Solve (75/120+55/66)*44/25=

$$( \frac { 75 } { 120 } + \frac { 55 } { 66 } ) \cdot \frac { 44 } { 25 } =$$

Evaluate

$$\frac{77}{30}\approx 2.566666667$$

Solution Steps

Reduce the fraction \frac{75}{120} to lowest terms by extracting and canceling out 15.

$$\left(\frac{5}{8}+\frac{55}{66}\right)\times \frac{44}{25}$$

Reduce the fraction \frac{55}{66} to lowest terms by extracting and canceling out 11.

$$\left(\frac{5}{8}+\frac{5}{6}\right)\times \frac{44}{25}$$

Least common multiple of 8 and 6 is 24. Convert \frac{5}{8} and \frac{5}{6} to fractions with denominator 24.

$$\left(\frac{15}{24}+\frac{20}{24}\right)\times \frac{44}{25}$$

Since \frac{15}{24} and \frac{20}{24} have the same denominator, add them by adding their numerators.

$$\frac{15+20}{24}\times \frac{44}{25}$$

Add 15 and 20 to get 35.

$$\frac{35}{24}\times \frac{44}{25}$$

Multiply \frac{35}{24} times \frac{44}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{35\times 44}{24\times 25}$$

Do the multiplications in the fraction \frac{35\times 44}{24\times 25}.

$$\frac{1540}{600}$$

Reduce the fraction \frac{1540}{600} to lowest terms by extracting and canceling out 20.

$$\frac{77}{30}$$

Factor

$$\frac{7 \cdot 11}{2 \cdot 3 \cdot 5} = 2\frac{17}{30} = 2.566666666666667$$