Perform the operation below. Express your answer as a mixed number in simplest form.

minus, 3, start fraction, 4, divided by, 5, end fraction, minus, 2, start fraction, 5, divided by, 8, end fraction




To perform the operation \( -3 \frac{4}{5} - 2 \frac{5}{8} \), follow these steps:

### Step 1: Convert the mixed numbers to improper fractions.

- \( -3 \frac{4}{5} = -\left( 3 + \frac{4}{5} \right) = -\frac{19}{5} \)
- \( -2 \frac{5}{8} = -\left( 2 + \frac{5}{8} \right) = -\frac{21}{8} \)

### Step 2: Find a common denominator.

The denominators are 5 and 8. The least common denominator (LCD) is 40.

Now, rewrite both fractions with the common denominator:
- \( -\frac{19}{5} = -\frac{152}{40} \)
- \( -\frac{21}{8} = -\frac{105}{40} \)

### Step 3: Subtract the fractions.

\[
-\frac{152}{40} - \frac{105}{40} = -\frac{152 + 105}{40} = -\frac{257}{40}
\]

### Step 4: Convert the improper fraction to a mixed number.

\[
-\frac{257}{40} = -6 \frac{17}{40}
\]

So, the final answer is \( -6 \frac{17}{40} \).

Would you like any further details or clarifications?

Here are 5 related questions:
1. How do you simplify fractions with large numbers?
2. Why is it necessary to find a common denominator when subtracting fractions?
3. What is the process for converting mixed numbers into improper fractions?
4. How can you check your work when dealing with mixed numbers and improper fractions?
5. Can you multiply and divide mixed numbers without converting them to improper fractions?

**Tip:** When subtracting fractions, always make sure to use the least common denominator to keep the numbers manageable!

Perform the operation below. Express your answer as a mixed number in simplest form.

minus, 3, start fraction, 4, divided by, 5, end fraction, minus, 2, start fraction, 5, divided by, 8, end fraction

Learn how to subtract mixed numbers, such as -3 4/5 and -2 5/8, by converting them to improper fractions, finding a common denominator, and simplifying the result to a mixed number. A detailed solution suitable for students in Grades 6-8.

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