Solve 3-111/12div24/21

$$3- 1 \frac { 11 } { 12 } \div 2 \frac { 4 } { 21 }$$

Evaluate

$$\frac{17}{8}=2.125$$

Solution Steps

Divide \frac{1\times 12+11}{12} by \frac{2\times 21+4}{21} by multiplying \frac{1\times 12+11}{12} by the reciprocal of \frac{2\times 21+4}{21}.

$$3-\frac{\left(1\times 12+11\right)\times 21}{12\left(2\times 21+4\right)}$$

Cancel out 3 in both numerator and denominator.

$$3-\frac{7\left(11+12\right)}{4\left(4+2\times 21\right)}$$

Add 11 and 12 to get 23.

$$3-\frac{7\times 23}{4\left(4+2\times 21\right)}$$

Multiply 7 and 23 to get 161.

$$3-\frac{161}{4\left(4+2\times 21\right)}$$

Multiply 2 and 21 to get 42.

$$3-\frac{161}{4\left(4+42\right)}$$

Add 4 and 42 to get 46.

$$3-\frac{161}{4\times 46}$$

Multiply 4 and 46 to get 184.

$$3-\frac{161}{184}$$

Reduce the fraction \frac{161}{184} to lowest terms by extracting and canceling out 23.

$$3-\frac{7}{8}$$

Convert 3 to fraction \frac{24}{8}.

$$\frac{24}{8}-\frac{7}{8}$$

Since \frac{24}{8} and \frac{7}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{24-7}{8}$$

Subtract 7 from 24 to get 17.

$$\frac{17}{8}$$

Factor

$$\frac{17}{2 ^ {3}} = 2\frac{1}{8} = 2.125$$