Solve |-1.5-31/4|+|2.75+(-51/2)|

$$| - 1.5 - 3 \frac { 1 } { 4 } | + | 2.75 + ( - 5 \frac { 1 } { 2 } ) |$$

Evaluate

$$7.5$$

Solution Steps

Multiply 3 and 4 to get 12.

$$|-1.5-\frac{12+1}{4}|+|2.75-\frac{5\times 2+1}{2}|$$

Add 12 and 1 to get 13.

$$|-1.5-\frac{13}{4}|+|2.75-\frac{5\times 2+1}{2}|$$

Convert decimal number -1.5 to fraction -\frac{15}{10}. Reduce the fraction -\frac{15}{10} to lowest terms by extracting and canceling out 5.

$$|-\frac{3}{2}-\frac{13}{4}|+|2.75-\frac{5\times 2+1}{2}|$$

Least common multiple of 2 and 4 is 4. Convert -\frac{3}{2} and \frac{13}{4} to fractions with denominator 4.

$$|-\frac{6}{4}-\frac{13}{4}|+|2.75-\frac{5\times 2+1}{2}|$$

Since -\frac{6}{4} and \frac{13}{4} have the same denominator, subtract them by subtracting their numerators.

$$|\frac{-6-13}{4}|+|2.75-\frac{5\times 2+1}{2}|$$

Subtract 13 from -6 to get -19.

$$|-\frac{19}{4}|+|2.75-\frac{5\times 2+1}{2}|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{19}{4} is \frac{19}{4}.

$$\frac{19}{4}+|2.75-\frac{5\times 2+1}{2}|$$

Multiply 5 and 2 to get 10.

$$\frac{19}{4}+|2.75-\frac{10+1}{2}|$$

Add 10 and 1 to get 11.

$$\frac{19}{4}+|2.75-\frac{11}{2}|$$

Convert decimal number 2.75 to fraction \frac{275}{100}. Reduce the fraction \frac{275}{100} to lowest terms by extracting and canceling out 25.

$$\frac{19}{4}+|\frac{11}{4}-\frac{11}{2}|$$

Least common multiple of 4 and 2 is 4. Convert \frac{11}{4} and \frac{11}{2} to fractions with denominator 4.

$$\frac{19}{4}+|\frac{11}{4}-\frac{22}{4}|$$

Since \frac{11}{4} and \frac{22}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{19}{4}+|\frac{11-22}{4}|$$

Subtract 22 from 11 to get -11.

$$\frac{19}{4}+|-\frac{11}{4}|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{11}{4} is \frac{11}{4}.

$$\frac{19}{4}+\frac{11}{4}$$

Since \frac{19}{4} and \frac{11}{4} have the same denominator, add them by adding their numerators.

$$\frac{19+11}{4}$$

Add 19 and 11 to get 30.

$$\frac{30}{4}$$

Reduce the fraction \frac{30}{4} to lowest terms by extracting and canceling out 2.

$$\frac{15}{2}$$

Factor

$$\frac{3 \cdot 5}{2} = 7\frac{1}{2} = 7.5$$