdot \frac{6}{13} + \frac{3}{9}$

Cancel the common factor of $6$ .

Factor $6$ out of $18$ .

$\frac{1}{6 (3)} \cdot \frac{6}{13} + \frac{3}{9}$

Cancel the common factor.

$\frac{1}{6 \cdot 3} \cdot \frac{6}{13} + \frac{3}{9}$

Rewrite the expression.

$\frac{1}{3} \cdot \frac{1}{13} + \frac{3}{9}$

Multiply $\frac{1}{3}$ by $\frac{1}{13}$ .

$\frac{1}{3 \cdot 13} + \frac{3}{9}$

Multiply $3$ by $13$ .

$\frac{1}{39} + \frac{3}{9}$

Cancel the common factor of $3$ and $9$ .

Factor $3$ out of $3$ .

$\frac{1}{39} + \frac{3 (1)}{9}$

Cancel the common factors.

Factor $3$ out of $9$ .

$\frac{1}{39} + \frac{3 \cdot 1}{3 \cdot 3}$

Cancel the common factor.

$\frac{1}{39} + \frac{3 \cdot 1}{3 \cdot 3}$

Rewrite the expression.

$\frac{1}{39} + \frac{1}{3}$

Step 11

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{13}{13}$ .

$\frac{1}{39} + \frac{1}{3} \cdot \frac{13}{13}$

Step 12

Write each expression with a common denominator of $39$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{3}$ by $\frac{13}{13}$ .

$\frac{1}{39} + \frac{13}{3 \cdot 13}$

Multiply $3$ by $13$ .

$\frac{1}{39} + \frac{13}{39}$

Step 13

Combine the numerators over the common denominator.

$\frac{1 + 13}{39}$

Step 14

Add $1$ and $13$ .

$\frac{14}{39}$

Step 15

The result can be shown in multiple forms.

Exact Form:

$\frac{14}{39}$

Decimal Form:

$0.\overline{358974}$

Evaluate (1/2-19/9+15/9)/(1/4+1/3+19/12)+3/9

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