Let's analyze the questions and solve them:

Question 21:

John answered $\frac{7}{8}$ of the 40 questions correctly. We need to find how many items he answered incorrectly.

• Total questions = 40
• Correct answers = $\frac{7}{8} \times 40 = 35$ (since $\frac{7}{8} \times 40 = \frac{280}{8} = 35$)
• Incorrect answers = $40 - 35 = 5$

Thus, John answered 5 items incorrectly. The answer to question 21 is A. 5.

Question 22:

Which procedure can be used to find how many items John answered incorrectly? Let's analyze each statement:

• I. Subtract $\frac{7}{8}$ from 1 and multiply the difference by 40.

  • $1 - \frac{7}{8} = \frac{1}{8}$, and $\frac{1}{8} \times 40 = 5$ (Correct method).

• II. Subtract $\frac{7}{8}$ from 1 and divide the difference by 40.

  • $\frac{1}{8} \div 40$ does not give the correct result (Incorrect method).

• III. Multiply 40 by $\frac{7}{8}$ and subtract the product from 40.

  • $40 \times \frac{7}{8} = 35$, and $40 - 35 = 5$ (Correct method).

• IV. Multiply 40 by $\frac{7}{8}$ and subtract the product from 40.

  • This is the same as statement III and is also correct.

The correct options are I and III, so the answer to question 22 is B. I and III.

Question 23:

The friends ordered two pizzas. One had 8 slices, and the other had 6 slices. They ate 3 slices from the first pizza and 2 slices from the second pizza. We need to determine how much pizza is left.

• First pizza: 8 slices in total, 3 slices eaten, so 5 slices left.
• Second pizza: 6 slices in total, 2 slices eaten, so 4 slices left.

The total pizza left can be expressed as: $\text{Remaining pizza} = \frac{5}{8} + \frac{4}{6}$

Converting both fractions to have a common denominator: $\frac{4}{6} = \frac{16}{24}, \quad \frac{5}{8} = \frac{15}{24}$ Adding them together: $\frac{15}{24} + \frac{16}{24} = \frac{31}{24} = 1\frac{7}{24}$

So, the amount of pizza left is 1 and $\frac{7}{24}$, which is option B. 1 $\frac{7}{24}$.

Would you like more details on any of these solutions?

Here are 5 related questions for further practice:

1. If John answered $\frac{5}{6}$ of the 40 items correctly, how many did he get wrong?
2. How would you calculate the number of correct items if John had answered $\frac{3}{4}$ of the test correctly?
3. What fraction of a pizza is left if 3 slices are eaten from a pizza with 12 slices?
4. How many questions did John answer incorrectly if he answered $\frac{4}{5}$ of the 50-item test correctly?
5. Can you devise a formula to find the number of incorrect answers if the correct fraction and total number of items are given?

Tip: When adding or subtracting fractions, always find the least common denominator (LCD) for easier calculations.