Solve 564/7*242/5-232/5*564/7=?

$$56 \frac { 4 } { 7 } \times 24 \frac { 2 } { 5 } - 23 \frac { 2 } { 5 } \times 56 \frac { 4 } { 7 } = ?$$

Evaluate

$$\frac{396}{7}\approx 56.571428571$$

Solution Steps

Multiply 56 and 7 to get 392.

$$\frac{392+4}{7}\times \frac{24\times 5+2}{5}-\frac{23\times 5+2}{5}\times \frac{56\times 7+4}{7}$$

Add 392 and 4 to get 396.

$$\frac{396}{7}\times \frac{24\times 5+2}{5}-\frac{23\times 5+2}{5}\times \frac{56\times 7+4}{7}$$

Multiply 24 and 5 to get 120.

$$\frac{396}{7}\times \frac{120+2}{5}-\frac{23\times 5+2}{5}\times \frac{56\times 7+4}{7}$$

Add 120 and 2 to get 122.

$$\frac{396}{7}\times \frac{122}{5}-\frac{23\times 5+2}{5}\times \frac{56\times 7+4}{7}$$

Multiply \frac{396}{7} times \frac{122}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{396\times 122}{7\times 5}-\frac{23\times 5+2}{5}\times \frac{56\times 7+4}{7}$$

Do the multiplications in the fraction \frac{396\times 122}{7\times 5}.

$$\frac{48312}{35}-\frac{23\times 5+2}{5}\times \frac{56\times 7+4}{7}$$

Multiply 23 and 5 to get 115.

$$\frac{48312}{35}-\frac{115+2}{5}\times \frac{56\times 7+4}{7}$$

Add 115 and 2 to get 117.

$$\frac{48312}{35}-\frac{117}{5}\times \frac{56\times 7+4}{7}$$

Multiply 56 and 7 to get 392.

$$\frac{48312}{35}-\frac{117}{5}\times \frac{392+4}{7}$$

Add 392 and 4 to get 396.

$$\frac{48312}{35}-\frac{117}{5}\times \frac{396}{7}$$

Multiply \frac{117}{5} times \frac{396}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{48312}{35}-\frac{117\times 396}{5\times 7}$$

Do the multiplications in the fraction \frac{117\times 396}{5\times 7}.

$$\frac{48312}{35}-\frac{46332}{35}$$

Since \frac{48312}{35} and \frac{46332}{35} have the same denominator, subtract them by subtracting their numerators.

$$\frac{48312-46332}{35}$$

Subtract 46332 from 48312 to get 1980.

$$\frac{1980}{35}$$

Reduce the fraction \frac{1980}{35} to lowest terms by extracting and canceling out 5.

$$\frac{396}{7}$$

Factor

$$\frac{2 ^ {2} \cdot 3 ^ {2} \cdot 11}{7} = 56\frac{4}{7} = 56.57142857142857$$