Question

which model matches the word problem? the gardener has 1/2 of a box of plant food. he uses an equal amount of the food on 4 gardens. how much does he use on each garden?

Explanation:

Step1: Analyze the problem

The gardener has $\frac{1}{2}$ of a box of plant - food and divides it among 4 gardens. We need to find $\frac{1}{2}\div4$. When dividing a fraction by a whole number, we multiply the fraction by the reciprocal of the whole number, so $\frac{1}{2}\div4=\frac{1}{2}\times\frac{1}{4}=\frac{1}{8}$.

Step2: Check the models

We are looking for a model that shows $\frac{1}{2}$ of a whole divided into 4 equal parts. The model that represents $\frac{1}{2}$ of a rectangle (divided into 2 equal parts with 1 part shaded) and then that $\frac{1}{2}$ part further divided into 4 equal sub - parts is the correct one.

Answer:

The model that shows a rectangle divided into 2 equal parts with 1 part shaded (representing $\frac{1}{2}$) and then that shaded part divided into 4 equal sub - parts.