Solve [54+(4/5+2/3)*5/11]*7/4

$$[ 54 + ( \frac { 4 } { 5 } + \frac { 2 } { 3 } ) \times \frac { 5 } { 11 } ] \times \frac { 7 } { 4 }$$

Evaluate

$$\frac{287}{3}\approx 95.666666667$$

Solution Steps

Least common multiple of 5 and 3 is 15. Convert \frac{4}{5} and \frac{2}{3} to fractions with denominator 15.

$$\left(54+\left(\frac{12}{15}+\frac{10}{15}\right)\times \frac{5}{11}\right)\times \frac{7}{4}$$

Since \frac{12}{15} and \frac{10}{15} have the same denominator, add them by adding their numerators.

$$\left(54+\frac{12+10}{15}\times \frac{5}{11}\right)\times \frac{7}{4}$$

Add 12 and 10 to get 22.

$$\left(54+\frac{22}{15}\times \frac{5}{11}\right)\times \frac{7}{4}$$

Multiply \frac{22}{15} times \frac{5}{11} by multiplying numerator times numerator and denominator times denominator.

$$\left(54+\frac{22\times 5}{15\times 11}\right)\times \frac{7}{4}$$

Do the multiplications in the fraction \frac{22\times 5}{15\times 11}.

$$\left(54+\frac{110}{165}\right)\times \frac{7}{4}$$

Reduce the fraction \frac{110}{165} to lowest terms by extracting and canceling out 55.

$$\left(54+\frac{2}{3}\right)\times \frac{7}{4}$$

Convert 54 to fraction \frac{162}{3}.

$$\left(\frac{162}{3}+\frac{2}{3}\right)\times \frac{7}{4}$$

Since \frac{162}{3} and \frac{2}{3} have the same denominator, add them by adding their numerators.

$$\frac{162+2}{3}\times \frac{7}{4}$$

Add 162 and 2 to get 164.

$$\frac{164}{3}\times \frac{7}{4}$$

Multiply \frac{164}{3} times \frac{7}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{164\times 7}{3\times 4}$$

Do the multiplications in the fraction \frac{164\times 7}{3\times 4}.

$$\frac{1148}{12}$$

Reduce the fraction \frac{1148}{12} to lowest terms by extracting and canceling out 4.

$$\frac{287}{3}$$

Factor

$$\frac{7 \cdot 41}{3} = 95\frac{2}{3} = 95.66666666666667$$