Let's break down the problem step by step, following each clue.

Step 1: Total Pizzas

• The total number of pizzas is 16.

Step 2: Cheese Pizzas

• One fourth of the pizzas are cheese pizzas.
  $\frac{1}{4} \times 16 = 4$ So, 4 pizzas have just cheese.
  Remaining pizzas: $16 - 4 = 12$

Step 3: Pepperoni Pizzas

• One third of the remaining pizzas have pepperoni only.
  $\frac{1}{3} \times 12 = 4$ So, 4 pizzas have only pepperoni.
  Remaining pizzas: $12 - 4 = 8$

Step 4: Mushroom and Sausage Pizzas

• One fourth of the remaining pizzas have mushrooms and sausage.
  $\frac{1}{4} \times 8 = 2$ So, 2 pizzas have mushrooms and sausage.
  Remaining pizzas: $8 - 2 = 6$

Step 5: Ham and Pineapple Pizzas

• One half of the remaining pizzas have ham and pineapple.
  $\frac{1}{2} \times 6 = 3$ So, 3 pizzas have ham and pineapple.
  Remaining pizzas: $6 - 3 = 3$

Step 6: Mushroom and Olive Pizzas

• One third of the remaining pizzas have mushrooms and olives.
  $\frac{1}{3} \times 3 = 1$ So, 1 pizza has mushrooms and olives.
  Remaining pizzas: $3 - 1 = 2$

Step 7: Hamburger and Bacon & Onion Pizzas

• Half of the remaining pizzas have hamburger, and the other half have bacon and onion.
  Since 2 pizzas remain, this means:
  • 1 pizza has hamburger.
  • 1 pizza has bacon and onion.

Summary:

1. 4 pizzas have just cheese.
2. 4 pizzas have only pepperoni.
3. 2 pizzas have mushrooms and sausage.
4. 3 pizzas have ham and pineapple.
5. 1 pizza has mushrooms and olives.
6. 1 pizza has hamburger.
7. 1 pizza has bacon and onion.

Would you like more details or further clarifications?

Here are 5 relative questions to extend your understanding:

1. How can fractions help in dividing larger quantities?
2. What would happen if the total number of pizzas was different, say 24 instead of 16?
3. How can we adjust the problem if the proportions of pizza types were changed?
4. How does understanding fractions help in everyday decision-making like ordering food?
5. What happens if one more pizza type is added to the mix?

Tip: Always reduce fractions to simplify your calculations and better understand the distribution.