Solve (2/3+4/5)+(6/2*3/4)

$$( \frac { 2 } { 3 } + \frac { 4 } { 5 } ) + ( \frac { 6 } { 2 } \cdot \frac { 3 } { 4 } )$$

Evaluate

$$\frac{223}{60}\approx 3.716666667$$

Solution Steps

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

$$\frac{10}{15}+\frac{12}{15}+\frac{6}{2}\times \frac{3}{4}$$

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

$$\frac{10+12}{15}+\frac{6}{2}\times \frac{3}{4}$$

Add 10 and 12 to get 22.

$$\frac{22}{15}+\frac{6}{2}\times \frac{3}{4}$$

Divide 6 by 2 to get 3.

$$\frac{22}{15}+3\times \frac{3}{4}$$

Express 3\times \frac{3}{4} as a single fraction.

$$\frac{22}{15}+\frac{3\times 3}{4}$$

Multiply 3 and 3 to get 9.

$$\frac{22}{15}+\frac{9}{4}$$

Least common multiple of 15 and 4 is 60. Convert \frac{22}{15} and \frac{9}{4} to fractions with denominator 60.

$$\frac{88}{60}+\frac{135}{60}$$

Since \frac{88}{60} and \frac{135}{60} have the same denominator, add them by adding their numerators.

$$\frac{88+135}{60}$$

Add 88 and 135 to get 223.

$$\frac{223}{60}$$

Factor

$$\frac{223}{2 ^ {2} \cdot 3 \cdot 5} = 3\frac{43}{60} = 3.716666666666667$$