Solve (11/5*23/4+11/5)*8

$$( 1 \frac { 1 } { 5 } \times 2 \frac { 3 } { 4 } + 1 \frac { 1 } { 5 } ) \times 8$$

Evaluate

$$36$$

Solution Steps

Multiply 1 and 5 to get 5.

$$\left(\frac{5+1}{5}\times \frac{2\times 4+3}{4}+\frac{1\times 5+1}{5}\right)\times 8$$

Add 5 and 1 to get 6.

$$\left(\frac{6}{5}\times \frac{2\times 4+3}{4}+\frac{1\times 5+1}{5}\right)\times 8$$

Multiply 2 and 4 to get 8.

$$\left(\frac{6}{5}\times \frac{8+3}{4}+\frac{1\times 5+1}{5}\right)\times 8$$

Add 8 and 3 to get 11.

$$\left(\frac{6}{5}\times \frac{11}{4}+\frac{1\times 5+1}{5}\right)\times 8$$

Multiply \frac{6}{5} times \frac{11}{4} by multiplying numerator times numerator and denominator times denominator.

$$\left(\frac{6\times 11}{5\times 4}+\frac{1\times 5+1}{5}\right)\times 8$$

Do the multiplications in the fraction \frac{6\times 11}{5\times 4}.

$$\left(\frac{66}{20}+\frac{1\times 5+1}{5}\right)\times 8$$

Reduce the fraction \frac{66}{20} to lowest terms by extracting and canceling out 2.

$$\left(\frac{33}{10}+\frac{1\times 5+1}{5}\right)\times 8$$

Multiply 1 and 5 to get 5.

$$\left(\frac{33}{10}+\frac{5+1}{5}\right)\times 8$$

Add 5 and 1 to get 6.

$$\left(\frac{33}{10}+\frac{6}{5}\right)\times 8$$

Least common multiple of 10 and 5 is 10. Convert \frac{33}{10} and \frac{6}{5} to fractions with denominator 10.

$$\left(\frac{33}{10}+\frac{12}{10}\right)\times 8$$

Since \frac{33}{10} and \frac{12}{10} have the same denominator, add them by adding their numerators.

$$\frac{33+12}{10}\times 8$$

Add 33 and 12 to get 45.

$$\frac{45}{10}\times 8$$

Reduce the fraction \frac{45}{10} to lowest terms by extracting and canceling out 5.

$$\frac{9}{2}\times 8$$

Express \frac{9}{2}\times 8 as a single fraction.

$$\frac{9\times 8}{2}$$

Multiply 9 and 8 to get 72.

$$\frac{72}{2}$$

Divide 72 by 2 to get 36.

$$36$$

Factor

$$2^{2}\times 3^{2}$$