Solve 5 1/2 - [7 3/4 - \{3 2/3 + (1/2 - 2 3/5 - 1 1/2 * 3/4 * of * 20/33)\}]

Question

$$5\frac{1}{2}-[7\frac{3}{4}-\{3\frac{2}{3}+(\frac{1}{2}-2\frac{3}{5}-1\frac{1}{2}\times\frac{3}{4}of\frac{20}{33})\}]$$

Evaluate

$-\frac{15fo}{22}-\frac{41}{60}$

Solution Steps

Multiply $5$ and $2$ to get $10$.

$$\frac{10+1}{2}-\left(\frac{7\times 4+3}{4}-\left(\frac{3\times 3+2}{3}+\frac{1}{2}-\frac{2\times 5+3}{5}-\frac{1\times 2+1}{2}\times \frac{3}{4}of\times \frac{20}{33}\right)\right)$$

Add $10$ and $1$ to get $11$.

$$\frac{11}{2}-\left(\frac{7\times 4+3}{4}-\left(\frac{3\times 3+2}{3}+\frac{1}{2}-\frac{2\times 5+3}{5}-\frac{1\times 2+1}{2}\times \frac{3}{4}of\times \frac{20}{33}\right)\right)$$

Multiply $7$ and $4$ to get $28$.

$$\frac{11}{2}-\left(\frac{28+3}{4}-\left(\frac{3\times 3+2}{3}+\frac{1}{2}-\frac{2\times 5+3}{5}-\frac{1\times 2+1}{2}\times \frac{3}{4}of\times \frac{20}{33}\right)\right)$$

Add $28$ and $3$ to get $31$.

$$\frac{11}{2}-\left(\frac{31}{4}-\left(\frac{3\times 3+2}{3}+\frac{1}{2}-\frac{2\times 5+3}{5}-\frac{1\times 2+1}{2}\times \frac{3}{4}of\times \frac{20}{33}\right)\right)$$

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

$$\frac{11}{2}-\left(\frac{31}{4}-\left(\frac{9+2}{3}+\frac{1}{2}-\frac{2\times 5+3}{5}-\frac{1\times 2+1}{2}\times \frac{3}{4}of\times \frac{20}{33}\right)\right)$$

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

$$\frac{11}{2}-\left(\frac{31}{4}-\left(\frac{11}{3}+\frac{1}{2}-\frac{2\times 5+3}{5}-\frac{1\times 2+1}{2}\times \frac{3}{4}of\times \frac{20}{33}\right)\right)$$

Multiply $2$ and $5$ to get $10$.

$$\frac{11}{2}-\left(\frac{31}{4}-\left(\frac{11}{3}+\frac{1}{2}-\frac{10+3}{5}-\frac{1\times 2+1}{2}\times \frac{3}{4}of\times \frac{20}{33}\right)\right)$$

Add $10$ and $3$ to get $13$.

$$\frac{11}{2}-\left(\frac{31}{4}-\left(\frac{11}{3}+\frac{1}{2}-\frac{13}{5}-\frac{1\times 2+1}{2}\times \frac{3}{4}of\times \frac{20}{33}\right)\right)$$

Least common multiple of $2$ and $5$ is $10$. Convert $\frac{1}{2}$ and $\frac{13}{5}$ to fractions with denominator $10$.

$$\frac{11}{2}-\left(\frac{31}{4}-\left(\frac{11}{3}+\frac{5}{10}-\frac{26}{10}-\frac{1\times 2+1}{2}\times \frac{3}{4}of\times \frac{20}{33}\right)\right)$$

Since $\frac{5}{10}$ and $\frac{26}{10}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{11}{2}-\left(\frac{31}{4}-\left(\frac{11}{3}+\frac{5-26}{10}-\frac{1\times 2+1}{2}\times \frac{3}{4}of\times \frac{20}{33}\right)\right)$$

Subtract $26$ from $5$ to get $-21$.

$$\frac{11}{2}-\left(\frac{31}{4}-\left(\frac{11}{3}+-\frac{21}{10}-\frac{1\times 2+1}{2}\times \frac{3}{4}of\times \frac{20}{33}\right)\right)$$

