Solve 3left(4/5-3/7right)+1/2

$$3 \left( \frac{ 4 }{ 5 } - \frac{ 3 }{ 7 } \right) + \frac{ 1 }{ 2 }$$

Evaluate

$$\frac{113}{70}\approx 1.614285714$$

Solution Steps

Least common multiple of 5 and 7 is 35. Convert \frac{4}{5} and \frac{3}{7} to fractions with denominator 35.

$$3\left(\frac{28}{35}-\frac{15}{35}\right)+\frac{1}{2}$$

Since \frac{28}{35} and \frac{15}{35} have the same denominator, subtract them by subtracting their numerators.

$$3\times \frac{28-15}{35}+\frac{1}{2}$$

Subtract 15 from 28 to get 13.

$$3\times \frac{13}{35}+\frac{1}{2}$$

Express 3\times \frac{13}{35} as a single fraction.

$$\frac{3\times 13}{35}+\frac{1}{2}$$

Multiply 3 and 13 to get 39.

$$\frac{39}{35}+\frac{1}{2}$$

Least common multiple of 35 and 2 is 70. Convert \frac{39}{35} and \frac{1}{2} to fractions with denominator 70.

$$\frac{78}{70}+\frac{35}{70}$$

Since \frac{78}{70} and \frac{35}{70} have the same denominator, add them by adding their numerators.

$$\frac{78+35}{70}$$

Add 78 and 35 to get 113.

$$\frac{113}{70}$$

Factor

$$\frac{113}{2 \cdot 5 \cdot 7} = 1\frac{43}{70} = 1.6142857142857143$$