Solve 1/2+2/3*5+2/4*6+2/5*7

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

Evaluate

$$\frac{65}{84}\approx 0.773809524$$

Solution Steps

Multiply 3 and 5 to get 15.

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

Least common multiple of 2 and 15 is 30. Convert \frac{1}{2} and \frac{2}{15} to fractions with denominator 30.

$$\frac{15}{30}+\frac{4}{30}+\frac{2}{4\times 6}+\frac{2}{5\times 7}$$

Since \frac{15}{30} and \frac{4}{30} have the same denominator, add them by adding their numerators.

$$\frac{15+4}{30}+\frac{2}{4\times 6}+\frac{2}{5\times 7}$$

Add 15 and 4 to get 19.

$$\frac{19}{30}+\frac{2}{4\times 6}+\frac{2}{5\times 7}$$

Multiply 4 and 6 to get 24.

$$\frac{19}{30}+\frac{2}{24}+\frac{2}{5\times 7}$$

Reduce the fraction \frac{2}{24} to lowest terms by extracting and canceling out 2.

$$\frac{19}{30}+\frac{1}{12}+\frac{2}{5\times 7}$$

Least common multiple of 30 and 12 is 60. Convert \frac{19}{30} and \frac{1}{12} to fractions with denominator 60.

$$\frac{38}{60}+\frac{5}{60}+\frac{2}{5\times 7}$$

Since \frac{38}{60} and \frac{5}{60} have the same denominator, add them by adding their numerators.

$$\frac{38+5}{60}+\frac{2}{5\times 7}$$

Add 38 and 5 to get 43.

$$\frac{43}{60}+\frac{2}{5\times 7}$$

Multiply 5 and 7 to get 35.

$$\frac{43}{60}+\frac{2}{35}$$

Least common multiple of 60 and 35 is 420. Convert \frac{43}{60} and \frac{2}{35} to fractions with denominator 420.

$$\frac{301}{420}+\frac{24}{420}$$

Since \frac{301}{420} and \frac{24}{420} have the same denominator, add them by adding their numerators.

$$\frac{301+24}{420}$$

Add 301 and 24 to get 325.

$$\frac{325}{420}$$

Reduce the fraction \frac{325}{420} to lowest terms by extracting and canceling out 5.

$$\frac{65}{84}$$

Factor

$$\frac{5 \cdot 13}{2 ^ {2} \cdot 3 \cdot 7} = 0.7738095238095238$$