Solve 1/3+3/4*1/3-1/4*frac{2}{3}+1

$$\frac { 1 } { 3 } + \frac { 3 } { 4 } \cdot \frac { 1 } { 3 } - \frac { 1 } { 4 } \cdot \frac { 2 } { 3 } + 1$$

Evaluate

$$\frac{17}{12}\approx 1.416666667$$

Solution Steps

Multiply \frac{3}{4} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{3}+\frac{3\times 1}{4\times 3}-\frac{1}{4}\times \frac{2}{3}+1$$

Cancel out 3 in both numerator and denominator.

$$\frac{1}{3}+\frac{1}{4}-\frac{1}{4}\times \frac{2}{3}+1$$

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

$$\frac{4}{12}+\frac{3}{12}-\frac{1}{4}\times \frac{2}{3}+1$$

Since \frac{4}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

$$\frac{4+3}{12}-\frac{1}{4}\times \frac{2}{3}+1$$

Add 4 and 3 to get 7.

$$\frac{7}{12}-\frac{1}{4}\times \frac{2}{3}+1$$

Multiply \frac{1}{4} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7}{12}-\frac{1\times 2}{4\times 3}+1$$

Do the multiplications in the fraction \frac{1\times 2}{4\times 3}.

$$\frac{7}{12}-\frac{2}{12}+1$$

Since \frac{7}{12} and \frac{2}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7-2}{12}+1$$

Subtract 2 from 7 to get 5.

$$\frac{5}{12}+1$$

Convert 1 to fraction \frac{12}{12}.

$$\frac{5}{12}+\frac{12}{12}$$

Since \frac{5}{12} and \frac{12}{12} have the same denominator, add them by adding their numerators.

$$\frac{5+12}{12}$$

Add 5 and 12 to get 17.

$$\frac{17}{12}$$

Factor

$$\frac{17}{2 ^ {2} \cdot 3} = 1\frac{5}{12} = 1.4166666666666667$$