Solve 28/32div42/14div25/35*40/18*frac{24}{5}*8frac{1}{8}

$$\frac { 28 } { 32 } \div \frac { 42 } { 14 } \div \frac { 25 } { 35 } \cdot \frac { 40 } { 18 } \cdot \frac { 24 } { 5 } \cdot 8 \frac { 1 } { 8 }$$

Evaluate

$$\frac{637}{18}\approx 35.388888889$$

Solution Steps

Divide \frac{\frac{28}{32}}{\frac{42}{14}} by \frac{25}{35} by multiplying \frac{\frac{28}{32}}{\frac{42}{14}} by the reciprocal of \frac{25}{35}.

$$\frac{\frac{28}{32}\times 35}{\frac{42}{14}\times 25}\times \frac{40}{18}\times \frac{24}{5}\times \frac{8\times 8+1}{8}$$

Reduce the fraction \frac{28}{32} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{7}{8}\times 35}{\frac{42}{14}\times 25}\times \frac{40}{18}\times \frac{24}{5}\times \frac{8\times 8+1}{8}$$

Express \frac{7}{8}\times 35 as a single fraction.

$$\frac{\frac{7\times 35}{8}}{\frac{42}{14}\times 25}\times \frac{40}{18}\times \frac{24}{5}\times \frac{8\times 8+1}{8}$$

Multiply 7 and 35 to get 245.

$$\frac{\frac{245}{8}}{\frac{42}{14}\times 25}\times \frac{40}{18}\times \frac{24}{5}\times \frac{8\times 8+1}{8}$$

Divide 42 by 14 to get 3.

$$\frac{\frac{245}{8}}{3\times 25}\times \frac{40}{18}\times \frac{24}{5}\times \frac{8\times 8+1}{8}$$

Multiply 3 and 25 to get 75.

$$\frac{\frac{245}{8}}{75}\times \frac{40}{18}\times \frac{24}{5}\times \frac{8\times 8+1}{8}$$

Express \frac{\frac{245}{8}}{75} as a single fraction.

$$\frac{245}{8\times 75}\times \frac{40}{18}\times \frac{24}{5}\times \frac{8\times 8+1}{8}$$

Multiply 8 and 75 to get 600.

$$\frac{245}{600}\times \frac{40}{18}\times \frac{24}{5}\times \frac{8\times 8+1}{8}$$

Reduce the fraction \frac{245}{600} to lowest terms by extracting and canceling out 5.

$$\frac{49}{120}\times \frac{40}{18}\times \frac{24}{5}\times \frac{8\times 8+1}{8}$$

Reduce the fraction \frac{40}{18} to lowest terms by extracting and canceling out 2.

$$\frac{49}{120}\times \frac{20}{9}\times \frac{24}{5}\times \frac{8\times 8+1}{8}$$

Multiply \frac{49}{120} times \frac{20}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{49\times 20}{120\times 9}\times \frac{24}{5}\times \frac{8\times 8+1}{8}$$

Do the multiplications in the fraction \frac{49\times 20}{120\times 9}.

$$\frac{980}{1080}\times \frac{24}{5}\times \frac{8\times 8+1}{8}$$

Reduce the fraction \frac{980}{1080} to lowest terms by extracting and canceling out 20.

$$\frac{49}{54}\times \frac{24}{5}\times \frac{8\times 8+1}{8}$$

Multiply \frac{49}{54} times \frac{24}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{49\times 24}{54\times 5}\times \frac{8\times 8+1}{8}$$

Do the multiplications in the fraction \frac{49\times 24}{54\times 5}.

$$\frac{1176}{270}\times \frac{8\times 8+1}{8}$$

Reduce the fraction \frac{1176}{270} to lowest terms by extracting and canceling out 6.

$$\frac{196}{45}\times \frac{8\times 8+1}{8}$$

Multiply 8 and 8 to get 64.

$$\frac{196}{45}\times \frac{64+1}{8}$$

Add 64 and 1 to get 65.

$$\frac{196}{45}\times \frac{65}{8}$$

Multiply \frac{196}{45} times \frac{65}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{196\times 65}{45\times 8}$$

Do the multiplications in the fraction \frac{196\times 65}{45\times 8}.

$$\frac{12740}{360}$$

Reduce the fraction \frac{12740}{360} to lowest terms by extracting and canceling out 20.

$$\frac{637}{18}$$

Factor

$$\frac{7 ^ {2} \cdot 13}{2 \cdot 3 ^ {2}} = 35\frac{7}{18} = 35.388888888888886$$