Solve 1 7/53 * of[1 1/5 - \{(3 4/5) / (1/2 + 1/3)\} * 3 3/4]

Question

$$1\frac{7}{53}of[1\frac{1}{5}-\{3\frac{4}{5}\div(\frac{1}{2}+\frac{1}{3})\}\times3\frac{3}{4}]$$

Evaluate

$-18fo$

Solution Steps

Multiply $1$ and $53$ to get $53$.

$$\frac{53+7}{53}of\left(\frac{1\times 5+1}{5}-\frac{\frac{3\times 5+4}{5}}{\frac{1}{2}+\frac{1}{3}}\times \frac{3\times 4+3}{4}\right)$$

Add $53$ and $7$ to get $60$.

$$\frac{60}{53}of\left(\frac{1\times 5+1}{5}-\frac{\frac{3\times 5+4}{5}}{\frac{1}{2}+\frac{1}{3}}\times \frac{3\times 4+3}{4}\right)$$

Multiply $1$ and $5$ to get $5$.

$$\frac{60}{53}of\left(\frac{5+1}{5}-\frac{\frac{3\times 5+4}{5}}{\frac{1}{2}+\frac{1}{3}}\times \frac{3\times 4+3}{4}\right)$$

Add $5$ and $1$ to get $6$.

$$\frac{60}{53}of\left(\frac{6}{5}-\frac{\frac{3\times 5+4}{5}}{\frac{1}{2}+\frac{1}{3}}\times \frac{3\times 4+3}{4}\right)$$

Multiply $3$ and $5$ to get $15$.

$$\frac{60}{53}of\left(\frac{6}{5}-\frac{\frac{15+4}{5}}{\frac{1}{2}+\frac{1}{3}}\times \frac{3\times 4+3}{4}\right)$$

Add $15$ and $4$ to get $19$.

$$\frac{60}{53}of\left(\frac{6}{5}-\frac{\frac{19}{5}}{\frac{1}{2}+\frac{1}{3}}\times \frac{3\times 4+3}{4}\right)$$

Least common multiple of $2$ and $3$ is $6$. Convert $\frac{1}{2}$ and $\frac{1}{3}$ to fractions with denominator $6$.

$$\frac{60}{53}of\left(\frac{6}{5}-\frac{\frac{19}{5}}{\frac{3}{6}+\frac{2}{6}}\times \frac{3\times 4+3}{4}\right)$$

Since $\frac{3}{6}$ and $\frac{2}{6}$ have the same denominator, add them by adding their numerators.

$$\frac{60}{53}of\left(\frac{6}{5}-\frac{\frac{19}{5}}{\frac{3+2}{6}}\times \frac{3\times 4+3}{4}\right)$$

Add $3$ and $2$ to get $5$.

$$\frac{60}{53}of\left(\frac{6}{5}-\frac{\frac{19}{5}}{\frac{5}{6}}\times \frac{3\times 4+3}{4}\right)$$

Divide $\frac{19}{5}$ by $\frac{5}{6}$ by multiplying $\frac{19}{5}$ by the reciprocal of $\frac{5}{6}$.

$$\frac{60}{53}of\left(\frac{6}{5}-\frac{19}{5}\times \frac{6}{5}\times \frac{3\times 4+3}{4}\right)$$

Multiply $\frac{19}{5}$ times $\frac{6}{5}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{60}{53}of\left(\frac{6}{5}-\frac{19\times 6}{5\times 5}\times \frac{3\times 4+3}{4}\right)$$

Do the multiplications in the fraction $\frac{19\times 6}{5\times 5}$.

$$\frac{60}{53}of\left(\frac{6}{5}-\frac{114}{25}\times \frac{3\times 4+3}{4}\right)$$

Multiply $3$ and $4$ to get $12$.

$$\frac{60}{53}of\left(\frac{6}{5}-\frac{114}{25}\times \frac{12+3}{4}\right)$$

Add $12$ and $3$ to get $15$.

$$\frac{60}{53}of\left(\frac{6}{5}-\frac{114}{25}\times \frac{15}{4}\right)$$

Multiply $\frac{114}{25}$ times $\frac{15}{4}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{60}{53}of\left(\frac{6}{5}-\frac{114\times 15}{25\times 4}\right)$$

Do the multiplications in the fraction $\frac{114\times 15}{25\times 4}$.

$$\frac{60}{53}of\left(\frac{6}{5}-\frac{1710}{100}\right)$$

Reduce the fraction $\frac{1710}{100}$ to lowest terms by extracting and canceling out $10$.

$$\frac{60}{53}of\left(\frac{6}{5}-\frac{171}{10}\right)$$

Least common multiple of $5$ and $10$ is $10$. Convert $\frac{6}{5}$ and $\frac{171}{10}$ to fractions with denominator $10$.

$$\frac{60}{53}of\left(\frac{12}{10}-\frac{171}{10}\right)$$

Since $\frac{12}{10}$ and $\frac{171}{10}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{60}{53}of\times \frac{12-171}{10}$$

Subtract $171$ from $12$ to get $-159$.

$$\frac{60}{53}of\left(-\frac{159}{10}\right)$$

Multiply $\frac{60}{53}$ times $-\frac{159}{10}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{60\left(-159\right)}{53\times 10}of$$

Do the multiplications in the fraction $\frac{60\left(-159\right)}{53\times 10}$.

