To determine how many jars, each with a capacity of [tex]\(2 \frac{1}{2}\)[/tex] litres, are needed to empty a vessel containing 50 litres of milk, follow these steps:
1. Convert the mixed number to an improper fraction:
The jar capacity is given as [tex]\(2 \frac{1}{2}\)[/tex] litres. First, convert this to an improper fraction:
[tex]\[
2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2} \text{ litres}
\][/tex]
2. Divide the total volume by the capacity of one jar:
Next, divide the total volume of milk by the capacity of one jar to find out how many jars are needed:
[tex]\[
\text{Number of jars} = \frac{\text{Total volume of milk}}{\text{Capacity of one jar}} = \frac{50 \text{ litres}}{\frac{5}{2} \text{ litres}}
\][/tex]
3. Simplify the fraction:
To divide by a fraction, multiply by its reciprocal:
[tex]\[
\frac{50}{\frac{5}{2}} = 50 \times \frac{2}{5} = \frac{100}{5} = 20
\][/tex]
Therefore, you need 20 jars, each with a capacity of [tex]\(2 \frac{1}{2}\)[/tex] litres, to completely empty a vessel containing 50 litres of milk.
