Solve 6/5+5/6*7/16+2/3

$$\frac { 6 } { 5 } + \frac { 5 } { 6 } \times \frac { 7 } { 16 } + \frac { 2 } { 3 }$$

Evaluate

$$\frac{357}{160}=2.23125$$

Solution Steps

Multiply \frac{5}{6} times \frac{7}{16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{6}{5}+\frac{5\times 7}{6\times 16}+\frac{2}{3}$$

Do the multiplications in the fraction \frac{5\times 7}{6\times 16}.

$$\frac{6}{5}+\frac{35}{96}+\frac{2}{3}$$

Least common multiple of 5 and 96 is 480. Convert \frac{6}{5} and \frac{35}{96} to fractions with denominator 480.

$$\frac{576}{480}+\frac{175}{480}+\frac{2}{3}$$

Since \frac{576}{480} and \frac{175}{480} have the same denominator, add them by adding their numerators.

$$\frac{576+175}{480}+\frac{2}{3}$$

Add 576 and 175 to get 751.

$$\frac{751}{480}+\frac{2}{3}$$

Least common multiple of 480 and 3 is 480. Convert \frac{751}{480} and \frac{2}{3} to fractions with denominator 480.

$$\frac{751}{480}+\frac{320}{480}$$

Since \frac{751}{480} and \frac{320}{480} have the same denominator, add them by adding their numerators.

$$\frac{751+320}{480}$$

Add 751 and 320 to get 1071.

$$\frac{1071}{480}$$

Reduce the fraction \frac{1071}{480} to lowest terms by extracting and canceling out 3.

$$\frac{357}{160}$$

Factor

$$\frac{3 \cdot 7 \cdot 17}{2 ^ {5} \cdot 5} = 2\frac{37}{160} = 2.23125$$