https://file.aiquickdraw.com/mathbot/file/1729520617734axsmwlwd.jpg

Let's go step by step to solve the problem shown in the image, which involves dividing two mixed numbers.

### Problem:
You are asked to find how many medium bumper stickers Damon can fit side by side on his car bumper. The mathematical expression to solve is:

\[
37 \frac{1}{2} \div 10 \frac{3}{4}
\]

### Step 1: Convert the mixed numbers to improper fractions.
1. Convert \( 37 \frac{1}{2} \) to an improper fraction:
   \[
   37 \frac{1}{2} = \frac{2 \times 37 + 1}{2} = \frac{75}{2}
   \]

2. Convert \( 10 \frac{3}{4} \) to an improper fraction:
   \[
   10 \frac{3}{4} = \frac{4 \times 10 + 3}{4} = \frac{43}{4}
   \]

Now, the division problem becomes:
\[
\frac{75}{2} \div \frac{43}{4}
\]

### Step 2: Rewrite the division as multiplication by the reciprocal.
When dividing fractions, you multiply the first fraction by the reciprocal of the second fraction:
\[
\frac{75}{2} \times \frac{4}{43}
\]

### Step 3: Perform the multiplication.
Multiply the numerators together and the denominators together:
\[
\frac{75 \times 4}{2 \times 43} = \frac{300}{86}
\]

### Step 4: Simplify the fraction.
Simplify \( \frac{300}{86} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
\[
\frac{300 \div 2}{86 \div 2} = \frac{150}{43}
\]

### Step 5: Convert the improper fraction to a mixed number.
To convert \( \frac{150}{43} \) to a mixed number, divide 150 by 43:
\[
150 \div 43 = 3 \text{ remainder } 21
\]

So, \( \frac{150}{43} = 3 \frac{21}{43} \).

Thus, Damon can fit **3 medium bumper stickers** side by side on his car bumper, with a little space left.

### Convince Me! Why do you multiply \( \frac{75}{2} \) by \( \frac{4}{43} \)?
When dividing fractions, you are essentially asking "how many times does the second fraction fit into the first?" To do this, you multiply by the reciprocal of the second fraction, which reverses the roles of the numerator and denominator.

---

Do you want further details or have any questions? Here are some related questions to expand your understanding:

1. What is the process for converting mixed numbers to improper fractions?
2. Why do we multiply by the reciprocal when dividing fractions?
3. How can you check your result to ensure it's correct?
4. How do you simplify large fractions efficiently?
5. Could the space left over on Damon's bumper fit a smaller sticker?

**Tip**: When simplifying fractions, always look for the greatest common divisor to make your work easier and avoid mistakes!

How many medium bumper stickers can Damon fit side by side on his car bumper? Find 37 1/2 ÷ 10 3/4.

Learn how to solve the problem of dividing mixed numbers: 37 1/2 ÷ 10 3/4. Convert mixed numbers into improper fractions and use reciprocal multiplication to get the answer. Perfect for students in Grades 6-8.

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