Solve 75div63/7*8/21text{of}3/5*1/2

$$75 \div 6 \frac { 3 } { 7 } \times \frac { 8 } { 21 } \text { of } \frac { 3 } { 5 } \times \frac { 1 } { 2 }$$

Evaluate

$$\frac{4}{3}\approx 1.333333333$$

Solution Steps

Divide 75 by \frac{6\times 7+3}{7} by multiplying 75 by the reciprocal of \frac{6\times 7+3}{7}.

$$\frac{75\times 7}{6\times 7+3}\times \frac{8}{21}\times \frac{3}{5}\times \frac{1}{2}$$

Multiply 75 and 7 to get 525.

$$\frac{525}{6\times 7+3}\times \frac{8}{21}\times \frac{3}{5}\times \frac{1}{2}$$

Multiply 6 and 7 to get 42.

$$\frac{525}{42+3}\times \frac{8}{21}\times \frac{3}{5}\times \frac{1}{2}$$

Add 42 and 3 to get 45.

$$\frac{525}{45}\times \frac{8}{21}\times \frac{3}{5}\times \frac{1}{2}$$

Reduce the fraction \frac{525}{45} to lowest terms by extracting and canceling out 15.

$$\frac{35}{3}\times \frac{8}{21}\times \frac{3}{5}\times \frac{1}{2}$$

Multiply \frac{35}{3} times \frac{8}{21} by multiplying numerator times numerator and denominator times denominator.

$$\frac{35\times 8}{3\times 21}\times \frac{3}{5}\times \frac{1}{2}$$

Do the multiplications in the fraction \frac{35\times 8}{3\times 21}.

$$\frac{280}{63}\times \frac{3}{5}\times \frac{1}{2}$$

Reduce the fraction \frac{280}{63} to lowest terms by extracting and canceling out 7.

$$\frac{40}{9}\times \frac{3}{5}\times \frac{1}{2}$$

Multiply \frac{40}{9} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{40\times 3}{9\times 5}\times \frac{1}{2}$$

Do the multiplications in the fraction \frac{40\times 3}{9\times 5}.

$$\frac{120}{45}\times \frac{1}{2}$$

Reduce the fraction \frac{120}{45} to lowest terms by extracting and canceling out 15.

$$\frac{8}{3}\times \frac{1}{2}$$

Multiply \frac{8}{3} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8\times 1}{3\times 2}$$

Do the multiplications in the fraction \frac{8\times 1}{3\times 2}.

$$\frac{8}{6}$$

Reduce the fraction \frac{8}{6} to lowest terms by extracting and canceling out 2.

$$\frac{4}{3}$$

Factor

$$\frac{2 ^ {2}}{3} = 1\frac{1}{3} = 1.3333333333333333$$