Solve 7-41/6div62/3

$$7 - 4 \frac { 1 } { 6 } \div 6 \frac { 2 } { 3 }$$

Evaluate

$$\frac{51}{8}=6.375$$

Solution Steps

Divide \frac{4\times 6+1}{6} by \frac{6\times 3+2}{3} by multiplying \frac{4\times 6+1}{6} by the reciprocal of \frac{6\times 3+2}{3}.

$$7-\frac{\left(4\times 6+1\right)\times 3}{6\left(6\times 3+2\right)}$$

Cancel out 3 in both numerator and denominator.

$$7-\frac{1+4\times 6}{2\left(2+3\times 6\right)}$$

Multiply 4 and 6 to get 24.

$$7-\frac{1+24}{2\left(2+3\times 6\right)}$$

Add 1 and 24 to get 25.

$$7-\frac{25}{2\left(2+3\times 6\right)}$$

Multiply 3 and 6 to get 18.

$$7-\frac{25}{2\left(2+18\right)}$$

Add 2 and 18 to get 20.

$$7-\frac{25}{2\times 20}$$

Multiply 2 and 20 to get 40.

$$7-\frac{25}{40}$$

Reduce the fraction \frac{25}{40} to lowest terms by extracting and canceling out 5.

$$7-\frac{5}{8}$$

Convert 7 to fraction \frac{56}{8}.

$$\frac{56}{8}-\frac{5}{8}$$

Since \frac{56}{8} and \frac{5}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{56-5}{8}$$

Subtract 5 from 56 to get 51.

$$\frac{51}{8}$$

Factor

$$\frac{3 \cdot 17}{2 ^ {3}} = 6\frac{3}{8} = 6.375$$