To find the value of the expression $-4 - 5 \frac{1}{3} + \left(-\frac{5}{2}\right)$, follow these steps:

Step 1: Convert the mixed number to an improper fraction

The mixed number $5 \frac{1}{3}$ can be converted to an improper fraction:

$5 \frac{1}{3} = \frac{5 \times 3 + 1}{3} = \frac{15 + 1}{3} = \frac{16}{3}$

Step 2: Rewrite the expression with fractions

The expression now becomes:

$-4 - \frac{16}{3} + \left(-\frac{5}{2}\right)$

Step 3: Convert $-4$ to a fraction with a common denominator

To add or subtract fractions, it's easier if they have the same denominator. Let's convert $-4$ to a fraction with a denominator of 6 (the least common multiple of 3 and 2):

$-4 = \frac{-4 \times 6}{1 \times 6} = \frac{-24}{6}$

Step 4: Convert all fractions to have a common denominator

Convert the other fractions to have the denominator 6:

• For $\frac{16}{3}$, multiply both the numerator and denominator by 2: $\frac{16}{3} = \frac{16 \times 2}{3 \times 2} = \frac{32}{6}$

• For $-\frac{5}{2}$, multiply both the numerator and denominator by 3: $-\frac{5}{2} = \frac{-5 \times 3}{2 \times 3} = \frac{-15}{6}$

Now the expression is:

$\frac{-24}{6} - \frac{32}{6} + \frac{-15}{6}$

Step 5: Combine the fractions

Since all fractions have the same denominator, combine the numerators:

$\frac{-24 - 32 - 15}{6} = \frac{-71}{6}$

Final Answer

The value of the expression is $\frac{-71}{6}$.

Would you like more details or have any questions?

Here are some related questions you might find interesting:

1. How do you convert a mixed number to an improper fraction?
2. What are the steps to add and subtract fractions with different denominators?
3. How do you simplify complex fractions?
4. How can you convert an improper fraction back to a mixed number?
5. What is the least common multiple, and how do you find it for different denominators?

Tip: When dealing with mixed numbers and fractions in expressions, always convert mixed numbers to improper fractions first for easier computation.