Solve 102/3+4/5-3/4

$$10 \frac { 2 } { 3 } + \frac { 4 } { 5 } - \frac { 3 } { 4 }$$

Evaluate

$$\frac{643}{60}\approx 10.716666667$$

Solution Steps

Multiply 10 and 3 to get 30.

$$\frac{30+2}{3}+\frac{4}{5}-\frac{3}{4}$$

Add 30 and 2 to get 32.

$$\frac{32}{3}+\frac{4}{5}-\frac{3}{4}$$

Least common multiple of 3 and 5 is 15. Convert \frac{32}{3} and \frac{4}{5} to fractions with denominator 15.

$$\frac{160}{15}+\frac{12}{15}-\frac{3}{4}$$

Since \frac{160}{15} and \frac{12}{15} have the same denominator, add them by adding their numerators.

$$\frac{160+12}{15}-\frac{3}{4}$$

Add 160 and 12 to get 172.

$$\frac{172}{15}-\frac{3}{4}$$

Least common multiple of 15 and 4 is 60. Convert \frac{172}{15} and \frac{3}{4} to fractions with denominator 60.

$$\frac{688}{60}-\frac{45}{60}$$

Since \frac{688}{60} and \frac{45}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{688-45}{60}$$

Subtract 45 from 688 to get 643.

$$\frac{643}{60}$$

Factor

$$\frac{643}{2 ^ {2} \cdot 3 \cdot 5} = 10\frac{43}{60} = 10.716666666666667$$