Explain what 1 divided by 2/3 is, and draw a visual representation of your answer.
Note: Instead of using the formula to flip and multiply, show a conceptual understanding using an image.
The Correct Answer and Explanation is:
To understand what ( 1 \div \frac{2}{3} ) means, we can visualize the problem using the concept of partitioning and proportions. Dividing by a fraction is equivalent to finding out how many times that fraction can fit into the whole number.
Conceptual Explanation
When we consider the operation ( 1 \div \frac{2}{3} ), we can reframe it in a more intuitive way. Imagine that the number ( 1 ) represents a whole, such as a single pizza. If we want to divide this pizza into pieces that are each ( \frac{2}{3} ) of a pizza, we can visualize it by cutting the pizza into sections that are each ( \frac{1}{3} ) of the whole.
From the visual representation, we can see that we can fit ( \frac{2}{3} ) of the pizza into the whole. This means that if we take two sections (each ( \frac{1}{3} )), we have ( \frac{2}{3} ) of the pizza covered. In total, we can fit 1 and a half of these ( \frac{2}{3} ) portions into the whole pizza.
In mathematical terms, we find that:
[
1 \div \frac{2}{3} = 1 \times \frac{3}{2} = \frac{3}{2} = 1.5
]
This means that the result of dividing ( 1 ) by ( \frac{2}{3} ) is ( 1.5 ), which can also be interpreted as needing one and a half pieces of ( \frac{2}{3} ) to make up the whole ( 1 ).
Thus, the answer to ( 1 \div \frac{2}{3} ) is ( 1.5 ), indicating that one whole can be filled by one and a half servings of ( \frac{2}{3} ). The visual aid helps to reinforce this understanding by clearly showing the sections and how they combine to form the whole.