Solve 21/2div21/4

$$2 \frac { 1 } { 2 } \div 2 \frac { 1 } { 4 }$$

Evaluate

$$\frac{10}{9}\approx 1.111111111$$

Solution Steps

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

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

Cancel out 2 in both numerator and denominator.

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

Multiply 2 and 2 to get 4.

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

Add 1 and 4 to get 5.

$$\frac{2\times 5}{1+2\times 4}$$

Multiply 2 and 5 to get 10.

$$\frac{10}{1+2\times 4}$$

Multiply 2 and 4 to get 8.

$$\frac{10}{1+8}$$

Add 1 and 8 to get 9.

$$\frac{10}{9}$$

Factor

$$\frac{2 \cdot 5}{3 ^ {2}} = 1\frac{1}{9} = 1.1111111111111112$$