Solve (1/4+2/3+7/8+4/7)=

$$( \frac { 1 } { 4 } + \frac { 2 } { 3 } + \frac { 7 } { 8 } + \frac { 4 } { 7 } ) =$$

Evaluate

$$\frac{397}{168}\approx 2.363095238$$

Solution Steps

Least common multiple of 4 and 3 is 12. Convert \frac{1}{4} and \frac{2}{3} to fractions with denominator 12.

$$\frac{3}{12}+\frac{8}{12}+\frac{7}{8}+\frac{4}{7}$$

Since \frac{3}{12} and \frac{8}{12} have the same denominator, add them by adding their numerators.

$$\frac{3+8}{12}+\frac{7}{8}+\frac{4}{7}$$

Add 3 and 8 to get 11.

$$\frac{11}{12}+\frac{7}{8}+\frac{4}{7}$$

Least common multiple of 12 and 8 is 24. Convert \frac{11}{12} and \frac{7}{8} to fractions with denominator 24.

$$\frac{22}{24}+\frac{21}{24}+\frac{4}{7}$$

Since \frac{22}{24} and \frac{21}{24} have the same denominator, add them by adding their numerators.

$$\frac{22+21}{24}+\frac{4}{7}$$

Add 22 and 21 to get 43.

$$\frac{43}{24}+\frac{4}{7}$$

Least common multiple of 24 and 7 is 168. Convert \frac{43}{24} and \frac{4}{7} to fractions with denominator 168.

$$\frac{301}{168}+\frac{96}{168}$$

Since \frac{301}{168} and \frac{96}{168} have the same denominator, add them by adding their numerators.

$$\frac{301+96}{168}$$

Add 301 and 96 to get 397.

$$\frac{397}{168}$$

Factor

$$\frac{397}{2 ^ {3} \cdot 3 \cdot 7} = 2\frac{61}{168} = 2.363095238095238$$