$$\frac{-9540}{530}of$$

Divide $-9540$ by $530$ to get $-18$.

$$-18of$$

Show Solution

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$-18fo$

Solution Steps

Multiply $1$ and $53$ to get $53$.

$$\frac{53+7}{53}of\left(\frac{1\times 5+1}{5}-\frac{\frac{3\times 5+4}{5}}{\frac{1}{2}+\frac{1}{3}}\times \frac{3\times 4+3}{4}\right)$$

Add $53$ and $7$ to get $60$.

$$\frac{60}{53}of\left(\frac{1\times 5+1}{5}-\frac{\frac{3\times 5+4}{5}}{\frac{1}{2}+\frac{1}{3}}\times \frac{3\times 4+3}{4}\right)$$

Multiply $1$ and $5$ to get $5$.

$$\frac{60}{53}of\left(\frac{5+1}{5}-\frac{\frac{3\times 5+4}{5}}{\frac{1}{2}+\frac{1}{3}}\times \frac{3\times 4+3}{4}\right)$$

Add $5$ and $1$ to get $6$.

$$\frac{60}{53}of\left(\frac{6}{5}-\frac{\frac{3\times 5+4}{5}}{\frac{1}{2}+\frac{1}{3}}\times \frac{3\times 4+3}{4}\right)$$

Multiply $3$ and $5$ to get $15$.

$$\frac{60}{53}of\left(\frac{6}{5}-\frac{\frac{15+4}{5}}{\frac{1}{2}+\frac{1}{3}}\times \frac{3\times 4+3}{4}\right)$$

Add $15$ and $4$ to get $19$.

$$\frac{60}{53}of\left(\frac{6}{5}-\frac{\frac{19}{5}}{\frac{1}{2}+\frac{1}{3}}\times \frac{3\times 4+3}{4}\right)$$

Least common multiple of $2$ and $3$ is $6$. Convert $\frac{1}{2}$ and $\frac{1}{3}$ to fractions with denominator $6$.

$$\frac{60}{53}of\left(\frac{6}{5}-\frac{\frac{19}{5}}{\frac{3}{6}+\frac{2}{6}}\times \frac{3\times 4+3}{4}\right)$$

Since $\frac{3}{6}$ and $\frac{2}{6}$ have the same denominator, add them by adding their numerators.

$$\frac{60}{53}of\left(\frac{6}{5}-\frac{\frac{19}{5}}{\frac{3+2}{6}}\times \frac{3\times 4+3}{4}\right)$$

Add $3$ and $2$ to get $5$.

$$\frac{60}{53}of\left(\frac{6}{5}-\frac{\frac{19}{5}}{\frac{5}{6}}\times \frac{3\times 4+3}{4}\right)$$

Divide $\frac{19}{5}$ by $\frac{5}{6}$ by multiplying $\frac{19}{5}$ by the reciprocal of $\frac{5}{6}$.

$$\frac{60}{53}of\left(\frac{6}{5}-\frac{19}{5}\times \frac{6}{5}\times \frac{3\times 4+3}{4}\right)$$

Multiply $\frac{19}{5}$ times $\frac{6}{5}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{60}{53}of\left(\frac{6}{5}-\frac{19\times 6}{5\times 5}\times \frac{3\times 4+3}{4}\right)$$

Do the multiplications in the fraction $\frac{19\times 6}{5\times 5}$.

$$\frac{60}{53}of\left(\frac{6}{5}-\frac{114}{25}\times \frac{3\times 4+3}{4}\right)$$

Multiply $3$ and $4$ to get $12$.

$$\frac{60}{53}of\left(\frac{6}{5}-\frac{114}{25}\times \frac{12+3}{4}\right)$$

Add $12$ and $3$ to get $15$.

$$\frac{60}{53}of\left(\frac{6}{5}-\frac{114}{25}\times \frac{15}{4}\right)$$

Multiply $\frac{114}{25}$ times $\frac{15}{4}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{60}{53}of\left(\frac{6}{5}-\frac{114\times 15}{25\times 4}\right)$$

Do the multiplications in the fraction $\frac{114\times 15}{25\times 4}$.

$$\frac{60}{53}of\left(\frac{6}{5}-\frac{1710}{100}\right)$$

Reduce the fraction $\frac{1710}{100}$ to lowest terms by extracting and canceling out $10$.

$$\frac{60}{53}of\left(\frac{6}{5}-\frac{171}{10}\right)$$

Least common multiple of $5$ and $10$ is $10$. Convert $\frac{6}{5}$ and $\frac{171}{10}$ to fractions with denominator $10$.

$$\frac{60}{53}of\left(\frac{12}{10}-\frac{171}{10}\right)$$

Since $\frac{12}{10}$ and $\frac{171}{10}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{60}{53}of\times \frac{12-171}{10}$$

Subtract $171$ from $12$ to get $-159$.

$$\frac{60}{53}of\left(-\frac{159}{10}\right)$$

Multiply $\frac{60}{53}$ times $-\frac{159}{10}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{60\left(-159\right)}{53\times 10}of$$

Do the multiplications in the fraction $\frac{60\left(-159\right)}{53\times 10}$.

$$\frac{-9540}{530}of$$

Divide $-9540$ by $530$ to get $-18$.

$$-18of$$

Show Solution

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