Solve 3.2--3/4-5/24

$$3.2-- \frac{ 3 }{ 4 } - \frac{ 5 }{ 24 }$$

Evaluate

$$\frac{449}{120}\approx 3.741666667$$

Solution Steps

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

$$3.2+\frac{3}{4}-\frac{5}{24}$$

Convert decimal number 3.2 to fraction \frac{32}{10}. Reduce the fraction \frac{32}{10} to lowest terms by extracting and canceling out 2.

$$\frac{16}{5}+\frac{3}{4}-\frac{5}{24}$$

Least common multiple of 5 and 4 is 20. Convert \frac{16}{5} and \frac{3}{4} to fractions with denominator 20.

$$\frac{64}{20}+\frac{15}{20}-\frac{5}{24}$$

Since \frac{64}{20} and \frac{15}{20} have the same denominator, add them by adding their numerators.

$$\frac{64+15}{20}-\frac{5}{24}$$

Add 64 and 15 to get 79.

$$\frac{79}{20}-\frac{5}{24}$$

Least common multiple of 20 and 24 is 120. Convert \frac{79}{20} and \frac{5}{24} to fractions with denominator 120.

$$\frac{474}{120}-\frac{25}{120}$$

Since \frac{474}{120} and \frac{25}{120} have the same denominator, subtract them by subtracting their numerators.

$$\frac{474-25}{120}$$

Subtract 25 from 474 to get 449.

$$\frac{449}{120}$$

Factor

$$\frac{449}{3 \cdot 5 \cdot 2 ^ {3}} = 3\frac{89}{120} = 3.7416666666666667$$