Solve 17/3-19/3+8/7*4/5+frac{11}{5}+frac{11}{4}

$$\frac { 17 } { 3 } - \frac { 19 } { 3 } + \frac { 8 } { 7 } \times \frac { 4 } { 5 } + \frac { 11 } { 5 } + \frac { 11 } { 4 }$$

Evaluate

$$\frac{2183}{420}\approx 5.197619048$$

Solution Steps

Since \frac{17}{3} and \frac{19}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{17-19}{3}+\frac{8}{7}\times \frac{4}{5}+\frac{11}{5}+\frac{11}{4}$$

Subtract 19 from 17 to get -2.

$$-\frac{2}{3}+\frac{8}{7}\times \frac{4}{5}+\frac{11}{5}+\frac{11}{4}$$

Multiply \frac{8}{7} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{2}{3}+\frac{8\times 4}{7\times 5}+\frac{11}{5}+\frac{11}{4}$$

Do the multiplications in the fraction \frac{8\times 4}{7\times 5}.

$$-\frac{2}{3}+\frac{32}{35}+\frac{11}{5}+\frac{11}{4}$$

Least common multiple of 3 and 35 is 105. Convert -\frac{2}{3} and \frac{32}{35} to fractions with denominator 105.

$$-\frac{70}{105}+\frac{96}{105}+\frac{11}{5}+\frac{11}{4}$$

Since -\frac{70}{105} and \frac{96}{105} have the same denominator, add them by adding their numerators.

$$\frac{-70+96}{105}+\frac{11}{5}+\frac{11}{4}$$

Add -70 and 96 to get 26.

$$\frac{26}{105}+\frac{11}{5}+\frac{11}{4}$$

Least common multiple of 105 and 5 is 105. Convert \frac{26}{105} and \frac{11}{5} to fractions with denominator 105.

$$\frac{26}{105}+\frac{231}{105}+\frac{11}{4}$$

Since \frac{26}{105} and \frac{231}{105} have the same denominator, add them by adding their numerators.

$$\frac{26+231}{105}+\frac{11}{4}$$

Add 26 and 231 to get 257.

$$\frac{257}{105}+\frac{11}{4}$$

Least common multiple of 105 and 4 is 420. Convert \frac{257}{105} and \frac{11}{4} to fractions with denominator 420.

$$\frac{1028}{420}+\frac{1155}{420}$$

Since \frac{1028}{420} and \frac{1155}{420} have the same denominator, add them by adding their numerators.

$$\frac{1028+1155}{420}$$

Add 1028 and 1155 to get 2183.

$$\frac{2183}{420}$$

Factor

$$\frac{37 \cdot 59}{2 ^ {2} \cdot 3 \cdot 5 \cdot 7} = 5\frac{83}{420} = 5.197619047619048$$