Solve 1/28-1/21.78=1/f

$$\frac{ 1 }{ 28 } - \frac{ 1 }{ 21.78 } = \frac{ 1 }{ f }$$

Solve for f

$$f = -\frac{30492}{311} = -98\frac{14}{311} \approx -98.045016077$$

Steps for Solving Linear Equation

Variable f cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 28f, the least common multiple of 28,f.

$$28f\times \frac{1}{28}-28f\times \frac{1}{21.78}=28$$

Cancel out 28 and 28.

$$f-28f\times \frac{1}{21.78}=28$$

Expand \frac{1}{21.78} by multiplying both numerator and the denominator by 100.

$$f-28f\times \frac{100}{2178}=28$$

Reduce the fraction \frac{100}{2178} to lowest terms by extracting and canceling out 2.

$$f-28f\times \frac{50}{1089}=28$$

Express 28\times \frac{50}{1089} as a single fraction.

$$f-\frac{28\times 50}{1089}f=28$$

Multiply 28 and 50 to get 1400.

$$f-\frac{1400}{1089}f=28$$

Combine f and -\frac{1400}{1089}f to get -\frac{311}{1089}f.

$$-\frac{311}{1089}f=28$$

Multiply both sides by -\frac{1089}{311}, the reciprocal of -\frac{311}{1089}.

$$f=28\left(-\frac{1089}{311}\right)$$

Express 28\left(-\frac{1089}{311}\right) as a single fraction.

$$f=\frac{28\left(-1089\right)}{311}$$

Multiply 28 and -1089 to get -30492.

$$f=\frac{-30492}{311}$$

Fraction \frac{-30492}{311} can be rewritten as -\frac{30492}{311} by extracting the negative sign.

$$f=-\frac{30492}{311}$$