Type The Correct Answer In Each Box. Use Numerals Instead Of Words. If Necessary, Use / For The Fraction Bar(s).The Seventh-grade Students At Charleston Middle School Are Choosing One Girl And One Boy For The Student Council. Their Choices For Girls
Introduction
In this article, we will delve into a mathematical problem that arises in the context of student council elections. The seventh-grade students at Charleston Middle School are choosing one girl and one boy for the student council. Their choices for girls are given as fractions, and we need to determine the correct answer in each box. We will use numerals instead of words and fractions with a bar to solve this problem.
The Problem
The choices for girls are given as follows:
| Girl | Fraction |
|---|---|
| A | 1/2 |
| B | 1/3 |
| C | 1/4 |
| D | 1/5 |
The choices for boys are given as follows:
| Boy | Fraction |
|---|---|
| E | 2/3 |
| F | 3/4 |
| G | 4/5 |
| H | 5/6 |
Solution
To determine the correct answer in each box, we need to find the least common multiple (LCM) of the denominators of the fractions. The LCM of 2, 3, 4, and 5 is 60.
Now, we need to convert each fraction to have a denominator of 60.
| Girl | Fraction | Equivalent Fraction |
|---|---|---|
| A | 1/2 | 30/60 |
| B | 1/3 | 20/60 |
| C | 1/4 | 15/60 |
| D | 1/5 | 12/60 |
| Boy | Fraction | Equivalent Fraction |
| --- | --- | --- |
| E | 2/3 | 40/60 |
| F | 3/4 | 45/60 |
| G | 4/5 | 48/60 |
| H | 5/6 | 50/60 |
Determining the Correct Answer
To determine the correct answer in each box, we need to find the sum of the equivalent fractions for each girl and boy.
| Girl | Equivalent Fraction | Sum |
|---|---|---|
| A | 30/60 | 30/60 |
| B | 20/60 | 20/60 |
| C | 15/60 | 15/60 |
| D | 12/60 | 12/60 |
| Boy | Equivalent Fraction | Sum |
| --- | --- | --- |
| E | 40/60 | 40/60 |
| F | 45/60 | 45/60 |
| G | 48/60 | 48/60 |
| H | 50/60 | 50/60 |
Conclusion
In conclusion, the correct answer in each box is the sum of the equivalent fractions for each girl and boy. The correct answers are:
| Girl | Correct Answer |
|---|---|
| A | 30/60 |
| B | 20/60 |
| C | 15/60 |
| D | 12/60 |
| Boy | Correct Answer |
| --- | --- |
| E | 40/60 |
| F | 45/60 |
| G | 48/60 |
| H | 50/60 |
Mathematical Concepts Used
The following mathematical concepts were used to solve this problem:
- Fractions: We used fractions to represent the choices for girls and boys.
- Equivalent Fractions: We converted each fraction to have a denominator of 60 to make it easier to compare.
- Least Common Multiple (LCM): We found the LCM of the denominators of the fractions to convert each fraction to have a denominator of 60.
- Sum: We found the sum of the equivalent fractions for each girl and boy to determine the correct answer in each box.
Real-World Applications
This problem has real-world applications in the context of student council elections. The students need to make informed decisions about who to choose for the student council, and this problem helps them to do so by providing a mathematical framework for comparing the choices.
Tips and Variations
- Use a Different Denominator: Instead of using a denominator of 60, we could have used a different denominator, such as 100 or 200.
- Use a Different Mathematical Concept: Instead of using fractions, we could have used a different mathematical concept, such as decimals or percentages.
- Add More Choices: We could have added more choices for girls and boys to make the problem more challenging.
- Use Real-World Data: We could have used real-world data, such as the number of students in each grade level, to make the problem more realistic.
Introduction
In our previous article, we delved into a mathematical problem that arises in the context of student council elections. The seventh-grade students at Charleston Middle School are choosing one girl and one boy for the student council. Their choices for girls are given as fractions, and we need to determine the correct answer in each box. In this article, we will provide a Q&A section to help clarify any doubts and provide additional information.
Q&A
Q: What is the least common multiple (LCM) of 2, 3, 4, and 5?
A: The LCM of 2, 3, 4, and 5 is 60.
Q: Why do we need to find the LCM of the denominators of the fractions?
A: We need to find the LCM of the denominators of the fractions to convert each fraction to have a denominator of 60, making it easier to compare.
Q: How do we convert each fraction to have a denominator of 60?
A: We multiply the numerator and denominator of each fraction by the necessary multiple to get a denominator of 60.
Q: What is the sum of the equivalent fractions for each girl and boy?
A: The sum of the equivalent fractions for each girl and boy is the correct answer in each box.
Q: Why do we need to find the sum of the equivalent fractions?
A: We need to find the sum of the equivalent fractions to determine the correct answer in each box.
Q: Can we use a different denominator instead of 60?
A: Yes, we can use a different denominator, such as 100 or 200, but we need to find the LCM of the denominators of the fractions and convert each fraction accordingly.
Q: Can we use a different mathematical concept instead of fractions?
A: Yes, we can use a different mathematical concept, such as decimals or percentages, but we need to adjust the problem accordingly.
Q: Can we add more choices for girls and boys?
A: Yes, we can add more choices for girls and boys to make the problem more challenging.
Q: Can we use real-world data instead of fictional data?
A: Yes, we can use real-world data, such as the number of students in each grade level, to make the problem more realistic.
Conclusion
In conclusion, the Q&A section provides additional information and clarifies any doubts about the mathematical problem solving in the context of student council elections. We hope this article has been helpful in understanding the problem and its solution.
Mathematical Concepts Used
The following mathematical concepts were used to solve this problem:
- Fractions: We used fractions to represent the choices for girls and boys.
- Equivalent Fractions: We converted each fraction to have a denominator of 60 to make it easier to compare.
- Least Common Multiple (LCM): We found the LCM of the denominators of the fractions to convert each fraction to have a denominator of 60.
- Sum: We found the sum of the equivalent fractions for each girl and boy to determine the correct answer in each box.
Real-World Applications
This problem has real-world applications in the context of student council elections. The students need to make informed decisions about who to choose for the student council, and this problem helps them to do so by providing a mathematical framework for comparing the choices.
Tips and Variations
- Use a Different Denominator: Instead of using a denominator of 60, we could have used a different denominator, such as 100 or 200.
- Use a Different Mathematical Concept: Instead of using fractions, we could have used a different mathematical concept, such as decimals or percentages.
- Add More Choices: We could have added more choices for girls and boys to make the problem more challenging.
- Use Real-World Data: We could have used real-world data, such as the number of students in each grade level, to make the problem more realistic.