Solve 16/5*[(12/3+1/5)*15/7]

$$\frac { 16 } { 5 } \times [ ( 1 \frac { 2 } { 3 } + \frac { 1 } { 5 } ) \times \frac { 15 } { 7 } ]$$

Evaluate

$$\frac{64}{5}=12.8$$

Solution Steps

Multiply 1 and 3 to get 3.

$$\frac{16}{5}\left(\frac{3+2}{3}+\frac{1}{5}\right)\times \frac{15}{7}$$

Add 3 and 2 to get 5.

$$\frac{16}{5}\left(\frac{5}{3}+\frac{1}{5}\right)\times \frac{15}{7}$$

Least common multiple of 3 and 5 is 15. Convert \frac{5}{3} and \frac{1}{5} to fractions with denominator 15.

$$\frac{16}{5}\left(\frac{25}{15}+\frac{3}{15}\right)\times \frac{15}{7}$$

Since \frac{25}{15} and \frac{3}{15} have the same denominator, add them by adding their numerators.

$$\frac{16}{5}\times \frac{25+3}{15}\times \frac{15}{7}$$

Add 25 and 3 to get 28.

$$\frac{16}{5}\times \frac{28}{15}\times \frac{15}{7}$$

Multiply \frac{16}{5} times \frac{28}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{16\times 28}{5\times 15}\times \frac{15}{7}$$

Do the multiplications in the fraction \frac{16\times 28}{5\times 15}.

$$\frac{448}{75}\times \frac{15}{7}$$

Multiply \frac{448}{75} times \frac{15}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{448\times 15}{75\times 7}$$

Do the multiplications in the fraction \frac{448\times 15}{75\times 7}.

$$\frac{6720}{525}$$

Reduce the fraction \frac{6720}{525} to lowest terms by extracting and canceling out 105.

$$\frac{64}{5}$$

Factor

$$\frac{2 ^ {6}}{5} = 12\frac{4}{5} = 12.8$$