Solve left|29/90-31/10right|

$$\left| \frac{ 29 }{ 90 } - \frac{ 31 }{ 10 } \right|$$

Evaluate

$$\frac{25}{9}\approx 2.777777778$$

Solution Steps

Least common multiple of 90 and 10 is 90. Convert \frac{29}{90} and \frac{31}{10} to fractions with denominator 90.

$$|\frac{29}{90}-\frac{279}{90}|$$

Since \frac{29}{90} and \frac{279}{90} have the same denominator, subtract them by subtracting their numerators.

$$|\frac{29-279}{90}|$$

Subtract 279 from 29 to get -250.

$$|\frac{-250}{90}|$$

Reduce the fraction \frac{-250}{90} to lowest terms by extracting and canceling out 10.

$$|-\frac{25}{9}|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{25}{9} is \frac{25}{9}.

$$\frac{25}{9}$$

Factor

$$\frac{5 ^ {2}}{3 ^ {2}} = 2\frac{7}{9} = 2.7777777777777777$$