Solve f(3/4-1/3)*(2-1/3)

$$f ( \frac { 3 } { 4 } - \frac { 1 } { 3 } ) \cdot ( 2 - \frac { 1 } { 3 } )$$

Evaluate

$$\frac{25f}{36}$$

Solution Steps

Least common multiple of 4 and 3 is 12. Convert \frac{3}{4} and \frac{1}{3} to fractions with denominator 12.

$$f\left(\frac{9}{12}-\frac{4}{12}\right)\left(2-\frac{1}{3}\right)$$

Since \frac{9}{12} and \frac{4}{12} have the same denominator, subtract them by subtracting their numerators.

$$f\times \frac{9-4}{12}\left(2-\frac{1}{3}\right)$$

Subtract 4 from 9 to get 5.

$$f\times \frac{5}{12}\left(2-\frac{1}{3}\right)$$

Convert 2 to fraction \frac{6}{3}.

$$f\times \frac{5}{12}\left(\frac{6}{3}-\frac{1}{3}\right)$$

Since \frac{6}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$f\times \frac{5}{12}\times \frac{6-1}{3}$$

Subtract 1 from 6 to get 5.

$$f\times \frac{5}{12}\times \frac{5}{3}$$

Multiply \frac{5}{12} times \frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

$$f\times \frac{5\times 5}{12\times 3}$$

Do the multiplications in the fraction \frac{5\times 5}{12\times 3}.

$$f\times \frac{25}{36}$$

Expand

$$\frac{25f}{36}$$

Solution Steps

Least common multiple of 4 and 3 is 12. Convert \frac{3}{4} and \frac{1}{3} to fractions with denominator 12.

$$f\left(\frac{9}{12}-\frac{4}{12}\right)\left(2-\frac{1}{3}\right)$$

Since \frac{9}{12} and \frac{4}{12} have the same denominator, subtract them by subtracting their numerators.

$$f\times \frac{9-4}{12}\left(2-\frac{1}{3}\right)$$

Subtract 4 from 9 to get 5.

$$f\times \frac{5}{12}\left(2-\frac{1}{3}\right)$$

Convert 2 to fraction \frac{6}{3}.

$$f\times \frac{5}{12}\left(\frac{6}{3}-\frac{1}{3}\right)$$

Since \frac{6}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$f\times \frac{5}{12}\times \frac{6-1}{3}$$

Subtract 1 from 6 to get 5.

$$f\times \frac{5}{12}\times \frac{5}{3}$$

Multiply \frac{5}{12} times \frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

$$f\times \frac{5\times 5}{12\times 3}$$

Do the multiplications in the fraction \frac{5\times 5}{12\times 3}.

$$f\times \frac{25}{36}$$