Solve 5*(11/3-3/5)+25div(25-1)

$$5 \times ( 1 \frac { 1 } { 3 } - \frac { 3 } { 5 } ) + 25 \div ( 25 - 1 )$$

Evaluate

$$\frac{113}{24}\approx 4.708333333$$

Solution Steps

Multiply 1 and 3 to get 3.

$$5\left(\frac{3+1}{3}-\frac{3}{5}\right)+\frac{25}{25-1}$$

Add 3 and 1 to get 4.

$$5\left(\frac{4}{3}-\frac{3}{5}\right)+\frac{25}{25-1}$$

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

$$5\left(\frac{20}{15}-\frac{9}{15}\right)+\frac{25}{25-1}$$

Since \frac{20}{15} and \frac{9}{15} have the same denominator, subtract them by subtracting their numerators.

$$5\times \frac{20-9}{15}+\frac{25}{25-1}$$

Subtract 9 from 20 to get 11.

$$5\times \frac{11}{15}+\frac{25}{25-1}$$

Express 5\times \frac{11}{15} as a single fraction.

$$\frac{5\times 11}{15}+\frac{25}{25-1}$$

Multiply 5 and 11 to get 55.

$$\frac{55}{15}+\frac{25}{25-1}$$

Reduce the fraction \frac{55}{15} to lowest terms by extracting and canceling out 5.

$$\frac{11}{3}+\frac{25}{25-1}$$

Subtract 1 from 25 to get 24.

$$\frac{11}{3}+\frac{25}{24}$$

Least common multiple of 3 and 24 is 24. Convert \frac{11}{3} and \frac{25}{24} to fractions with denominator 24.

$$\frac{88}{24}+\frac{25}{24}$$

Since \frac{88}{24} and \frac{25}{24} have the same denominator, add them by adding their numerators.

$$\frac{88+25}{24}$$

Add 88 and 25 to get 113.

$$\frac{113}{24}$$

Factor

$$\frac{113}{2 ^ {3} \cdot 3} = 4\frac{17}{24} = 4.708333333333333$$