Solve 4*12/5*16+(12/5)^2-[16-(12/5)2]/2*4*frac{12{5}}

$$4 \times \frac { 12 } { 5 } \times \frac { 16 + ( \frac { 12 } { 5 } ) ^ { 2 } - [ 16 - ( \frac { 12 } { 5 } ) 2 ] } { 2 \times 4 \times \frac { 12 } { 5 } }$$

Evaluate

$$\frac{132}{25}=5.28$$

Solution Steps

Express 4\times \frac{12}{5} as a single fraction.

$$\frac{4\times 12}{5}\times \frac{16+\left(\frac{12}{5}\right)^{2}-\left(16-\frac{12}{5}\times 2\right)}{2\times 4\times \frac{12}{5}}$$

Multiply 4 and 12 to get 48.

$$\frac{48}{5}\times \frac{16+\left(\frac{12}{5}\right)^{2}-\left(16-\frac{12}{5}\times 2\right)}{2\times 4\times \frac{12}{5}}$$

Calculate \frac{12}{5} to the power of 2 and get \frac{144}{25}.

$$\frac{48}{5}\times \frac{16+\frac{144}{25}-\left(16-\frac{12}{5}\times 2\right)}{2\times 4\times \frac{12}{5}}$$

Convert 16 to fraction \frac{400}{25}.

$$\frac{48}{5}\times \frac{\frac{400}{25}+\frac{144}{25}-\left(16-\frac{12}{5}\times 2\right)}{2\times 4\times \frac{12}{5}}$$

Since \frac{400}{25} and \frac{144}{25} have the same denominator, add them by adding their numerators.

$$\frac{48}{5}\times \frac{\frac{400+144}{25}-\left(16-\frac{12}{5}\times 2\right)}{2\times 4\times \frac{12}{5}}$$

Add 400 and 144 to get 544.

$$\frac{48}{5}\times \frac{\frac{544}{25}-\left(16-\frac{12}{5}\times 2\right)}{2\times 4\times \frac{12}{5}}$$

Express \frac{12}{5}\times 2 as a single fraction.

$$\frac{48}{5}\times \frac{\frac{544}{25}-\left(16-\frac{12\times 2}{5}\right)}{2\times 4\times \frac{12}{5}}$$

Multiply 12 and 2 to get 24.

$$\frac{48}{5}\times \frac{\frac{544}{25}-\left(16-\frac{24}{5}\right)}{2\times 4\times \frac{12}{5}}$$

Convert 16 to fraction \frac{80}{5}.

$$\frac{48}{5}\times \frac{\frac{544}{25}-\left(\frac{80}{5}-\frac{24}{5}\right)}{2\times 4\times \frac{12}{5}}$$

Since \frac{80}{5} and \frac{24}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{48}{5}\times \frac{\frac{544}{25}-\frac{80-24}{5}}{2\times 4\times \frac{12}{5}}$$

Subtract 24 from 80 to get 56.

$$\frac{48}{5}\times \frac{\frac{544}{25}-\frac{56}{5}}{2\times 4\times \frac{12}{5}}$$

Least common multiple of 25 and 5 is 25. Convert \frac{544}{25} and \frac{56}{5} to fractions with denominator 25.

$$\frac{48}{5}\times \frac{\frac{544}{25}-\frac{280}{25}}{2\times 4\times \frac{12}{5}}$$

Since \frac{544}{25} and \frac{280}{25} have the same denominator, subtract them by subtracting their numerators.

$$\frac{48}{5}\times \frac{\frac{544-280}{25}}{2\times 4\times \frac{12}{5}}$$

Subtract 280 from 544 to get 264.

$$\frac{48}{5}\times \frac{\frac{264}{25}}{2\times 4\times \frac{12}{5}}$$

Multiply 2 and 4 to get 8.

$$\frac{48}{5}\times \frac{\frac{264}{25}}{8\times \frac{12}{5}}$$

Express 8\times \frac{12}{5} as a single fraction.

$$\frac{48}{5}\times \frac{\frac{264}{25}}{\frac{8\times 12}{5}}$$

Multiply 8 and 12 to get 96.

$$\frac{48}{5}\times \frac{\frac{264}{25}}{\frac{96}{5}}$$

Divide \frac{264}{25} by \frac{96}{5} by multiplying \frac{264}{25} by the reciprocal of \frac{96}{5}.

$$\frac{48}{5}\times \frac{264}{25}\times \frac{5}{96}$$

Multiply \frac{264}{25} times \frac{5}{96} by multiplying numerator times numerator and denominator times denominator.

$$\frac{48}{5}\times \frac{264\times 5}{25\times 96}$$

Do the multiplications in the fraction \frac{264\times 5}{25\times 96}.

$$\frac{48}{5}\times \frac{1320}{2400}$$

Reduce the fraction \frac{1320}{2400} to lowest terms by extracting and canceling out 120.

$$\frac{48}{5}\times \frac{11}{20}$$

Multiply \frac{48}{5} times \frac{11}{20} by multiplying numerator times numerator and denominator times denominator.

$$\frac{48\times 11}{5\times 20}$$

Do the multiplications in the fraction \frac{48\times 11}{5\times 20}.

$$\frac{528}{100}$$

Reduce the fraction \frac{528}{100} to lowest terms by extracting and canceling out 4.

$$\frac{132}{25}$$

Factor

$$\frac{2 ^ {2} \cdot 3 \cdot 11}{5 ^ {2}} = 5\frac{7}{25} = 5.28$$