Solve 3-11/12div21/21

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

Evaluate

$$\frac{439}{172}\approx 2.552325581$$

Solution Steps

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

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

Cancel out 3 in both numerator and denominator.

$$3-\frac{7\times 11}{4\left(1+2\times 21\right)}$$

Multiply 7 and 11 to get 77.

$$3-\frac{77}{4\left(1+2\times 21\right)}$$

Multiply 2 and 21 to get 42.

$$3-\frac{77}{4\left(1+42\right)}$$

Add 1 and 42 to get 43.

$$3-\frac{77}{4\times 43}$$

Multiply 4 and 43 to get 172.

$$3-\frac{77}{172}$$

Convert 3 to fraction \frac{516}{172}.

$$\frac{516}{172}-\frac{77}{172}$$

Since \frac{516}{172} and \frac{77}{172} have the same denominator, subtract them by subtracting their numerators.

$$\frac{516-77}{172}$$

Subtract 77 from 516 to get 439.

$$\frac{439}{172}$$

Factor

$$\frac{439}{2 ^ {2} \cdot 43} = 2\frac{95}{172} = 2.552325581395349$$