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

$$\frac{11}{2}-\left(\frac{31}{4}-\left(\frac{11}{3}+-\frac{21}{10}-\frac{2+1}{2}\times \frac{3}{4}of\times \frac{20}{33}\right)\right)$$

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

$$\frac{11}{2}-\left(\frac{31}{4}-\left(\frac{11}{3}+-\frac{21}{10}-\frac{3}{2}\times \frac{3}{4}of\times \frac{20}{33}\right)\right)$$

Multiply $\frac{3}{2}$ times $\frac{3}{4}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{11}{2}-\left(\frac{31}{4}-\left(\frac{11}{3}+-\frac{21}{10}-\frac{3\times 3}{2\times 4}of\times \frac{20}{33}\right)\right)$$

Do the multiplications in the fraction $\frac{3\times 3}{2\times 4}$.

$$\frac{11}{2}-\left(\frac{31}{4}-\left(\frac{11}{3}+-\frac{21}{10}-\frac{9}{8}of\times \frac{20}{33}\right)\right)$$

Multiply $\frac{9}{8}$ times $\frac{20}{33}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{11}{2}-\left(\frac{31}{4}-\left(\frac{11}{3}+-\frac{21}{10}-\frac{9\times 20}{8\times 33}of\right)\right)$$

Do the multiplications in the fraction $\frac{9\times 20}{8\times 33}$.

$$\frac{11}{2}-\left(\frac{31}{4}-\left(\frac{11}{3}+-\frac{21}{10}-\frac{180}{264}of\right)\right)$$

Reduce the fraction $\frac{180}{264}$ to lowest terms by extracting and canceling out $12$.

$$\frac{11}{2}-\left(\frac{31}{4}-\left(\frac{11}{3}-\frac{21}{10}-\frac{15}{22}of\right)\right)$$

Least common multiple of $3$ and $10$ is $30$. Convert $\frac{11}{3}$ and $\frac{21}{10}$ to fractions with denominator $30$.

$$\frac{11}{2}-\left(\frac{31}{4}-\left(\frac{110}{30}-\frac{63}{30}-\frac{15}{22}of\right)\right)$$

Since $\frac{110}{30}$ and $\frac{63}{30}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{11}{2}-\left(\frac{31}{4}-\left(\frac{110-63}{30}-\frac{15}{22}of\right)\right)$$

Subtract $63$ from $110$ to get $47$.

$$\frac{11}{2}-\left(\frac{31}{4}-\left(\frac{47}{30}-\frac{15}{22}of\right)\right)$$

To find the opposite of $\frac{31}{4}-\left(\frac{47}{30}-\frac{15}{22}of\right)$, find the opposite of each term.

$$\frac{11}{2}-\frac{31}{4}-\left(-\left(\frac{47}{30}-\frac{15}{22}of\right)\right)$$

Least common multiple of $2$ and $4$ is $4$. Convert $\frac{11}{2}$ and $\frac{31}{4}$ to fractions with denominator $4$.

$$\frac{22}{4}-\frac{31}{4}-\left(-\left(\frac{47}{30}-\frac{15}{22}of\right)\right)$$

Since $\frac{22}{4}$ and $\frac{31}{4}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{22-31}{4}-\left(-\left(\frac{47}{30}-\frac{15}{22}of\right)\right)$$

Subtract $31$ from $22$ to get $-9$.

$$-\frac{9}{4}-\left(-\left(\frac{47}{30}-\frac{15}{22}of\right)\right)$$

The opposite of $-\left(\frac{47}{30}-\frac{15}{22}of\right)$ is $\frac{47}{30}-\frac{15}{22}of$.

$$-\frac{9}{4}+\frac{47}{30}-\frac{15}{22}of$$

Least common multiple of $4$ and $30$ is $60$. Convert $-\frac{9}{4}$ and $\frac{47}{30}$ to fractions with denominator $60$.

$$-\frac{135}{60}+\frac{94}{60}-\frac{15}{22}of$$

Since $-\frac{135}{60}$ and $\frac{94}{60}$ have the same denominator, add them by adding their numerators.

$$\frac{-135+94}{60}-\frac{15}{22}of$$

Add $-135$ and $94$ to get $-41$.

$$-\frac{41}{60}-\frac{15}{22}of$$

Show Solution

Expand