Solve |13/4-2/13|9/11+16/15

$$| \frac { 13 } { 4 } - \frac { 2 } { 13 } | \frac { 9 } { 11 } + \frac { 16 } { 15 }$$

Evaluate

$$\frac{30887}{8580}\approx 3.59988345$$

Solution Steps

Least common multiple of 4 and 13 is 52. Convert \frac{13}{4} and \frac{2}{13} to fractions with denominator 52.

$$|\frac{169}{52}-\frac{8}{52}|\times \frac{9}{11}+\frac{16}{15}$$

Since \frac{169}{52} and \frac{8}{52} have the same denominator, subtract them by subtracting their numerators.

$$|\frac{169-8}{52}|\times \frac{9}{11}+\frac{16}{15}$$

Subtract 8 from 169 to get 161.

$$|\frac{161}{52}|\times \frac{9}{11}+\frac{16}{15}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of \frac{161}{52} is \frac{161}{52}.

$$\frac{161}{52}\times \frac{9}{11}+\frac{16}{15}$$

Multiply \frac{161}{52} times \frac{9}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{161\times 9}{52\times 11}+\frac{16}{15}$$

Do the multiplications in the fraction \frac{161\times 9}{52\times 11}.

$$\frac{1449}{572}+\frac{16}{15}$$

Least common multiple of 572 and 15 is 8580. Convert \frac{1449}{572} and \frac{16}{15} to fractions with denominator 8580.

$$\frac{21735}{8580}+\frac{9152}{8580}$$

Since \frac{21735}{8580} and \frac{9152}{8580} have the same denominator, add them by adding their numerators.

$$\frac{21735+9152}{8580}$$

Add 21735 and 9152 to get 30887.

$$\frac{30887}{8580}$$

Factor

$$\frac{67 \cdot 461}{2 ^ {2} \cdot 3 \cdot 5 \cdot 11 \cdot 13} = 3\frac{5147}{8580} = 3.5998834498834498$$