https://file.aiquickdraw.com/mathbot/file/17260271555583062o72f.jpg

The expression in the image is:

\[
1 \frac{3}{4} - 3 \frac{9}{10}
\]

Let's solve this step-by-step:

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

1. \( 1 \frac{3}{4} \) can be written as:
\[
1 \frac{3}{4} = \frac{4 \times 1 + 3}{4} = \frac{7}{4}
\]

2. \( 3 \frac{9}{10} \) can be written as:
\[
3 \frac{9}{10} = \frac{10 \times 3 + 9}{10} = \frac{39}{10}
\]

### Step 2: Find a common denominator.

The least common denominator (LCD) between 4 and 10 is 20. So we will rewrite the fractions with a denominator of 20.

- For \( \frac{7}{4} \), multiply both the numerator and denominator by 5:
\[
\frac{7}{4} = \frac{7 \times 5}{4 \times 5} = \frac{35}{20}
\]

- For \( \frac{39}{10} \), multiply both the numerator and denominator by 2:
\[
\frac{39}{10} = \frac{39 \times 2}{10 \times 2} = \frac{78}{20}
\]

### Step 3: Subtract the fractions.

Now subtract \( \frac{78}{20} \) from \( \frac{35}{20} \):

\[
\frac{35}{20} - \frac{78}{20} = \frac{35 - 78}{20} = \frac{-43}{20}
\]

### Step 4: Convert to a mixed number (if needed).

The fraction \( \frac{-43}{20} \) can be written as a mixed number:
\[
\frac{-43}{20} = -2 \frac{3}{20}
\]

So, the result of the expression is:

\[
-2 \frac{3}{20}
\]

Would you like more details or have any questions about this solution?

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Here are some related questions for further practice:
1. How do you convert improper fractions to mixed numbers?
2. What is the process for finding the least common denominator between two fractions?
3. How would you solve a similar problem if both mixed numbers were negative?
4. What are the steps to multiply mixed numbers?
5. How can you check if a fraction is simplified?

**Tip:** Always check if fractions can be simplified after performing arithmetic operations, especially if you need to present the final answer in its simplest form.

Learn how to subtract mixed numbers with different denominators in the example 1 3/4 - 3 9/10. This problem involves converting mixed numbers to improper fractions, finding a common denominator, and simplifying the result. Suitable for students in Grades 5-7.

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