Solve |(-15/24)+[(-23/4)+(21/14)]=

$$| ( - \frac { 15 } { 24 } ) + [ ( - 2 \frac { 3 } { 4 } ) + ( 2 \frac { 1 } { 14 } ) ] =$$

Evaluate

$$\frac{73}{56}\approx 1.303571429$$

Solution Steps

Reduce the fraction \frac{15}{24} to lowest terms by extracting and canceling out 3.

$$|-\frac{5}{8}-\frac{2\times 4+3}{4}+\frac{2\times 14+1}{14}|$$

Multiply 2 and 4 to get 8.

$$|-\frac{5}{8}-\frac{8+3}{4}+\frac{2\times 14+1}{14}|$$

Add 8 and 3 to get 11.

$$|-\frac{5}{8}-\frac{11}{4}+\frac{2\times 14+1}{14}|$$

Least common multiple of 8 and 4 is 8. Convert -\frac{5}{8} and \frac{11}{4} to fractions with denominator 8.

$$|-\frac{5}{8}-\frac{22}{8}+\frac{2\times 14+1}{14}|$$

Since -\frac{5}{8} and \frac{22}{8} have the same denominator, subtract them by subtracting their numerators.

$$|\frac{-5-22}{8}+\frac{2\times 14+1}{14}|$$

Subtract 22 from -5 to get -27.

$$|-\frac{27}{8}+\frac{2\times 14+1}{14}|$$

Multiply 2 and 14 to get 28.

$$|-\frac{27}{8}+\frac{28+1}{14}|$$

Add 28 and 1 to get 29.

$$|-\frac{27}{8}+\frac{29}{14}|$$

Least common multiple of 8 and 14 is 56. Convert -\frac{27}{8} and \frac{29}{14} to fractions with denominator 56.

$$|-\frac{189}{56}+\frac{116}{56}|$$

Since -\frac{189}{56} and \frac{116}{56} have the same denominator, add them by adding their numerators.

$$|\frac{-189+116}{56}|$$

Add -189 and 116 to get -73.

$$|-\frac{73}{56}|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{73}{56} is \frac{73}{56}.

$$\frac{73}{56}$$

Factor

$$\frac{73}{2 ^ {3} \cdot 7} = 1\frac{17}{56} = 1.3035714285714286$$