Question
Describe what makes a proportion. Give an example of a proportion.(2 points)
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Math Short Answer Rubric (2 points)
This table shows the criteria for awarding points and the corresponding point values.
Points Awarded Criteria
2
The answer is correct. The student made no errors while solving.
The answer shows that the student used problem-solving skills and reasoning.
All work is shown or explained.
1
The answer is partially correct. The student made errors while solving.
The answer shows little problem-solving skills or reasoning.
Some work is shown or explained.
0 The question is not answered.
BoldItalicUnderlineIncrease indentDecrease indentFormula keypadUndoRedo
Math Short Answer Rubric (2 points)
This table shows the criteria for awarding points and the corresponding point values.
Points Awarded Criteria
2
The answer is correct. The student made no errors while solving.
The answer shows that the student used problem-solving skills and reasoning.
All work is shown or explained.
1
The answer is partially correct. The student made errors while solving.
The answer shows little problem-solving skills or reasoning.
Some work is shown or explained.
0 The question is not answered.
Answers
Answered by
GPT-4o mini
A proportion is an equation that states that two ratios are equal. It represents a relationship between two sets of quantities, showing that the relative sizes of the two quantities are consistent. Proportions can be expressed in the form of a:b = c:d or as a fraction: \(\frac{a}{b} = \frac{c}{d}\).
### Example of a Proportion:
Consider the ratio of boys to girls in a classroom. If there are 8 boys and 12 girls, we can express this as the ratio 8:12. This can be simplified to 2:3.
Now, if we find another classroom with 10 boys, we can determine the number of girls that would keep the same ratio of boys to girls. Let's denote the number of girls in the second classroom as \(x\). So, we set up the proportion:
\[
\frac{8}{12} = \frac{10}{x}
\]
To solve for \(x\), we can cross-multiply:
\[
8x = 120 \implies x = 15
\]
This means that for the second classroom with 10 boys, there would be 15 girls to maintain the same ratio of boys to girls as in the first classroom. Thus, \( \frac{8}{12} = \frac{10}{15} \) is a proportion.
### Example of a Proportion:
Consider the ratio of boys to girls in a classroom. If there are 8 boys and 12 girls, we can express this as the ratio 8:12. This can be simplified to 2:3.
Now, if we find another classroom with 10 boys, we can determine the number of girls that would keep the same ratio of boys to girls. Let's denote the number of girls in the second classroom as \(x\). So, we set up the proportion:
\[
\frac{8}{12} = \frac{10}{x}
\]
To solve for \(x\), we can cross-multiply:
\[
8x = 120 \implies x = 15
\]
This means that for the second classroom with 10 boys, there would be 15 girls to maintain the same ratio of boys to girls as in the first classroom. Thus, \( \frac{8}{12} = \frac{10}{15} \) is a proportion.