Division for Ratios: Explaining Value of Fractions

In summary: Therefore, division is used in ratios because the two concepts are directly related. In terms of significance, the value of the fraction in a ratio can give you an immediate idea of the relationship between the two quantities being compared. For example, a ratio of 0.50 means that one quantity is half of the other quantity. This can be useful in understanding and evaluating relationships between quantities, especially when dealing with larger numbers. Additionally, the ratio also gives you the percentage of one quantity compared to the other, which can provide further insight and understanding.
  • #1
Mr Davis 97
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Why is division used for ratios? For example, if we have 1 dog for every 2 cats, then why can this relation be modeled by the division? Since the ratio can essentially have the value of 1/2 or 2, then what is the significance of these two distinct numbers in relation to the ratio? How does the value of the fraction 1/2, which is 0.50, relate to the ratio 1 dog to 2 cats? If we said we had a 0.50 ratio of dogs to cats, what does that mean?
 
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  • #2
There are different reasons. First of all the ratio is a much easier number to understand, depending if it is greater or smaller than 1 (and how much grater/smaller it is) you can have an immediate idea of what's going on. If you are using small numbers (as in your example) it is clear that the ratio doesn't really add any information. However if the numbers you are dealing with are high it is much more complicated to evaluate the relationship between the two quantities just "by eye".

Moreover, the ratio gives you the percentage. For example, as you said, if I know that the ratio dogs/cats is 0.37 then this means that the number of dogs is the 37% of the number of cats.
 
  • #3
Mr Davis 97 said:
Why is division used for ratios?
Because it works.

Mr Davis 97 said:
For example, if we have 1 dog for every 2 cats, then why can this relation be modeled by the division?
Because 1 dog for every 2 cats is the same as ## \frac12 ## a dog for every 1 cat.

Mr Davis 97 said:
Since the ratio can essentially have the value of 1/2 or 2, then what is the significance of these two distinct numbers in relation to the ratio?
The significance of ## \frac12 ## is that we have ## \frac12 ## a dog for every 1 cat, and the siginficance of 2 is that we have 2 cats for every 1 dog.

Mr Davis 97 said:
If we said we had a 0.50 ratio of dogs to cats, what does that mean?
That we have 0.5 dogs for every cat (which is the same as 1 dog for every 2 cats, or 2 cats for every 1 dog etc...)
 
  • #4
Mr Davis 97 said:
Why is division used for ratios?

What would you prefer to use? Do you want everyone to spell it out in words every time?
 
  • #5
A "ratio" is defined as a fraction which is an implied division.
 

1. What is division for ratios?

Division for ratios is a mathematical operation used to compare the relative sizes of two quantities. It involves dividing one quantity by another to find the ratio between them.

2. How is division for ratios related to fractions?

Division for ratios is closely related to fractions because it is used to explain the value of fractions. Fractions represent a part of a whole, and division for ratios helps us understand how many equal parts make up the whole.

3. What is the process for dividing for ratios?

The process for dividing for ratios involves first identifying the two quantities that are being compared. Then, divide the first quantity by the second quantity to find the ratio. This can be represented as a fraction or a decimal.

4. How can division for ratios be used in real-world situations?

Division for ratios can be used in many real-world situations, such as cooking, budgeting, and measuring. For example, if a recipe calls for 1/2 cup of flour and you only have 1/4 cup, you can use division for ratios to determine that you need to double the recipe to get the correct amount of flour.

5. What are some common mistakes people make when dividing for ratios?

One common mistake people make when dividing for ratios is mixing up the order of the quantities. It is important to always divide the first quantity by the second quantity. Another mistake is forgetting to simplify the fraction or round the decimal to the appropriate number of digits.

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