Solve 22/5+[33/4div{16/21+(3-1/3div2frac{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

$$\frac{26331}{7690}\approx 3.424057217$$

Solution Steps

Multiply 2 and 5 to get 10.

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

Add 10 and 2 to get 12.

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

Multiply 3 and 4 to get 12.

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

Add 12 and 3 to get 15.

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

Divide \frac{1}{3} by \frac{2\times 2+1}{2} by multiplying \frac{1}{3} by the reciprocal of \frac{2\times 2+1}{2}.

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

Multiply 2 and 2 to get 4.

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

Add 4 and 1 to get 5.

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

Multiply 3 and 5 to get 15.

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

Multiply \frac{2}{15} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{2\times 3}{15\times 4}.

$$\frac{12}{5}+\frac{\frac{15}{4}}{\frac{16}{21}+3-\frac{6}{60}}$$

Reduce the fraction \frac{6}{60} to lowest terms by extracting and canceling out 6.

$$\frac{12}{5}+\frac{\frac{15}{4}}{\frac{16}{21}+3-\frac{1}{10}}$$

Convert 3 to fraction \frac{30}{10}.

$$\frac{12}{5}+\frac{\frac{15}{4}}{\frac{16}{21}+\frac{30}{10}-\frac{1}{10}}$$

Since \frac{30}{10} and \frac{1}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{12}{5}+\frac{\frac{15}{4}}{\frac{16}{21}+\frac{30-1}{10}}$$

Subtract 1 from 30 to get 29.

$$\frac{12}{5}+\frac{\frac{15}{4}}{\frac{16}{21}+\frac{29}{10}}$$

Least common multiple of 21 and 10 is 210. Convert \frac{16}{21} and \frac{29}{10} to fractions with denominator 210.

$$\frac{12}{5}+\frac{\frac{15}{4}}{\frac{160}{210}+\frac{609}{210}}$$

Since \frac{160}{210} and \frac{609}{210} have the same denominator, add them by adding their numerators.

$$\frac{12}{5}+\frac{\frac{15}{4}}{\frac{160+609}{210}}$$

Add 160 and 609 to get 769.

$$\frac{12}{5}+\frac{\frac{15}{4}}{\frac{769}{210}}$$

Divide \frac{15}{4} by \frac{769}{210} by multiplying \frac{15}{4} by the reciprocal of \frac{769}{210}.

$$\frac{12}{5}+\frac{15}{4}\times \frac{210}{769}$$

Multiply \frac{15}{4} times \frac{210}{769} by multiplying numerator times numerator and denominator times denominator.

$$\frac{12}{5}+\frac{15\times 210}{4\times 769}$$

Do the multiplications in the fraction \frac{15\times 210}{4\times 769}.

$$\frac{12}{5}+\frac{3150}{3076}$$

Reduce the fraction \frac{3150}{3076} to lowest terms by extracting and canceling out 2.

$$\frac{12}{5}+\frac{1575}{1538}$$

Least common multiple of 5 and 1538 is 7690. Convert \frac{12}{5} and \frac{1575}{1538} to fractions with denominator 7690.

$$\frac{18456}{7690}+\frac{7875}{7690}$$

Since \frac{18456}{7690} and \frac{7875}{7690} have the same denominator, add them by adding their numerators.

$$\frac{18456+7875}{7690}$$

Add 18456 and 7875 to get 26331.

$$\frac{26331}{7690}$$

Factor

$$\frac{3 \cdot 67 \cdot 131}{2 \cdot 5 \cdot 769} = 3\frac{3261}{7690} = 3.4240572171651493$$