Solve 1/1-0.42*(1-frac{1{1.335})}=

$$\frac { 1 } { 1 - 0.42 \times ( 1 - \frac { 1 } { 1.335 } ) } =$$

Evaluate

$$\frac{4450}{3981}\approx 1.117809596$$

Solution Steps

Expand \frac{1}{1.335} by multiplying both numerator and the denominator by 1000.

$$\frac{1}{1-0.42\left(1-\frac{1000}{1335}\right)}$$

Reduce the fraction \frac{1000}{1335} to lowest terms by extracting and canceling out 5.

$$\frac{1}{1-0.42\left(1-\frac{200}{267}\right)}$$

Convert 1 to fraction \frac{267}{267}.

$$\frac{1}{1-0.42\left(\frac{267}{267}-\frac{200}{267}\right)}$$

Since \frac{267}{267} and \frac{200}{267} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{1-0.42\times \frac{267-200}{267}}$$

Subtract 200 from 267 to get 67.

$$\frac{1}{1-0.42\times \frac{67}{267}}$$

Convert decimal number 0.42 to fraction \frac{42}{100}. Reduce the fraction \frac{42}{100} to lowest terms by extracting and canceling out 2.

$$\frac{1}{1-\frac{21}{50}\times \frac{67}{267}}$$

Multiply \frac{21}{50} times \frac{67}{267} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{1-\frac{21\times 67}{50\times 267}}$$

Do the multiplications in the fraction \frac{21\times 67}{50\times 267}.

$$\frac{1}{1-\frac{1407}{13350}}$$

Reduce the fraction \frac{1407}{13350} to lowest terms by extracting and canceling out 3.

$$\frac{1}{1-\frac{469}{4450}}$$

Convert 1 to fraction \frac{4450}{4450}.

$$\frac{1}{\frac{4450}{4450}-\frac{469}{4450}}$$

Since \frac{4450}{4450} and \frac{469}{4450} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{\frac{4450-469}{4450}}$$

Subtract 469 from 4450 to get 3981.

$$\frac{1}{\frac{3981}{4450}}$$

Divide 1 by \frac{3981}{4450} by multiplying 1 by the reciprocal of \frac{3981}{4450}.

$$1\times \frac{4450}{3981}$$

Multiply 1 and \frac{4450}{3981} to get \frac{4450}{3981}.

$$\frac{4450}{3981}$$

Factor

$$\frac{2 \cdot 89 \cdot 5 ^ {2}}{3 \cdot 1327} = 1\frac{469}{3981} = 1.1178095955790002$$