Solve varphi(20)=20(1-1/4)(1-1/5)

$$\varphi ( 20 ) = 20 ( 1 - \frac { 1 } { 4 } ) ( 1 - \frac { 1 } { 5 } )$$

Evaluate

$$12$$

Solution Steps

Convert 1 to fraction \frac{4}{4}.

$$20\left(\frac{4}{4}-\frac{1}{4}\right)\left(1-\frac{1}{5}\right)$$

Since \frac{4}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$20\times \frac{4-1}{4}\left(1-\frac{1}{5}\right)$$

Subtract 1 from 4 to get 3.

$$20\times \frac{3}{4}\left(1-\frac{1}{5}\right)$$

Express 20\times \frac{3}{4} as a single fraction.

$$\frac{20\times 3}{4}\left(1-\frac{1}{5}\right)$$

Multiply 20 and 3 to get 60.

$$\frac{60}{4}\left(1-\frac{1}{5}\right)$$

Divide 60 by 4 to get 15.

$$15\left(1-\frac{1}{5}\right)$$

Convert 1 to fraction \frac{5}{5}.

$$15\left(\frac{5}{5}-\frac{1}{5}\right)$$

Since \frac{5}{5} and \frac{1}{5} have the same denominator, subtract them by subtracting their numerators.

$$15\times \frac{5-1}{5}$$

Subtract 1 from 5 to get 4.

$$15\times \frac{4}{5}$$

Express 15\times \frac{4}{5} as a single fraction.

$$\frac{15\times 4}{5}$$

Multiply 15 and 4 to get 60.

$$\frac{60}{5}$$

Divide 60 by 5 to get 12.

$$12$$

Factor

$$2^{2}\times 3$$