Solve 12/3+52/5*5-7*(52/5-12/3)

$$1 \frac { 2 } { 3 } + 5 \frac { 2 } { 5 } \cdot 5 - 7 \cdot ( 5 \frac { 2 } { 5 } - 1 \frac { 2 } { 3 } )$$

Evaluate

$$\frac{38}{15}\approx 2.533333333$$

Solution Steps

Multiply 1 and 3 to get 3.

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

Add 3 and 2 to get 5.

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

Multiply 5 and 5 to get 25.

$$\frac{5}{3}+\frac{25+2}{5}\times 5-7\left(\frac{5\times 5+2}{5}-\frac{1\times 3+2}{3}\right)$$

Add 25 and 2 to get 27.

$$\frac{5}{3}+\frac{27}{5}\times 5-7\left(\frac{5\times 5+2}{5}-\frac{1\times 3+2}{3}\right)$$

Cancel out 5 and 5.

$$\frac{5}{3}+27-7\left(\frac{5\times 5+2}{5}-\frac{1\times 3+2}{3}\right)$$

Convert 27 to fraction \frac{81}{3}.

$$\frac{5}{3}+\frac{81}{3}-7\left(\frac{5\times 5+2}{5}-\frac{1\times 3+2}{3}\right)$$

Since \frac{5}{3} and \frac{81}{3} have the same denominator, add them by adding their numerators.

$$\frac{5+81}{3}-7\left(\frac{5\times 5+2}{5}-\frac{1\times 3+2}{3}\right)$$

Add 5 and 81 to get 86.

$$\frac{86}{3}-7\left(\frac{5\times 5+2}{5}-\frac{1\times 3+2}{3}\right)$$

Multiply 5 and 5 to get 25.

$$\frac{86}{3}-7\left(\frac{25+2}{5}-\frac{1\times 3+2}{3}\right)$$

Add 25 and 2 to get 27.

$$\frac{86}{3}-7\left(\frac{27}{5}-\frac{1\times 3+2}{3}\right)$$

Multiply 1 and 3 to get 3.

$$\frac{86}{3}-7\left(\frac{27}{5}-\frac{3+2}{3}\right)$$

Add 3 and 2 to get 5.

$$\frac{86}{3}-7\left(\frac{27}{5}-\frac{5}{3}\right)$$

Least common multiple of 5 and 3 is 15. Convert \frac{27}{5} and \frac{5}{3} to fractions with denominator 15.

$$\frac{86}{3}-7\left(\frac{81}{15}-\frac{25}{15}\right)$$

Since \frac{81}{15} and \frac{25}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{86}{3}-7\times \frac{81-25}{15}$$

Subtract 25 from 81 to get 56.

$$\frac{86}{3}-7\times \frac{56}{15}$$

Express 7\times \frac{56}{15} as a single fraction.

$$\frac{86}{3}-\frac{7\times 56}{15}$$

Multiply 7 and 56 to get 392.

$$\frac{86}{3}-\frac{392}{15}$$

Least common multiple of 3 and 15 is 15. Convert \frac{86}{3} and \frac{392}{15} to fractions with denominator 15.

$$\frac{430}{15}-\frac{392}{15}$$

Since \frac{430}{15} and \frac{392}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{430-392}{15}$$

Subtract 392 from 430 to get 38.

$$\frac{38}{15}$$

Factor

$$\frac{2 \cdot 19}{3 \cdot 5} = 2\frac{8}{15} = 2.533333333333333$$