Solve 1/3-3/frac{1{0.9375}-1}

$$\frac{ \frac{ 1 }{ 3 } -3 }{ \frac{ 1 }{ 0.9375 } -1 }$$

Evaluate

$$-40$$

Solution Steps

Convert 3 to fraction \frac{9}{3}.

$$\frac{\frac{1}{3}-\frac{9}{3}}{\frac{1}{0.9375}-1}$$

Since \frac{1}{3} and \frac{9}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1-9}{3}}{\frac{1}{0.9375}-1}$$

Subtract 9 from 1 to get -8.

$$\frac{-\frac{8}{3}}{\frac{1}{0.9375}-1}$$

Expand \frac{1}{0.9375} by multiplying both numerator and the denominator by 10000.

$$\frac{-\frac{8}{3}}{\frac{10000}{9375}-1}$$

Reduce the fraction \frac{10000}{9375} to lowest terms by extracting and canceling out 625.

$$\frac{-\frac{8}{3}}{\frac{16}{15}-1}$$

Convert 1 to fraction \frac{15}{15}.

$$\frac{-\frac{8}{3}}{\frac{16}{15}-\frac{15}{15}}$$

Since \frac{16}{15} and \frac{15}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{8}{3}}{\frac{16-15}{15}}$$

Subtract 15 from 16 to get 1.

$$\frac{-\frac{8}{3}}{\frac{1}{15}}$$

Divide -\frac{8}{3} by \frac{1}{15} by multiplying -\frac{8}{3} by the reciprocal of \frac{1}{15}.

$$-\frac{8}{3}\times 15$$

Express -\frac{8}{3}\times 15 as a single fraction.

$$\frac{-8\times 15}{3}$$

Multiply -8 and 15 to get -120.

$$\frac{-120}{3}$$

Divide -120 by 3 to get -40.

$$-40$$

Factor

$$-40$$