Let's solve the problem step by step using the visual model provided.
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Problem:
$$
\frac{1}{3} \div 2 = ?
$$
We are dividing the fraction $ \frac{1}{3} $ by the whole number 2.
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Understanding the Model:
The image shows a visual representation:
1.
Top bar: A whole (represented as one rectangle) divided into three equal parts, each labeled $ \frac{1}{3} $. This represents the fraction $ \frac{1}{3} $.
2.
Middle bar: One of those thirds is shaded green — this is the $ \frac{1}{3} $ we're starting with.
3.
Bottom bar: This bar is divided into
6 equal parts. Why? Because we are dividing $ \frac{1}{3} $ into
2 equal parts, so each part will be half of $ \frac{1}{3} $.
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Step-by-Step Solution:
We want to divide $ \frac{1}{3} $ by 2.
This means:
> "How much is one-third split into two equal parts?"
So:
$$
\frac{1}{3} \div 2 = \frac{1}{3} \times \frac{1}{2} = \frac{1}{6}
$$
But let’s see how this works with the model.
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Using the Model:
- The
middle bar shows $ \frac{1}{3} $ shaded (one out of three equal parts).
- We now want to
divide that shaded $ \frac{1}{3} $ into 2 equal parts.
- So, in the
bottom bar, the same length as $ \frac{1}{3} $ is split into
2 smaller pieces.
- Since the whole is divided into 6 parts in the bottom bar (each $ \frac{1}{6} $), then:
- $ \frac{1}{3} = \frac{2}{6} $
- Dividing $ \frac{2}{6} $ into 2 equal parts gives $ \frac{1}{6} $ per part.
So each piece is $ \frac{1}{6} $.
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✔ Final Answer:
$$
\frac{1}{3} \div 2 = \frac{1}{6}
$$
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Explanation:
Dividing a fraction by a whole number means splitting that fraction into equal parts. Here, $ \frac{1}{3} $ is split into 2 equal parts, and each part is $ \frac{1}{6} $.
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Answer:
$$
\boxed{\frac{1}{6}}
$$
Parent Tip: Review the logic above to help your child master the concept of dividing a whole number by a fraction worksheet.
