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

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

Evaluate

$$\frac{1427}{840}\approx 1.698809524$$

Solution Steps

Multiply \frac{2}{5} times \frac{7}{16} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{2\times 7}{5\times 16}.

$$\frac{6}{7}+\frac{14}{80}+\frac{2}{3}$$

Reduce the fraction \frac{14}{80} to lowest terms by extracting and canceling out 2.

$$\frac{6}{7}+\frac{7}{40}+\frac{2}{3}$$

Least common multiple of 7 and 40 is 280. Convert \frac{6}{7} and \frac{7}{40} to fractions with denominator 280.

$$\frac{240}{280}+\frac{49}{280}+\frac{2}{3}$$

Since \frac{240}{280} and \frac{49}{280} have the same denominator, add them by adding their numerators.

$$\frac{240+49}{280}+\frac{2}{3}$$

Add 240 and 49 to get 289.

$$\frac{289}{280}+\frac{2}{3}$$

Least common multiple of 280 and 3 is 840. Convert \frac{289}{280} and \frac{2}{3} to fractions with denominator 840.

$$\frac{867}{840}+\frac{560}{840}$$

Since \frac{867}{840} and \frac{560}{840} have the same denominator, add them by adding their numerators.

$$\frac{867+560}{840}$$

Add 867 and 560 to get 1427.

$$\frac{1427}{840}$$

Factor

$$\frac{1427}{2 ^ {3} \cdot 3 \cdot 5 \cdot 7} = 1\frac{587}{840} = 1.6988095238095238$$