Solve 1-1/2/1-frac{1{1-335}}=0.42

$$\frac { 1 - \frac { 1 } { 2 } } { 1 - \frac { 1 } { 1 - 335 } } = 0.42$$

Verify

Solution Steps

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

$$\frac{\frac{2}{2}-\frac{1}{2}}{1-\frac{1}{1-335}}=0.42$$

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

$$\frac{\frac{2-1}{2}}{1-\frac{1}{1-335}}=0.42$$

Subtract 1 from 2 to get 1.

$$\frac{\frac{1}{2}}{1-\frac{1}{1-335}}=0.42$$

Subtract 335 from 1 to get -334.

$$\frac{\frac{1}{2}}{1-\frac{1}{-334}}=0.42$$

Fraction \frac{1}{-334} can be rewritten as -\frac{1}{334} by extracting the negative sign.

$$\frac{\frac{1}{2}}{1-\left(-\frac{1}{334}\right)}=0.42$$

The opposite of -\frac{1}{334} is \frac{1}{334}.

$$\frac{\frac{1}{2}}{1+\frac{1}{334}}=0.42$$

Convert 1 to fraction \frac{334}{334}.

$$\frac{\frac{1}{2}}{\frac{334}{334}+\frac{1}{334}}=0.42$$

Since \frac{334}{334} and \frac{1}{334} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1}{2}}{\frac{334+1}{334}}=0.42$$

Add 334 and 1 to get 335.

$$\frac{\frac{1}{2}}{\frac{335}{334}}=0.42$$

Divide \frac{1}{2} by \frac{335}{334} by multiplying \frac{1}{2} by the reciprocal of \frac{335}{334}.

$$\frac{1}{2}\times \frac{334}{335}=0.42$$

Multiply \frac{1}{2} times \frac{334}{335} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 334}{2\times 335}=0.42$$

Do the multiplications in the fraction \frac{1\times 334}{2\times 335}.

$$\frac{334}{670}=0.42$$

Reduce the fraction \frac{334}{670} to lowest terms by extracting and canceling out 2.

$$\frac{167}{335}=0.42$$

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.

$$\frac{167}{335}=\frac{21}{50}$$

Least common multiple of 335 and 50 is 3350. Convert \frac{167}{335} and \frac{21}{50} to fractions with denominator 3350.

$$\frac{1670}{3350}=\frac{1407}{3350}$$

Compare \frac{1670}{3350} and \frac{1407}{3350}.

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