Solve 11/2*11/3*11/4*11/5=?

$$1 \frac { 1 } { 2 } \times 1 \frac { 1 } { 3 } \times 1 \frac { 1 } { 4 } \times 1 \frac { 1 } { 5 } = ?$$

Evaluate

$$3$$

Solution Steps

Multiply 1 and 2 to get 2.

$$\frac{2+1}{2}\times \frac{1\times 3+1}{3}\times \frac{1\times 4+1}{4}\times \frac{1\times 5+1}{5}$$

Add 2 and 1 to get 3.

$$\frac{3}{2}\times \frac{1\times 3+1}{3}\times \frac{1\times 4+1}{4}\times \frac{1\times 5+1}{5}$$

Multiply 1 and 3 to get 3.

$$\frac{3}{2}\times \frac{3+1}{3}\times \frac{1\times 4+1}{4}\times \frac{1\times 5+1}{5}$$

Add 3 and 1 to get 4.

$$\frac{3}{2}\times \frac{4}{3}\times \frac{1\times 4+1}{4}\times \frac{1\times 5+1}{5}$$

Multiply \frac{3}{2} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 4}{2\times 3}\times \frac{1\times 4+1}{4}\times \frac{1\times 5+1}{5}$$

Cancel out 3 in both numerator and denominator.

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

Divide 4 by 2 to get 2.

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

Multiply 1 and 4 to get 4.

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

Add 4 and 1 to get 5.

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

Express 2\times \frac{5}{4} as a single fraction.

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

Multiply 2 and 5 to get 10.

$$\frac{10}{4}\times \frac{1\times 5+1}{5}$$

Reduce the fraction \frac{10}{4} to lowest terms by extracting and canceling out 2.

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

Multiply 1 and 5 to get 5.

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

Add 5 and 1 to get 6.

$$\frac{5}{2}\times \frac{6}{5}$$

Multiply \frac{5}{2} times \frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 6}{2\times 5}$$

Cancel out 5 in both numerator and denominator.

$$\frac{6}{2}$$

Divide 6 by 2 to get 3.

$$3$$

Factor

$$3$$