Let's get a feel for what the question is asking here, and what tools we can use to approach it. A quick list of information we're given:
- Small bottles can hold 2/5 L of vinegar
- Containers hold 5 L of vinegar
The question asks us specifically about the case where we have 3 containers; together, their volume totals to 3 x 5 = 15 L of vinegar.
We're asked to find the number of 2/5 L bottles we can make from those 15 L, or in other words, we're being asked to divide the 15 L up into 2/5 L portions. The math question at the core of this is really 15 ÷ 2/5.
If you have much familiarity with division by fractions, you might know that dividing by a fraction is the same as multiplying by its reciprocal. In this case, the reciprocal of 2/5 is 5/2, so 15 ÷ 2/5 is the same as 15 x 5/2. Solving that out, we get:
[tex]15\times \frac{5}{2} = \frac{15\times5}{2}= \frac{75}{2}[/tex]
75/2 as a mixed number is 37 1/2; if we were going for an exact answer, we could stop there and say that the containers fill exactly 37 1/2 bottles, but the question specifically asks how many containers can be completely filled, so we'll have to throw away the fractional part, leaving us with an answer of 37 bottles.
