Solve 32-(-3/4)-5/24+(-2.1)

$$32 - ( - \frac { 3 } { 4 } ) - \frac { 5 } { 24 } + ( - 2.1 )$$

Evaluate

$$\frac{3653}{120}\approx 30.441666667$$

Solution Steps

The opposite of -\frac{3}{4} is \frac{3}{4}.

$$32+\frac{3}{4}-\frac{5}{24}-2.1$$

Convert 32 to fraction \frac{128}{4}.

$$\frac{128}{4}+\frac{3}{4}-\frac{5}{24}-2.1$$

Since \frac{128}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

$$\frac{128+3}{4}-\frac{5}{24}-2.1$$

Add 128 and 3 to get 131.

$$\frac{131}{4}-\frac{5}{24}-2.1$$

Least common multiple of 4 and 24 is 24. Convert \frac{131}{4} and \frac{5}{24} to fractions with denominator 24.

$$\frac{786}{24}-\frac{5}{24}-2.1$$

Since \frac{786}{24} and \frac{5}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{786-5}{24}-2.1$$

Subtract 5 from 786 to get 781.

$$\frac{781}{24}-2.1$$

Convert decimal number 2.1 to fraction \frac{21}{10}.

$$\frac{781}{24}-\frac{21}{10}$$

Least common multiple of 24 and 10 is 120. Convert \frac{781}{24} and \frac{21}{10} to fractions with denominator 120.

$$\frac{3905}{120}-\frac{252}{120}$$

Since \frac{3905}{120} and \frac{252}{120} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3905-252}{120}$$

Subtract 252 from 3905 to get 3653.

$$\frac{3653}{120}$$

Factor

$$\frac{13 \cdot 281}{3 \cdot 5 \cdot 2 ^ {3}} = 30\frac{53}{120} = 30.441666666666666$$