Solve 2/3-3/4*4/11+1/3divfrac{3}{7}

$$\frac { 2 } { 3 } - \frac { 3 } { 4 } \times \frac { 4 } { 11 } + \frac { 1 } { 3 } \div \frac { 3 } { 7 }$$

Evaluate

$$\frac{116}{99}\approx 1.171717172$$

Solution Steps

Multiply \frac{3}{4} times \frac{4}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{3}-\frac{3\times 4}{4\times 11}+\frac{\frac{1}{3}}{\frac{3}{7}}$$

Cancel out 4 in both numerator and denominator.

$$\frac{2}{3}-\frac{3}{11}+\frac{\frac{1}{3}}{\frac{3}{7}}$$

Least common multiple of 3 and 11 is 33. Convert \frac{2}{3} and \frac{3}{11} to fractions with denominator 33.

$$\frac{22}{33}-\frac{9}{33}+\frac{\frac{1}{3}}{\frac{3}{7}}$$

Since \frac{22}{33} and \frac{9}{33} have the same denominator, subtract them by subtracting their numerators.

$$\frac{22-9}{33}+\frac{\frac{1}{3}}{\frac{3}{7}}$$

Subtract 9 from 22 to get 13.

$$\frac{13}{33}+\frac{\frac{1}{3}}{\frac{3}{7}}$$

Divide \frac{1}{3} by \frac{3}{7} by multiplying \frac{1}{3} by the reciprocal of \frac{3}{7}.

$$\frac{13}{33}+\frac{1}{3}\times \frac{7}{3}$$

Multiply \frac{1}{3} times \frac{7}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13}{33}+\frac{1\times 7}{3\times 3}$$

Do the multiplications in the fraction \frac{1\times 7}{3\times 3}.

$$\frac{13}{33}+\frac{7}{9}$$

Least common multiple of 33 and 9 is 99. Convert \frac{13}{33} and \frac{7}{9} to fractions with denominator 99.

$$\frac{39}{99}+\frac{77}{99}$$

Since \frac{39}{99} and \frac{77}{99} have the same denominator, add them by adding their numerators.

$$\frac{39+77}{99}$$

Add 39 and 77 to get 116.

$$\frac{116}{99}$$

Factor

$$\frac{2 ^ {2} \cdot 29}{3 ^ {2} \cdot 11} = 1\frac{17}{99} = 1.1717171717171717$$