Solve (41/3-2/5)-(63/5-52/3)

$$( 4 \frac { 1 } { 3 } - \frac { 2 } { 5 } ) - ( 6 \frac { 3 } { 5 } - 5 \frac { 2 } { 3 } )$$

Evaluate

$$3$$

Solution Steps

Multiply 4 and 3 to get 12.

$$\frac{12+1}{3}-\frac{2}{5}-\left(\frac{6\times 5+3}{5}-\frac{5\times 3+2}{3}\right)$$

Add 12 and 1 to get 13.

$$\frac{13}{3}-\frac{2}{5}-\left(\frac{6\times 5+3}{5}-\frac{5\times 3+2}{3}\right)$$

Least common multiple of 3 and 5 is 15. Convert \frac{13}{3} and \frac{2}{5} to fractions with denominator 15.

$$\frac{65}{15}-\frac{6}{15}-\left(\frac{6\times 5+3}{5}-\frac{5\times 3+2}{3}\right)$$

Since \frac{65}{15} and \frac{6}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{65-6}{15}-\left(\frac{6\times 5+3}{5}-\frac{5\times 3+2}{3}\right)$$

Subtract 6 from 65 to get 59.

$$\frac{59}{15}-\left(\frac{6\times 5+3}{5}-\frac{5\times 3+2}{3}\right)$$

Multiply 6 and 5 to get 30.

$$\frac{59}{15}-\left(\frac{30+3}{5}-\frac{5\times 3+2}{3}\right)$$

Add 30 and 3 to get 33.

$$\frac{59}{15}-\left(\frac{33}{5}-\frac{5\times 3+2}{3}\right)$$

Multiply 5 and 3 to get 15.

$$\frac{59}{15}-\left(\frac{33}{5}-\frac{15+2}{3}\right)$$

Add 15 and 2 to get 17.

$$\frac{59}{15}-\left(\frac{33}{5}-\frac{17}{3}\right)$$

Least common multiple of 5 and 3 is 15. Convert \frac{33}{5} and \frac{17}{3} to fractions with denominator 15.

$$\frac{59}{15}-\left(\frac{99}{15}-\frac{85}{15}\right)$$

Since \frac{99}{15} and \frac{85}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{59}{15}-\frac{99-85}{15}$$

Subtract 85 from 99 to get 14.

$$\frac{59}{15}-\frac{14}{15}$$

Since \frac{59}{15} and \frac{14}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{59-14}{15}$$

Subtract 14 from 59 to get 45.

$$\frac{45}{15}$$

Divide 45 by 15 to get 3.

$$3$$

Factor

$$3$$