Solve 6-[83/5-1.2*(2/3+1.5)+21/2*16%]+4=

$$6 - [ 8 \frac { 3 } { 5 } - 1.2 \times ( \frac { 2 } { 3 } + 1.5 ) + 2 \frac { 1 } { 2 } \times 16 \% ] + 4 =$$

Evaluate

$$3.6$$

Solution Steps

Multiply 8 and 5 to get 40.

$$6-\left(\frac{40+3}{5}-1.2\left(\frac{2}{3}+1.5\right)+\frac{2\times 2+1}{2}\times \frac{16}{100}\right)+4$$

Add 40 and 3 to get 43.

$$6-\left(\frac{43}{5}-1.2\left(\frac{2}{3}+1.5\right)+\frac{2\times 2+1}{2}\times \frac{16}{100}\right)+4$$

Convert decimal number 1.5 to fraction \frac{15}{10}. Reduce the fraction \frac{15}{10} to lowest terms by extracting and canceling out 5.

$$6-\left(\frac{43}{5}-1.2\left(\frac{2}{3}+\frac{3}{2}\right)+\frac{2\times 2+1}{2}\times \frac{16}{100}\right)+4$$

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

$$6-\left(\frac{43}{5}-1.2\left(\frac{4}{6}+\frac{9}{6}\right)+\frac{2\times 2+1}{2}\times \frac{16}{100}\right)+4$$

Since \frac{4}{6} and \frac{9}{6} have the same denominator, add them by adding their numerators.

$$6-\left(\frac{43}{5}-1.2\times \frac{4+9}{6}+\frac{2\times 2+1}{2}\times \frac{16}{100}\right)+4$$

Add 4 and 9 to get 13.

$$6-\left(\frac{43}{5}-1.2\times \frac{13}{6}+\frac{2\times 2+1}{2}\times \frac{16}{100}\right)+4$$

Convert decimal number 1.2 to fraction \frac{12}{10}. Reduce the fraction \frac{12}{10} to lowest terms by extracting and canceling out 2.

$$6-\left(\frac{43}{5}-\frac{6}{5}\times \frac{13}{6}+\frac{2\times 2+1}{2}\times \frac{16}{100}\right)+4$$

Multiply \frac{6}{5} times \frac{13}{6} by multiplying numerator times numerator and denominator times denominator.

$$6-\left(\frac{43}{5}-\frac{6\times 13}{5\times 6}+\frac{2\times 2+1}{2}\times \frac{16}{100}\right)+4$$

Cancel out 6 in both numerator and denominator.

$$6-\left(\frac{43}{5}-\frac{13}{5}+\frac{2\times 2+1}{2}\times \frac{16}{100}\right)+4$$

Since \frac{43}{5} and \frac{13}{5} have the same denominator, subtract them by subtracting their numerators.

$$6-\left(\frac{43-13}{5}+\frac{2\times 2+1}{2}\times \frac{16}{100}\right)+4$$

Subtract 13 from 43 to get 30.

$$6-\left(\frac{30}{5}+\frac{2\times 2+1}{2}\times \frac{16}{100}\right)+4$$

Divide 30 by 5 to get 6.

$$6-\left(6+\frac{2\times 2+1}{2}\times \frac{16}{100}\right)+4$$

Multiply 2 and 2 to get 4.

$$6-\left(6+\frac{4+1}{2}\times \frac{16}{100}\right)+4$$

Add 4 and 1 to get 5.

$$6-\left(6+\frac{5}{2}\times \frac{16}{100}\right)+4$$

Reduce the fraction \frac{16}{100} to lowest terms by extracting and canceling out 4.

$$6-\left(6+\frac{5}{2}\times \frac{4}{25}\right)+4$$

Multiply \frac{5}{2} times \frac{4}{25} by multiplying numerator times numerator and denominator times denominator.

$$6-\left(6+\frac{5\times 4}{2\times 25}\right)+4$$

Do the multiplications in the fraction \frac{5\times 4}{2\times 25}.

$$6-\left(6+\frac{20}{50}\right)+4$$

Reduce the fraction \frac{20}{50} to lowest terms by extracting and canceling out 10.

$$6-\left(6+\frac{2}{5}\right)+4$$

Convert 6 to fraction \frac{30}{5}.

$$6-\left(\frac{30}{5}+\frac{2}{5}\right)+4$$

Since \frac{30}{5} and \frac{2}{5} have the same denominator, add them by adding their numerators.

$$6-\frac{30+2}{5}+4$$

Add 30 and 2 to get 32.

$$6-\frac{32}{5}+4$$

Convert 6 to fraction \frac{30}{5}.

$$\frac{30}{5}-\frac{32}{5}+4$$

Since \frac{30}{5} and \frac{32}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{30-32}{5}+4$$

Subtract 32 from 30 to get -2.

$$-\frac{2}{5}+4$$

Convert 4 to fraction \frac{20}{5}.

$$-\frac{2}{5}+\frac{20}{5}$$

Since -\frac{2}{5} and \frac{20}{5} have the same denominator, add them by adding their numerators.

$$\frac{-2+20}{5}$$

Add -2 and 20 to get 18.

$$\frac{18}{5}$$

Factor

$$\frac{2 \cdot 3 ^ {2}}{5} = 3\frac{3}{5} = 3.6$$