Solve (1+1/1)(1+1/2)(1+1/3)(1+1/4)(1+frac{1}{5})(1+frac{1}{6})

$$( 1 + \frac { 1 } { 1 } ) ( 1 + \frac { 1 } { 2 } ) ( 1 + \frac { 1 } { 3 } ) ( 1 + \frac { 1 } { 4 } ) ( 1 + \frac { 1 } { 5 } ) ( 1 + \frac { 1 } { 6 } )$$

Evaluate

$$7$$

Solution Steps

Divide 1 by 1 to get 1.

$$\left(1+1\right)\left(1+\frac{1}{2}\right)\left(1+\frac{1}{3}\right)\left(1+\frac{1}{4}\right)\left(1+\frac{1}{5}\right)\left(1+\frac{1}{6}\right)$$

Add 1 and 1 to get 2.

$$2\left(1+\frac{1}{2}\right)\left(1+\frac{1}{3}\right)\left(1+\frac{1}{4}\right)\left(1+\frac{1}{5}\right)\left(1+\frac{1}{6}\right)$$

Convert 1 to fraction \frac{2}{2}.

$$2\left(\frac{2}{2}+\frac{1}{2}\right)\left(1+\frac{1}{3}\right)\left(1+\frac{1}{4}\right)\left(1+\frac{1}{5}\right)\left(1+\frac{1}{6}\right)$$

Since \frac{2}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$2\times \frac{2+1}{2}\left(1+\frac{1}{3}\right)\left(1+\frac{1}{4}\right)\left(1+\frac{1}{5}\right)\left(1+\frac{1}{6}\right)$$

Add 2 and 1 to get 3.

$$2\times \frac{3}{2}\left(1+\frac{1}{3}\right)\left(1+\frac{1}{4}\right)\left(1+\frac{1}{5}\right)\left(1+\frac{1}{6}\right)$$

Cancel out 2 and 2.

$$3\left(1+\frac{1}{3}\right)\left(1+\frac{1}{4}\right)\left(1+\frac{1}{5}\right)\left(1+\frac{1}{6}\right)$$

Convert 1 to fraction \frac{3}{3}.

$$3\left(\frac{3}{3}+\frac{1}{3}\right)\left(1+\frac{1}{4}\right)\left(1+\frac{1}{5}\right)\left(1+\frac{1}{6}\right)$$

Since \frac{3}{3} and \frac{1}{3} have the same denominator, add them by adding their numerators.

$$3\times \frac{3+1}{3}\left(1+\frac{1}{4}\right)\left(1+\frac{1}{5}\right)\left(1+\frac{1}{6}\right)$$

Add 3 and 1 to get 4.

$$3\times \frac{4}{3}\left(1+\frac{1}{4}\right)\left(1+\frac{1}{5}\right)\left(1+\frac{1}{6}\right)$$

Cancel out 3 and 3.

$$4\left(1+\frac{1}{4}\right)\left(1+\frac{1}{5}\right)\left(1+\frac{1}{6}\right)$$

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

$$4\left(\frac{4}{4}+\frac{1}{4}\right)\left(1+\frac{1}{5}\right)\left(1+\frac{1}{6}\right)$$

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

$$4\times \frac{4+1}{4}\left(1+\frac{1}{5}\right)\left(1+\frac{1}{6}\right)$$

Add 4 and 1 to get 5.

$$4\times \frac{5}{4}\left(1+\frac{1}{5}\right)\left(1+\frac{1}{6}\right)$$

Cancel out 4 and 4.

$$5\left(1+\frac{1}{5}\right)\left(1+\frac{1}{6}\right)$$

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

$$5\left(\frac{5}{5}+\frac{1}{5}\right)\left(1+\frac{1}{6}\right)$$

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

$$5\times \frac{5+1}{5}\left(1+\frac{1}{6}\right)$$

Add 5 and 1 to get 6.

$$5\times \frac{6}{5}\left(1+\frac{1}{6}\right)$$

Cancel out 5 and 5.

$$6\left(1+\frac{1}{6}\right)$$

Convert 1 to fraction \frac{6}{6}.

$$6\left(\frac{6}{6}+\frac{1}{6}\right)$$

Since \frac{6}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$6\times \frac{6+1}{6}$$

Add 6 and 1 to get 7.

$$6\times \frac{7}{6}$$

Cancel out 6 and 6.

$$7$$

Factor

$$7$$