https://file.aiquickdraw.com/mathbot/file/17266576386993m83hftp.jpg

The problem in the image asks you to subtract two mixed numbers and give the result as a mixed number in its simplest form. The expression is:

\[
3\frac{3}{4} - 2\frac{1}{5}
\]

### Step-by-Step Solution:

#### 1. Convert Mixed Numbers to Improper Fractions:
- For \(3\frac{3}{4}\):
  \[
  3\frac{3}{4} = \frac{3 \times 4 + 3}{4} = \frac{12 + 3}{4} = \frac{15}{4}
  \]

- For \(2\frac{1}{5}\):
  \[
  2\frac{1}{5} = \frac{2 \times 5 + 1}{5} = \frac{10 + 1}{5} = \frac{11}{5}
  \]

#### 2. Find a Common Denominator:
The denominators are 4 and 5, so the least common denominator (LCD) is 20. 

- Convert \(\frac{15}{4}\) to a fraction with denominator 20:
  \[
  \frac{15}{4} = \frac{15 \times 5}{4 \times 5} = \frac{75}{20}
  \]

- Convert \(\frac{11}{5}\) to a fraction with denominator 20:
  \[
  \frac{11}{5} = \frac{11 \times 4}{5 \times 4} = \frac{44}{20}
  \]

#### 3. Subtract the Fractions:
Now subtract the fractions:
\[
\frac{75}{20} - \frac{44}{20} = \frac{75 - 44}{20} = \frac{31}{20}
\]

#### 4. Convert the Improper Fraction Back to a Mixed Number:
\[
\frac{31}{20} = 1 \frac{11}{20}
\]

### Final Answer:
The result is \(1 \frac{11}{20}\), which is already in its simplest form.

Would you like more details on any part of the solution?

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Here are 5 related questions to expand on this:
1. How do you find the least common denominator for two fractions?
2. How do you convert between mixed numbers and improper fractions?
3. Can you solve the same problem using decimal numbers instead of fractions?
4. How would you add two mixed numbers instead of subtracting them?
5. What are the steps to simplify a complex fraction?

**Tip**: When subtracting mixed numbers, it’s often easier to convert them to improper fractions first, as this avoids dealing with borrowing between whole numbers and fractions.

Work out, giving your answer as a mixed number in its simplest form: 3 3/4 - 2 1/5

Learn how to subtract mixed numbers, including converting mixed numbers to improper fractions, finding a common denominator, and simplifying the result. Example problem: 3 3/4 - 2 1/5, solved step-by-step.

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