To solve the problem \( \frac{4}{6} \div \frac{2}{6} = 2 \), we need to interpret the models based on the division of fractions concept.
-
An area model has 4 shaded parts and 2 unshaded parts. 2 circles are each drawn around 2 shaded parts.
- This model suggests 4 shaded parts out of a total of 6 parts, and dividing the shaded areas grouped in circles could represent the division of fractions correctly.
-
A number line going from 0 to 1. An arrow goes from 0.6 to 0.4, and from 0.4 to 0.
- This number line representation does not directly illustrate the fraction division, as it looks more like a subtraction rather than showing how many times \( \frac{2}{6} \) fits into \( \frac{4}{6} \).
-
A fraction bar. The top bar is labeled 1. 6 bars underneath the bar are labeled one-sixth. 4 of the bars are circled.
- This fraction bar can illustrate that \( \frac{4}{6} \) consists of 4 out of 6 parts, but it doesn't explicitly show the division by \( \frac{2}{6} \). It represents the first number in the division, not the second one.
-
An area model has 2 shaded parts and 4 unshaded parts. The 2 shaded parts are circled.
- This model likely indicates the dividing of one shaded area by another, which seems more complete in context as it focuses on the instance of shaded sections but might not altogether sum the relationships identified in the problem since it's about splitting.
Out of the models provided, the first area model is most directly applicable to the equation \( \frac{4}{6} \div \frac{2}{6} = 2 \). The fraction bar could also be somewhat relevant because it represents parts, but definitely does not illustrate the division.
So the models that apply best to show the problem \( \frac{4}{6} \div \frac{2}{6} = 2 \) are:
- The area model with 4 shaded parts and 2 unshaded parts (Model 1).
- The fraction bar with 4 circled bars (Model 3), but it is a bit less direct.
So options 1 and 3 would apply most appropriately to illustrate the relationship in the problem.
1 answer