Solve 22/5+[33/4div{16/21+(3-1/3div2-frac{1}{2}*frac{3}{4})}]

$$2 \frac { 2 } { 5 } + [ 3 \frac { 3 } { 4 } \div \{ \frac { 16 } { 21 } + ( 3 - \frac { 1 } { 3 } \div 2 - \frac { 1 } { 2 } \times \frac { 3 } { 4 } ) \} ]$$

Evaluate

$$\frac{9642}{2705}\approx 3.564510166$$

Solution Steps

Multiply 2 and 5 to get 10.

$$\frac{10+2}{5}+\frac{\frac{3\times 4+3}{4}}{\frac{16}{21}+3-\frac{\frac{1}{3}}{2}-\frac{1}{2}\times \frac{3}{4}}$$

Add 10 and 2 to get 12.

$$\frac{12}{5}+\frac{\frac{3\times 4+3}{4}}{\frac{16}{21}+3-\frac{\frac{1}{3}}{2}-\frac{1}{2}\times \frac{3}{4}}$$

Multiply 3 and 4 to get 12.

$$\frac{12}{5}+\frac{\frac{12+3}{4}}{\frac{16}{21}+3-\frac{\frac{1}{3}}{2}-\frac{1}{2}\times \frac{3}{4}}$$

Add 12 and 3 to get 15.

$$\frac{12}{5}+\frac{\frac{15}{4}}{\frac{16}{21}+3-\frac{\frac{1}{3}}{2}-\frac{1}{2}\times \frac{3}{4}}$$

Express \frac{\frac{1}{3}}{2} as a single fraction.

$$\frac{12}{5}+\frac{\frac{15}{4}}{\frac{16}{21}+3-\frac{1}{3\times 2}-\frac{1}{2}\times \frac{3}{4}}$$

Multiply 3 and 2 to get 6.

$$\frac{12}{5}+\frac{\frac{15}{4}}{\frac{16}{21}+3-\frac{1}{6}-\frac{1}{2}\times \frac{3}{4}}$$

Convert 3 to fraction \frac{18}{6}.

$$\frac{12}{5}+\frac{\frac{15}{4}}{\frac{16}{21}+\frac{18}{6}-\frac{1}{6}-\frac{1}{2}\times \frac{3}{4}}$$

Since \frac{18}{6} and \frac{1}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{12}{5}+\frac{\frac{15}{4}}{\frac{16}{21}+\frac{18-1}{6}-\frac{1}{2}\times \frac{3}{4}}$$

Subtract 1 from 18 to get 17.

$$\frac{12}{5}+\frac{\frac{15}{4}}{\frac{16}{21}+\frac{17}{6}-\frac{1}{2}\times \frac{3}{4}}$$

Multiply \frac{1}{2} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{12}{5}+\frac{\frac{15}{4}}{\frac{16}{21}+\frac{17}{6}-\frac{1\times 3}{2\times 4}}$$

Do the multiplications in the fraction \frac{1\times 3}{2\times 4}.

$$\frac{12}{5}+\frac{\frac{15}{4}}{\frac{16}{21}+\frac{17}{6}-\frac{3}{8}}$$

Least common multiple of 6 and 8 is 24. Convert \frac{17}{6} and \frac{3}{8} to fractions with denominator 24.

$$\frac{12}{5}+\frac{\frac{15}{4}}{\frac{16}{21}+\frac{68}{24}-\frac{9}{24}}$$

Since \frac{68}{24} and \frac{9}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{12}{5}+\frac{\frac{15}{4}}{\frac{16}{21}+\frac{68-9}{24}}$$

Subtract 9 from 68 to get 59.

$$\frac{12}{5}+\frac{\frac{15}{4}}{\frac{16}{21}+\frac{59}{24}}$$

Least common multiple of 21 and 24 is 168. Convert \frac{16}{21} and \frac{59}{24} to fractions with denominator 168.

$$\frac{12}{5}+\frac{\frac{15}{4}}{\frac{128}{168}+\frac{413}{168}}$$

Since \frac{128}{168} and \frac{413}{168} have the same denominator, add them by adding their numerators.

$$\frac{12}{5}+\frac{\frac{15}{4}}{\frac{128+413}{168}}$$

Add 128 and 413 to get 541.

$$\frac{12}{5}+\frac{\frac{15}{4}}{\frac{541}{168}}$$

Divide \frac{15}{4} by \frac{541}{168} by multiplying \frac{15}{4} by the reciprocal of \frac{541}{168}.

$$\frac{12}{5}+\frac{15}{4}\times \frac{168}{541}$$

Multiply \frac{15}{4} times \frac{168}{541} by multiplying numerator times numerator and denominator times denominator.

$$\frac{12}{5}+\frac{15\times 168}{4\times 541}$$

Do the multiplications in the fraction \frac{15\times 168}{4\times 541}.

$$\frac{12}{5}+\frac{2520}{2164}$$

Reduce the fraction \frac{2520}{2164} to lowest terms by extracting and canceling out 4.

$$\frac{12}{5}+\frac{630}{541}$$

Least common multiple of 5 and 541 is 2705. Convert \frac{12}{5} and \frac{630}{541} to fractions with denominator 2705.

$$\frac{6492}{2705}+\frac{3150}{2705}$$

Since \frac{6492}{2705} and \frac{3150}{2705} have the same denominator, add them by adding their numerators.

$$\frac{6492+3150}{2705}$$

Add 6492 and 3150 to get 9642.

$$\frac{9642}{2705}$$

Factor

$$\frac{2 \cdot 3 \cdot 1607}{5 \cdot 541} = 3\frac{1527}{2705} = 3.564510166358595$$