Solve 4/5+7/8+59/14=

$$\frac{ 4 }{ 5 } + \frac{ 7 }{ 8 } + 5 \frac { 9 } { 14 } =$$

Evaluate

$$\frac{2049}{280}\approx 7.317857143$$

Solution Steps

Least common multiple of 5 and 8 is 40. Convert \frac{4}{5} and \frac{7}{8} to fractions with denominator 40.

$$\frac{32}{40}+\frac{35}{40}+\frac{5\times 14+9}{14}$$

Since \frac{32}{40} and \frac{35}{40} have the same denominator, add them by adding their numerators.

$$\frac{32+35}{40}+\frac{5\times 14+9}{14}$$

Add 32 and 35 to get 67.

$$\frac{67}{40}+\frac{5\times 14+9}{14}$$

Multiply 5 and 14 to get 70.

$$\frac{67}{40}+\frac{70+9}{14}$$

Add 70 and 9 to get 79.

$$\frac{67}{40}+\frac{79}{14}$$

Least common multiple of 40 and 14 is 280. Convert \frac{67}{40} and \frac{79}{14} to fractions with denominator 280.

$$\frac{469}{280}+\frac{1580}{280}$$

Since \frac{469}{280} and \frac{1580}{280} have the same denominator, add them by adding their numerators.

$$\frac{469+1580}{280}$$

Add 469 and 1580 to get 2049.

$$\frac{2049}{280}$$

Factor

$$\frac{3 \cdot 683}{2 ^ {3} \cdot 5 \cdot 7} = 7\frac{89}{280} = 7.317857142857143$$