Here’s the solution to the problems shown in your image:

Problem 1:

"3 is $\frac{1}{4}$ of what number?"

The question is asking for a number where $\frac{1}{4}$ equals 3.

• To find the number: $3 \div \frac{1}{4} = 3 \times 4 = 12$

• Verification: $\frac{1}{4} \text{ of } 12 = \frac{12}{4} = 3$

Thus, the answer is: $12$

Problem 2:

"5 is $\frac{1}{6}$ of what number?"

Here, the question is asking for a number where $\frac{1}{6}$ equals 5.

• To find the number: $5 \div \frac{1}{6} = 5 \times 6 = 30$

• Verification: $\frac{1}{6} \text{ of } 30 = \frac{30}{6} = 5$

Thus, the answer is: $30$

Problem 3:

"There are 15 books on a shelf of a bookcase. This is $\frac{1}{5}$ of the total number of books. How many books are on the bookcase?"

To solve this:

• If 15 represents $\frac{1}{5}$ of the total number of books, then: $15 \div \frac{1}{5} = 15 \times 5 = 75$

• Verification: $\frac{1}{5} \text{ of } 75 = \frac{75}{5} = 15$

Thus, the total number of books is: $75$

Summary of Solutions:

1. 12
2. 30
3. 75

Would you like detailed step-by-step explanations or assistance with anything else?

Related Questions:

1. How do you verify if a fraction is accurately represented in a division problem?
2. Can you explain the mathematical relationship between fractions and division?
3. Why do we multiply when dividing by a fraction?
4. How can you represent these problems using models or tape diagrams?
5. What are other real-life examples where fractions represent parts of a whole?

Tip:

When dividing by a fraction, always remember to multiply by its reciprocal!