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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$[ ( 5 + 9 \div 3 \div 6 \div 4 ) ( \frac { 3 } { 4 } \div \frac { 1 } { 9 } + 3 + \frac { 1 } { 5 } ) - [ \frac { 7 - 9 } { 3 } ] 5 ]$$

Evaluate

$\frac{26077}{480}\approx 54.327083333$

Solution Steps

Express $\frac{\frac{\frac{9}{3}}{6}}{4}$ as a single fraction.

$$\left(5+\frac{\frac{9}{3}}{6\times 4}\right)\left(\frac{\frac{3}{4}}{\frac{1}{9}}+3+\frac{1}{5}\right)-\frac{7-9}{3}\times 5$$

Divide $9$ by $3$ to get $3$.

$$\left(5+\frac{3}{6\times 4}\right)\left(\frac{\frac{3}{4}}{\frac{1}{9}}+3+\frac{1}{5}\right)-\frac{7-9}{3}\times 5$$

Multiply $6$ and $4$ to get $24$.

$$\left(5+\frac{3}{24}\right)\left(\frac{\frac{3}{4}}{\frac{1}{9}}+3+\frac{1}{5}\right)-\frac{7-9}{3}\times 5$$

Reduce the fraction $\frac{3}{24}$ to lowest terms by extracting and canceling out $3$.

$$\left(5+\frac{1}{8}\right)\left(\frac{\frac{3}{4}}{\frac{1}{9}}+3+\frac{1}{5}\right)-\frac{7-9}{3}\times 5$$

Convert $5$ to fraction $\frac{40}{8}$.

$$\left(\frac{40}{8}+\frac{1}{8}\right)\left(\frac{\frac{3}{4}}{\frac{1}{9}}+3+\frac{1}{5}\right)-\frac{7-9}{3}\times 5$$

Since $\frac{40}{8}$ and $\frac{1}{8}$ have the same denominator, add them by adding their numerators.

$$\frac{40+1}{8}\left(\frac{\frac{3}{4}}{\frac{1}{9}}+3+\frac{1}{5}\right)-\frac{7-9}{3}\times 5$$

Add $40$ and $1$ to get $41$.

$$\frac{41}{8}\left(\frac{\frac{3}{4}}{\frac{1}{9}}+3+\frac{1}{5}\right)-\frac{7-9}{3}\times 5$$

Divide $\frac{3}{4}$ by $\frac{1}{9}$ by multiplying $\frac{3}{4}$ by the reciprocal of $\frac{1}{9}$.

$$\frac{41}{8}\left(\frac{3}{4}\times 9+3+\frac{1}{5}\right)-\frac{7-9}{3}\times 5$$

Express $\frac{3}{4}\times 9$ as a single fraction.

$$\frac{41}{8}\left(\frac{3\times 9}{4}+3+\frac{1}{5}\right)-\frac{7-9}{3}\times 5$$

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

$$\frac{41}{8}\left(\frac{27}{4}+3+\frac{1}{5}\right)-\frac{7-9}{3}\times 5$$

Convert $3$ to fraction $\frac{12}{4}$.

$$\frac{41}{8}\left(\frac{27}{4}+\frac{12}{4}+\frac{1}{5}\right)-\frac{7-9}{3}\times 5$$

Since $\frac{27}{4}$ and $\frac{12}{4}$ have the same denominator, add them by adding their numerators.

$$\frac{41}{8}\left(\frac{27+12}{4}+\frac{1}{5}\right)-\frac{7-9}{3}\times 5$$

Add $27$ and $12$ to get $39$.

$$\frac{41}{8}\left(\frac{39}{4}+\frac{1}{5}\right)-\frac{7-9}{3}\times 5$$

Least common multiple of $4$ and $5$ is $20$. Convert $\frac{39}{4}$ and $\frac{1}{5}$ to fractions with denominator $20$.

$$\frac{41}{8}\left(\frac{195}{20}+\frac{4}{20}\right)-\frac{7-9}{3}\times 5$$

Since $\frac{195}{20}$ and $\frac{4}{20}$ have the same denominator, add them by adding their numerators.

$$\frac{41}{8}\times \frac{195+4}{20}-\frac{7-9}{3}\times 5$$

Add $195$ and $4$ to get $199$.

$$\frac{41}{8}\times \frac{199}{20}-\frac{7-9}{3}\times 5$$

Multiply $\frac{41}{8}$ times $\frac{199}{20}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{41\times 199}{8\times 20}-\frac{7-9}{3}\times 5$$

Do the multiplications in the fraction $\frac{41\times 199}{8\times 20}$.

$$\frac{8159}{160}-\frac{7-9}{3}\times 5$$

Subtract $9$ from $7$ to get $-2$.

$$\frac{8159}{160}-\frac{-2}{3}\times 5$$

Fraction $\frac{-2}{3}$ can be rewritten as $-\frac{2}{3}$ by extracting the negative sign.

$$\frac{8159}{160}-\left(-\frac{2}{3}\times 5\right)$$

Express $-\frac{2}{3}\times 5$ as a single fraction.

$$\frac{8159}{160}-\frac{-2\times 5}{3}$$

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

$$\frac{8159}{160}-\frac{-10}{3}$$

Fraction $\frac{-10}{3}$ can be rewritten as $-\frac{10}{3}$ by extracting the negative sign.

$$\frac{8159}{160}-\left(-\frac{10}{3}\right)$$

The opposite of $-\frac{10}{3}$ is $\frac{10}{3}$.

$$\frac{8159}{160}+\frac{10}{3}$$

Least common multiple of $160$ and $3$ is $480$. Convert $\frac{8159}{160}$ and $\frac{10}{3}$ to fractions with denominator $480$.

$$\frac{24477}{480}+\frac{1600}{480}$$

Since $\frac{24477}{480}$ and $\frac{1600}{480}$ have the same denominator, add them by adding their numerators.

$$\frac{24477+1600}{480}$$

Add $24477$ and $1600$ to get $26077$.

$$\frac{26077}{480}$$

Factor

$\frac{89 \cdot 293}{2 ^ {5} \cdot 3 \cdot 5} = 54\frac{157}{480} = 54.327083333333334$