https://file.aiquickdraw.com/mathbot/file/1725442913146kbmg8nv1.jpg

Let's solve the problems shown in the image:

### a) Change \( 7 \frac{1}{2} \) to a top-heavy fraction.
A top-heavy fraction (also known as an improper fraction) has a numerator larger than the denominator.

\[
7 \frac{1}{2} = \frac{7 \times 2 + 1}{2} = \frac{14 + 1}{2} = \frac{15}{2}
\]

So, the top-heavy fraction is \( \frac{15}{2} \).

### b) Change \( 3 \frac{2}{3} \) to a top-heavy fraction.

\[
3 \frac{2}{3} = \frac{3 \times 3 + 2}{3} = \frac{9 + 2}{3} = \frac{11}{3}
\]

So, the top-heavy fraction is \( \frac{11}{3} \).

### c) Work out \( 7 \frac{1}{2} \times 3 \frac{2}{3} \). Give your answer as a mixed number.
First, convert the mixed numbers to improper fractions:

\[
7 \frac{1}{2} = \frac{15}{2}, \quad 3 \frac{2}{3} = \frac{11}{3}
\]

Now multiply the fractions:

\[
\frac{15}{2} \times \frac{11}{3} = \frac{15 \times 11}{2 \times 3} = \frac{165}{6}
\]

Next, simplify \( \frac{165}{6} \):

\[
\frac{165 \div 3}{6 \div 3} = \frac{55}{2}
\]

Convert \( \frac{55}{2} \) back to a mixed number:

\[
\frac{55}{2} = 27 \frac{1}{2}
\]

So, the answer is \( 27 \frac{1}{2} \).

### d) Work out \( 7 \frac{1}{2} + 3 \frac{2}{3} \). Give your answer as a mixed number.
Again, convert the mixed numbers to improper fractions:

\[
7 \frac{1}{2} = \frac{15}{2}, \quad 3 \frac{2}{3} = \frac{11}{3}
\]

Find a common denominator for addition:

\[
\text{Common denominator of 2 and 3 is 6.}
\]

Convert each fraction:

\[
\frac{15}{2} = \frac{45}{6}, \quad \frac{11}{3} = \frac{22}{6}
\]

Now add the fractions:

\[
\frac{45}{6} + \frac{22}{6} = \frac{67}{6}
\]

Convert \( \frac{67}{6} \) back to a mixed number:

\[
\frac{67}{6} = 11 \frac{1}{6}
\]

So, the answer is \( 11 \frac{1}{6} \).

---

Do you need further details or have any questions?

Here are 5 questions related to this topic:
1. How do you simplify improper fractions to mixed numbers?
2. What are some methods to find a common denominator when adding fractions?
3. Can you explain the process of converting a mixed number to an improper fraction?
4. Why is it important to simplify fractions after multiplication or addition?
5. What is the difference between a top-heavy fraction and a proper fraction?

**Tip:** When multiplying fractions, always simplify before multiplying if possible to make calculations easier.

For the following, give each fraction in its simplest form.
1) Change 7 1/2 to a top-heavy fraction.
2) Change 3 2/3 to a top-heavy fraction.
3) Work out 7 1/2 x 3 2/3. Give your answer as a mixed number.
4) Work out 7 1/2 + 3 2/3. Give your answer as a mixed number.

Learn how to solve fraction problems, including converting mixed numbers to improper fractions, multiplying and adding fractions, and simplifying to mixed numbers. This tutorial is suitable for students in Grades 6-8.

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