Solve 5/11*61/15+5/11*74/15+frac{5}{11}*8frac{2}{3}

$$\frac { 5 } { 11 } \times 6 \frac { 1 } { 15 } + \frac { 5 } { 11 } \times 7 \frac { 4 } { 15 } + \frac { 5 } { 11 } \times 8 \frac { 2 } { 3 }$$

Evaluate

$$10$$

Solution Steps

Multiply 6 and 15 to get 90.

$$\frac{5}{11}\times \frac{90+1}{15}+\frac{5}{11}\times \frac{7\times 15+4}{15}+\frac{5}{11}\times \frac{8\times 3+2}{3}$$

Add 90 and 1 to get 91.

$$\frac{5}{11}\times \frac{91}{15}+\frac{5}{11}\times \frac{7\times 15+4}{15}+\frac{5}{11}\times \frac{8\times 3+2}{3}$$

Multiply \frac{5}{11} times \frac{91}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 91}{11\times 15}+\frac{5}{11}\times \frac{7\times 15+4}{15}+\frac{5}{11}\times \frac{8\times 3+2}{3}$$

Do the multiplications in the fraction \frac{5\times 91}{11\times 15}.

$$\frac{455}{165}+\frac{5}{11}\times \frac{7\times 15+4}{15}+\frac{5}{11}\times \frac{8\times 3+2}{3}$$

Reduce the fraction \frac{455}{165} to lowest terms by extracting and canceling out 5.

$$\frac{91}{33}+\frac{5}{11}\times \frac{7\times 15+4}{15}+\frac{5}{11}\times \frac{8\times 3+2}{3}$$

Multiply 7 and 15 to get 105.

$$\frac{91}{33}+\frac{5}{11}\times \frac{105+4}{15}+\frac{5}{11}\times \frac{8\times 3+2}{3}$$

Add 105 and 4 to get 109.

$$\frac{91}{33}+\frac{5}{11}\times \frac{109}{15}+\frac{5}{11}\times \frac{8\times 3+2}{3}$$

Multiply \frac{5}{11} times \frac{109}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{91}{33}+\frac{5\times 109}{11\times 15}+\frac{5}{11}\times \frac{8\times 3+2}{3}$$

Do the multiplications in the fraction \frac{5\times 109}{11\times 15}.

$$\frac{91}{33}+\frac{545}{165}+\frac{5}{11}\times \frac{8\times 3+2}{3}$$

Reduce the fraction \frac{545}{165} to lowest terms by extracting and canceling out 5.

$$\frac{91}{33}+\frac{109}{33}+\frac{5}{11}\times \frac{8\times 3+2}{3}$$

Since \frac{91}{33} and \frac{109}{33} have the same denominator, add them by adding their numerators.

$$\frac{91+109}{33}+\frac{5}{11}\times \frac{8\times 3+2}{3}$$

Add 91 and 109 to get 200.

$$\frac{200}{33}+\frac{5}{11}\times \frac{8\times 3+2}{3}$$

Multiply 8 and 3 to get 24.

$$\frac{200}{33}+\frac{5}{11}\times \frac{24+2}{3}$$

Add 24 and 2 to get 26.

$$\frac{200}{33}+\frac{5}{11}\times \frac{26}{3}$$

Multiply \frac{5}{11} times \frac{26}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{200}{33}+\frac{5\times 26}{11\times 3}$$

Do the multiplications in the fraction \frac{5\times 26}{11\times 3}.

$$\frac{200}{33}+\frac{130}{33}$$

Since \frac{200}{33} and \frac{130}{33} have the same denominator, add them by adding their numerators.

$$\frac{200+130}{33}$$

Add 200 and 130 to get 330.

$$\frac{330}{33}$$

Divide 330 by 33 to get 10.

$$10$$

Factor

$$2\times 5$$