To determine how many smaller bottles Clayton filled, we start with the given quantities:
1. Clayton has a total of [tex]\( \frac{1}{2} \)[/tex] of a liter of plant fertilizer.
2. He puts [tex]\( \frac{1}{4} \)[/tex] of a liter into each smaller bottle.
The problem requires us to find out how many bottles can be filled with the given amount of fertilizer. We need to divide the total amount of fertilizer by the amount of fertilizer per bottle.
Mathematically, this is represented as:
[tex]\[ \text{Number of bottles} = \frac{\text{Total fertilizer}}{\text{Fertilizer per bottle}} \][/tex]
Plugging in the given amounts:
[tex]\[ \text{Number of bottles} = \frac{\frac{1}{2} \text{ liter}}{\frac{1}{4} \text{ liter}} \][/tex]
To divide fractions, we multiply by the reciprocal of the divisor:
[tex]\[ \text{Number of bottles} = \frac{1}{2} \times \frac{4}{1} \][/tex]
Performing the multiplication:
[tex]\[ \text{Number of bottles} = \frac{1 \times 4}{2 \times 1} = \frac{4}{2} = 2 \][/tex]
So, Clayton filled 2 smaller bottles with plant fertilizer.
