Solve 11/9+3/8+16/9+13/8

$$\frac { 11 } { 9 } + \frac { 3 } { 8 } + \frac { 16 } { 9 } + \frac { 13 } { 8 }$$

Evaluate

$$5$$

Solution Steps

Least common multiple of 9 and 8 is 72. Convert \frac{11}{9} and \frac{3}{8} to fractions with denominator 72.

$$\frac{88}{72}+\frac{27}{72}+\frac{16}{9}+\frac{13}{8}$$

Since \frac{88}{72} and \frac{27}{72} have the same denominator, add them by adding their numerators.

$$\frac{88+27}{72}+\frac{16}{9}+\frac{13}{8}$$

Add 88 and 27 to get 115.

$$\frac{115}{72}+\frac{16}{9}+\frac{13}{8}$$

Least common multiple of 72 and 9 is 72. Convert \frac{115}{72} and \frac{16}{9} to fractions with denominator 72.

$$\frac{115}{72}+\frac{128}{72}+\frac{13}{8}$$

Since \frac{115}{72} and \frac{128}{72} have the same denominator, add them by adding their numerators.

$$\frac{115+128}{72}+\frac{13}{8}$$

Add 115 and 128 to get 243.

$$\frac{243}{72}+\frac{13}{8}$$

Reduce the fraction \frac{243}{72} to lowest terms by extracting and canceling out 9.

$$\frac{27}{8}+\frac{13}{8}$$

Since \frac{27}{8} and \frac{13}{8} have the same denominator, add them by adding their numerators.

$$\frac{27+13}{8}$$

Add 27 and 13 to get 40.

$$\frac{40}{8}$$

Divide 40 by 8 to get 5.

$$5$$

Factor

$$5$$