Solve =1/3div(2/3-2/35)*3/15

$$= \frac { 1 } { 3 } \div ( \frac { 2 } { 3 } - \frac { 2 } { 35 } ) \times \frac { 3 } { 15 }$$

Evaluate

$$\frac{7}{64}=0.109375$$

Solution Steps

Least common multiple of 3 and 35 is 105. Convert \frac{2}{3} and \frac{2}{35} to fractions with denominator 105.

$$\frac{\frac{1}{3}}{\frac{70}{105}-\frac{6}{105}}\times \frac{3}{15}$$

Since \frac{70}{105} and \frac{6}{105} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1}{3}}{\frac{70-6}{105}}\times \frac{3}{15}$$

Subtract 6 from 70 to get 64.

$$\frac{\frac{1}{3}}{\frac{64}{105}}\times \frac{3}{15}$$

Divide \frac{1}{3} by \frac{64}{105} by multiplying \frac{1}{3} by the reciprocal of \frac{64}{105}.

$$\frac{1}{3}\times \frac{105}{64}\times \frac{3}{15}$$

Multiply \frac{1}{3} times \frac{105}{64} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 105}{3\times 64}\times \frac{3}{15}$$

Do the multiplications in the fraction \frac{1\times 105}{3\times 64}.

$$\frac{105}{192}\times \frac{3}{15}$$

Reduce the fraction \frac{105}{192} to lowest terms by extracting and canceling out 3.

$$\frac{35}{64}\times \frac{3}{15}$$

Reduce the fraction \frac{3}{15} to lowest terms by extracting and canceling out 3.

$$\frac{35}{64}\times \frac{1}{5}$$

Multiply \frac{35}{64} times \frac{1}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{35\times 1}{64\times 5}$$

Do the multiplications in the fraction \frac{35\times 1}{64\times 5}.

$$\frac{35}{320}$$

Reduce the fraction \frac{35}{320} to lowest terms by extracting and canceling out 5.

$$\frac{7}{64}$$

Factor

$$\frac{7}{2 ^ {6}} = 0.109375$$