Respuesta :
A rate is a specific type of ratio. A rate is a comparison of two numbers with different units, whereas a ratio compares two numbers with the same unit.
For example, in a bowl, there are 12 fruits: 8 oranges and 4 apples. This means the ratio of oranges to apples is 8:4.
If we simplify the ratio, we can see that the ratio of oranges to apples is 2:1, because:
[tex]\frac{8}{4}=\frac{4\cdot2}{4\cdot1}=\frac{2}{1}=\frac{2}{1}[/tex]Then, there are 2 oranges in the bowl for every apple.
On the other hand, suppose we want to distribute the fruits to 3 people. We can use a rate to find out how many fruits correspond to each person because we have 2 different units:
[tex]\begin{gathered} \frac{12\text{ fruits}}{3\text{ people}}=\frac{x}{1\text{ person}} \\ \text{ Apply cross product} \\ 12\text{ fruits}\cdot1\text{ person}=x\cdot3\text{ people} \\ \text{ Divide by 3 people from both sides} \\ \frac{12\text{ fruits}\cdot1\text{ person}}{3\text{ people}}=\frac{x\cdot3\text{ people}}{3\text{ people}} \\ \frac{12\text{ fruits}}{3}=x \\ 4\text{ fruits }=x \end{gathered}[/tex]Now, we know that each person corresponds to 4 fruits, in other words, the rate is 4 fruits/person.
Therefore, we can see the similarities between rate and ratio are:
• Both are a comparison of two numbers.
,• Both can be written as fractions.
,• Both reduce to the lowest form.
