Khan Academy Kids adds new first-grade lessons - Khan Academy Blog - Free Printable

The worksheet provided is focused on dividing whole numbers by fractions, using the concept of reciprocals. Below, I will solve each problem step by step and explain the solution.

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Problem 1: What is the reciprocal of 4?

- Solution: The reciprocal of a number is obtained by flipping the numerator and the denominator. For the whole number 4, we can write it as the fraction \( \frac{4}{1} \). Flipping this gives \( \frac{1}{4} \).
- Answer: The reciprocal of 4 is \( \boxed{\frac{1}{4}} \).

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Problem 2: Rewrite \( 4 \div \frac{1}{3} \) as a multiplication expression

- Solution: Dividing by a fraction is equivalent to multiplying by its reciprocal. The reciprocal of \( \frac{1}{3} \) is \( 3 \). Therefore:
\[
4 \div \frac{1}{3} = 4 \times 3
\]
- Answer: The multiplication expression is \( \boxed{4 \times 3} \).

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Problem 3: Show how Sal used the reciprocal to solve the problem \( 4 \div \frac{1}{3} \)

- Solution: To solve \( 4 \div \frac{1}{3} \), Sal would use the rule of dividing by a fraction by multiplying by its reciprocal. The reciprocal of \( \frac{1}{3} \) is \( 3 \). So:
\[
4 \div \frac{1}{3} = 4 \times 3 = 12
\]
- Answer: Sal solved \( 4 \div \frac{1}{3} \) by rewriting it as \( 4 \times 3 \), which equals \( \boxed{12} \).

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Problem 4: Show how Sal visually explains the answer to \( 4 \div \frac{1}{3} \)

- Solution: Visually, dividing 4 by \( \frac{1}{3} \) means finding how many \( \frac{1}{3} \)-sized pieces fit into 4 whole units. If you divide each whole unit into 3 equal parts (each part being \( \frac{1}{3} \)), then:
- Each whole unit contains 3 parts of \( \frac{1}{3} \).
- Since there are 4 whole units, the total number of \( \frac{1}{3} \)-sized pieces is \( 4 \times 3 = 12 \).
- Answer: Sal would show this visually by breaking each of the 4 whole units into 3 parts, resulting in a total of 12 parts. The answer is \( \boxed{12} \).

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Problem 5: Show using the reciprocal: \( 3 \div \frac{1}{4} \)

- Solution: To solve \( 3 \div \frac{1}{4} \), we multiply 3 by the reciprocal of \( \frac{1}{4} \). The reciprocal of \( \frac{1}{4} \) is \( 4 \). So:
\[
3 \div \frac{1}{4} = 3 \times 4 = 12
\]
- Answer: Using the reciprocal, \( 3 \div \frac{1}{4} = \boxed{12} \).

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Problem 6: Show using a visual model: \( 3 \div \frac{1}{4} \)

- Solution: Visually, dividing 3 by \( \frac{1}{4} \) means finding how many \( \frac{1}{4} \)-sized pieces fit into 3 whole units. If you divide each whole unit into 4 equal parts (each part being \( \frac{1}{4} \)), then:
- Each whole unit contains 4 parts of \( \frac{1}{4} \).
- Since there are 3 whole units, the total number of \( \frac{1}{4} \)-sized pieces is \( 3 \times 4 = 12 \).
- Answer: Sal would show this visually by breaking each of the 3 whole units into 4 parts, resulting in a total of 12 parts. The answer is \( \boxed{12} \).

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Final Answers:

1. The reciprocal of 4 is \( \boxed{\frac{1}{4}} \).
2. \( 4 \div \frac{1}{3} \) as a multiplication expression is \( \boxed{4 \times 3} \).
3. Sal solved \( 4 \div \frac{1}{3} \) by rewriting it as \( 4 \times 3 \), which equals \( \boxed{12} \).
4. Sal visually explained the answer to \( 4 \div \frac{1}{3} \) by showing 12 parts, resulting in \( \boxed{12} \).
5. Using the reciprocal, \( 3 \div \frac{1}{4} = \boxed{12} \).
6. Using a visual model, \( 3 \div \frac{1}{4} = \boxed{12} \).

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Boxed Final Answer:
\[
\boxed{12}
\]