Solve 23/5*81/3+71/6*22/5=?

$$2 \frac { 3 } { 5 } \times 8 \frac { 1 } { 3 } + 7 \frac { 1 } { 6 } \times 2 \frac { 2 } { 5 } = ?$$

Evaluate

$$\frac{583}{15}\approx 38.866666667$$

Solution Steps

Multiply 2 and 5 to get 10.

$$\frac{10+3}{5}\times \frac{8\times 3+1}{3}+\frac{7\times 6+1}{6}\times \frac{2\times 5+2}{5}$$

Add 10 and 3 to get 13.

$$\frac{13}{5}\times \frac{8\times 3+1}{3}+\frac{7\times 6+1}{6}\times \frac{2\times 5+2}{5}$$

Multiply 8 and 3 to get 24.

$$\frac{13}{5}\times \frac{24+1}{3}+\frac{7\times 6+1}{6}\times \frac{2\times 5+2}{5}$$

Add 24 and 1 to get 25.

$$\frac{13}{5}\times \frac{25}{3}+\frac{7\times 6+1}{6}\times \frac{2\times 5+2}{5}$$

Multiply \frac{13}{5} times \frac{25}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13\times 25}{5\times 3}+\frac{7\times 6+1}{6}\times \frac{2\times 5+2}{5}$$

Do the multiplications in the fraction \frac{13\times 25}{5\times 3}.

$$\frac{325}{15}+\frac{7\times 6+1}{6}\times \frac{2\times 5+2}{5}$$

Reduce the fraction \frac{325}{15} to lowest terms by extracting and canceling out 5.

$$\frac{65}{3}+\frac{7\times 6+1}{6}\times \frac{2\times 5+2}{5}$$

Multiply 7 and 6 to get 42.

$$\frac{65}{3}+\frac{42+1}{6}\times \frac{2\times 5+2}{5}$$

Add 42 and 1 to get 43.

$$\frac{65}{3}+\frac{43}{6}\times \frac{2\times 5+2}{5}$$

Multiply 2 and 5 to get 10.

$$\frac{65}{3}+\frac{43}{6}\times \frac{10+2}{5}$$

Add 10 and 2 to get 12.

$$\frac{65}{3}+\frac{43}{6}\times \frac{12}{5}$$

Multiply \frac{43}{6} times \frac{12}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{65}{3}+\frac{43\times 12}{6\times 5}$$

Do the multiplications in the fraction \frac{43\times 12}{6\times 5}.

$$\frac{65}{3}+\frac{516}{30}$$

Reduce the fraction \frac{516}{30} to lowest terms by extracting and canceling out 6.

$$\frac{65}{3}+\frac{86}{5}$$

Least common multiple of 3 and 5 is 15. Convert \frac{65}{3} and \frac{86}{5} to fractions with denominator 15.

$$\frac{325}{15}+\frac{258}{15}$$

Since \frac{325}{15} and \frac{258}{15} have the same denominator, add them by adding their numerators.

$$\frac{325+258}{15}$$

Add 325 and 258 to get 583.

$$\frac{583}{15}$$

Factor

$$\frac{11 \cdot 53}{3 \cdot 5} = 38\frac{13}{15} = 38.86666666666667$$