Solve 1-3/1-1{1-frac{1/3}}=

$$1 - \frac { 3 } { 1 - \frac { 1 } { 1 - \frac { 1 } { 3 } } } =$$

Evaluate

$$7$$

Solution Steps

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

$$1-\frac{3}{1-\frac{1}{\frac{3}{3}-\frac{1}{3}}}$$

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

$$1-\frac{3}{1-\frac{1}{\frac{3-1}{3}}}$$

Subtract 1 from 3 to get 2.

$$1-\frac{3}{1-\frac{1}{\frac{2}{3}}}$$

Divide 1 by \frac{2}{3} by multiplying 1 by the reciprocal of \frac{2}{3}.

$$1-\frac{3}{1-1\times \frac{3}{2}}$$

Multiply 1 and \frac{3}{2} to get \frac{3}{2}.

$$1-\frac{3}{1-\frac{3}{2}}$$

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

$$1-\frac{3}{\frac{2}{2}-\frac{3}{2}}$$

Since \frac{2}{2} and \frac{3}{2} have the same denominator, subtract them by subtracting their numerators.

$$1-\frac{3}{\frac{2-3}{2}}$$

Subtract 3 from 2 to get -1.

$$1-\frac{3}{-\frac{1}{2}}$$

Divide 3 by -\frac{1}{2} by multiplying 3 by the reciprocal of -\frac{1}{2}.

$$1-3\left(-2\right)$$

Multiply 3 and -2 to get -6.

$$1-\left(-6\right)$$

The opposite of -6 is 6.

$$1+6$$

Add 1 and 6 to get 7.

$$7$$

Factor

$$7$$