Solve 71/3div51/2div13/4

$$7 \frac { 1 } { 3 } \div 5 \frac { 1 } { 2 } \div 1 \frac { 3 } { 4 }$$

Evaluate

$$\frac{16}{21}\approx 0.761904762$$

Solution Steps

Divide \frac{\frac{7\times 3+1}{3}}{\frac{5\times 2+1}{2}} by \frac{1\times 4+3}{4} by multiplying \frac{\frac{7\times 3+1}{3}}{\frac{5\times 2+1}{2}} by the reciprocal of \frac{1\times 4+3}{4}.

$$\frac{\frac{7\times 3+1}{3}\times 4}{\frac{5\times 2+1}{2}\left(1\times 4+3\right)}$$

Multiply 7 and 3 to get 21.

$$\frac{\frac{21+1}{3}\times 4}{\frac{5\times 2+1}{2}\left(1\times 4+3\right)}$$

Add 21 and 1 to get 22.

$$\frac{\frac{22}{3}\times 4}{\frac{5\times 2+1}{2}\left(1\times 4+3\right)}$$

Express \frac{22}{3}\times 4 as a single fraction.

$$\frac{\frac{22\times 4}{3}}{\frac{5\times 2+1}{2}\left(1\times 4+3\right)}$$

Multiply 22 and 4 to get 88.

$$\frac{\frac{88}{3}}{\frac{5\times 2+1}{2}\left(1\times 4+3\right)}$$

Multiply 5 and 2 to get 10.

$$\frac{\frac{88}{3}}{\frac{10+1}{2}\left(1\times 4+3\right)}$$

Add 10 and 1 to get 11.

$$\frac{\frac{88}{3}}{\frac{11}{2}\left(1\times 4+3\right)}$$

Multiply 1 and 4 to get 4.

$$\frac{\frac{88}{3}}{\frac{11}{2}\left(4+3\right)}$$

Add 4 and 3 to get 7.

$$\frac{\frac{88}{3}}{\frac{11}{2}\times 7}$$

Express \frac{11}{2}\times 7 as a single fraction.

$$\frac{\frac{88}{3}}{\frac{11\times 7}{2}}$$

Multiply 11 and 7 to get 77.

$$\frac{\frac{88}{3}}{\frac{77}{2}}$$

Divide \frac{88}{3} by \frac{77}{2} by multiplying \frac{88}{3} by the reciprocal of \frac{77}{2}.

$$\frac{88}{3}\times \frac{2}{77}$$

Multiply \frac{88}{3} times \frac{2}{77} by multiplying numerator times numerator and denominator times denominator.

$$\frac{88\times 2}{3\times 77}$$

Do the multiplications in the fraction \frac{88\times 2}{3\times 77}.

$$\frac{176}{231}$$

Reduce the fraction \frac{176}{231} to lowest terms by extracting and canceling out 11.

$$\frac{16}{21}$$

Factor

$$\frac{2 ^ {4}}{3 \cdot 7} = 0.7619047619047619$$