Question

You are comparing apples to oranges in a fruit bowl. is the ratio 2 : 3 the same as the ratio 3 : 2? explain.

Answer 1

The ratios 2:3 and 3:2 are not the same because the order of the quantities compared is reversed. Understanding the order and comparison of ratios is fundamental in mathematics, as they represent the relationship between different quantities.

Step-by-step explanation:

The question asks whether the ratio 2:3 is the same as the ratio 3:2. The answer is no, these two ratios are not the same. Think of it in terms of apples and oranges in a fruit bowl. A ratio of 2:3 means for every 2 apples, there are 3 oranges, whereas a ratio of 3:2 means for every 3 apples, there are 2 oranges. The quantities of apples and oranges have been reversed.

When comparing ratios, it's crucial to understand that the order of terms matters. For example, a scale factor between two similar objects or figures is a ratio that describes how much one object is scaled with respect to the other. If you have two squares, one with a side length twice as long as the other, their areas would have a ratio of 4:1, since area scales with the square of the side length (2:1 side length ratio results in a 4:1 area ratio).

In terms of real-life applications, understanding ratios can be practical in situations like converting measurements or when using a unit scale such as a map scale. Ratios provide a way to represent quantities and their relationships in an easily understandable form.

Answer 2

To get the analogy of whether the ratios are same we will proceed as follows;
Ratios are used to show the number of times one value contained by another value in quantitative sense. In simple terms it shows how many times the first number contains the second number.
Ratios can be expressed as fractions:
2:3=2/3
3:2=3/2
from the two fractions we deduce that 2/3 ≠ 3/2. Hence we conclude that the two ratios are not the same.