Solve 3 3 2 2 2 2 3 7 -3 1 2 *\ 18 2 /(3 2 3 - overline 2 5 6 -1 1 2 )\ ] 172

Question

$$2 \frac { 3 } { 7 } - 3 \frac { 1 } { 2 } \times \{ \frac { 18 } { 2 } \div ( 3 \frac { 2 } { 3 } - 2 \frac { 5 } { 6 } - 1 \frac { 1 } { 2 } ) \} ]$$

Evaluate

$\frac{1391}{28}\approx 49.678571429$

Solution Steps

Multiply $2$ and $7$ to get $14$.

$$\frac{14+3}{7}-\frac{3\times 2+1}{2}\times \frac{\frac{18}{2}}{\frac{3\times 3+2}{3}-\frac{2\times 6+5}{6}-\frac{1\times 2+1}{2}}$$

Add $14$ and $3$ to get $17$.

$$\frac{17}{7}-\frac{3\times 2+1}{2}\times \frac{\frac{18}{2}}{\frac{3\times 3+2}{3}-\frac{2\times 6+5}{6}-\frac{1\times 2+1}{2}}$$

Multiply $3$ and $2$ to get $6$.

$$\frac{17}{7}-\frac{6+1}{2}\times \frac{\frac{18}{2}}{\frac{3\times 3+2}{3}-\frac{2\times 6+5}{6}-\frac{1\times 2+1}{2}}$$

Add $6$ and $1$ to get $7$.

$$\frac{17}{7}-\frac{7}{2}\times \frac{\frac{18}{2}}{\frac{3\times 3+2}{3}-\frac{2\times 6+5}{6}-\frac{1\times 2+1}{2}}$$

Divide $18$ by $2$ to get $9$.

$$\frac{17}{7}-\frac{7}{2}\times \frac{9}{\frac{3\times 3+2}{3}-\frac{2\times 6+5}{6}-\frac{1\times 2+1}{2}}$$

Multiply $3$ and $3$ to get $9$.

$$\frac{17}{7}-\frac{7}{2}\times \frac{9}{\frac{9+2}{3}-\frac{2\times 6+5}{6}-\frac{1\times 2+1}{2}}$$

Add $9$ and $2$ to get $11$.

$$\frac{17}{7}-\frac{7}{2}\times \frac{9}{\frac{11}{3}-\frac{2\times 6+5}{6}-\frac{1\times 2+1}{2}}$$

Multiply $2$ and $6$ to get $12$.

$$\frac{17}{7}-\frac{7}{2}\times \frac{9}{\frac{11}{3}-\frac{12+5}{6}-\frac{1\times 2+1}{2}}$$

Add $12$ and $5$ to get $17$.

$$\frac{17}{7}-\frac{7}{2}\times \frac{9}{\frac{11}{3}-\frac{17}{6}-\frac{1\times 2+1}{2}}$$

Least common multiple of $3$ and $6$ is $6$. Convert $\frac{11}{3}$ and $\frac{17}{6}$ to fractions with denominator $6$.

$$\frac{17}{7}-\frac{7}{2}\times \frac{9}{\frac{22}{6}-\frac{17}{6}-\frac{1\times 2+1}{2}}$$

Since $\frac{22}{6}$ and $\frac{17}{6}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{17}{7}-\frac{7}{2}\times \frac{9}{\frac{22-17}{6}-\frac{1\times 2+1}{2}}$$

Subtract $17$ from $22$ to get $5$.

$$\frac{17}{7}-\frac{7}{2}\times \frac{9}{\frac{5}{6}-\frac{1\times 2+1}{2}}$$

Multiply $1$ and $2$ to get $2$.

$$\frac{17}{7}-\frac{7}{2}\times \frac{9}{\frac{5}{6}-\frac{2+1}{2}}$$

Add $2$ and $1$ to get $3$.

$$\frac{17}{7}-\frac{7}{2}\times \frac{9}{\frac{5}{6}-\frac{3}{2}}$$

Least common multiple of $6$ and $2$ is $6$. Convert $\frac{5}{6}$ and $\frac{3}{2}$ to fractions with denominator $6$.

$$\frac{17}{7}-\frac{7}{2}\times \frac{9}{\frac{5}{6}-\frac{9}{6}}$$

Since $\frac{5}{6}$ and $\frac{9}{6}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{17}{7}-\frac{7}{2}\times \frac{9}{\frac{5-9}{6}}$$

Subtract $9$ from $5$ to get $-4$.

$$\frac{17}{7}-\frac{7}{2}\times \frac{9}{\frac{-4}{6}}$$

Reduce the fraction $\frac{-4}{6}$ to lowest terms by extracting and canceling out $2$.

$$\frac{17}{7}-\frac{7}{2}\times \frac{9}{-\frac{2}{3}}$$

Divide $9$ by $-\frac{2}{3}$ by multiplying $9$ by the reciprocal of $-\frac{2}{3}$.

$$\frac{17}{7}-\frac{7}{2}\times 9\left(-\frac{3}{2}\right)$$

Express $9\left(-\frac{3}{2}\right)$ as a single fraction.

$$\frac{17}{7}-\frac{7}{2}\times \frac{9\left(-3\right)}{2}$$

Multiply $9$ and $-3$ to get $-27$.

$$\frac{17}{7}-\frac{7}{2}\times \frac{-27}{2}$$

Fraction $\frac{-27}{2}$ can be rewritten as $-\frac{27}{2}$ by extracting the negative sign.

$$\frac{17}{7}-\frac{7}{2}\left(-\frac{27}{2}\right)$$

Multiply $\frac{7}{2}$ times $-\frac{27}{2}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{17}{7}-\frac{7\left(-27\right)}{2\times 2}$$

Do the multiplications in the fraction $\frac{7\left(-27\right)}{2\times 2}$.

$$\frac{17}{7}-\frac{-189}{4}$$

Fraction $\frac{-189}{4}$ can be rewritten as $-\frac{189}{4}$ by extracting the negative sign.

$$\frac{17}{7}-\left(-\frac{189}{4}\right)$$

The opposite of $-\frac{189}{4}$ is $\frac{189}{4}$.

$$\frac{17}{7}+\frac{189}{4}$$

Least common multiple of $7$ and $4$ is $28$. Convert $\frac{17}{7}$ and $\frac{189}{4}$ to fractions with denominator $28$.

$$\frac{68}{28}+\frac{1323}{28}$$

Since $\frac{68}{28}$ and $\frac{1323}{28}$ have the same denominator, add them by adding their numerators.

$$\frac{68+1323}{28}$$

Add $68$ and $1323$ to get $1391$.

$$\frac{1391}{28}$$

Show Solution

Factor

$\frac{13 \cdot 107}{2 ^ {2} \cdot 7} = 49\frac{19}{28} = 49.67857142857143$

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