Mrs. Robbins Divides 72 Lemons Into 8 Bowls And Uses Two Of The Bowls To Make Lemonade. How Many Lemons Does She Use To Make Lemonade?Janine Says The Equation $72 \div 8 \times 2 = ?$ Represents The Problem. Is Janine Correct? Explain.
Introduction
In this article, we will delve into a simple yet intriguing math problem presented by Mrs. Robbins, who divides 72 lemons into 8 bowls and uses two of the bowls to make lemonade. The question at hand is: how many lemons does she use to make lemonade? Furthermore, we will examine Janine's equation, $72 \div 8 \times 2 = ?$, to determine if it accurately represents the problem.
Breaking Down the Problem
To begin, let's break down the problem step by step. Mrs. Robbins has 72 lemons, which she divides into 8 bowls. This means each bowl contains an equal number of lemons, which can be calculated by dividing the total number of lemons (72) by the number of bowls (8).
72 \div 8 = 9
So, each bowl contains 9 lemons. Now, Mrs. Robbins uses two of the bowls to make lemonade. To find out how many lemons she uses, we need to multiply the number of lemons in each bowl (9) by the number of bowls she uses (2).
9 \times 2 = 18
Therefore, Mrs. Robbins uses 18 lemons to make lemonade.
Evaluating Janine's Equation
Janine's equation, $72 \div 8 \times 2 = ?$, seems to represent the problem, but let's examine it more closely. The equation starts with 72 lemons, which is correct. However, the next step is to divide 72 by 8, which is also correct, as we calculated earlier.
72 \div 8 = 9
The issue arises when we multiply the result (9) by 2. This is where the equation goes awry. Multiplying 9 by 2 gives us 18, which is the correct number of lemons used to make lemonade. However, the equation is written as $72 \div 8 \times 2 = ?$, implying that the result of the division (9) is then multiplied by 2, which is incorrect.
The Correct Order of Operations
To accurately represent the problem, the correct order of operations should be:
- Divide 72 by 8 to find the number of lemons in each bowl.
- Multiply the result by 2 to find the total number of lemons used to make lemonade.
The correct equation should be written as:
Therefore, Janine's equation is not entirely accurate, as it implies that the result of the division (9) is then multiplied by 2, which is incorrect.
Conclusion
In conclusion, Mrs. Robbins uses 18 lemons to make lemonade. Janine's equation, $72 \div 8 \times 2 = ?$, is close but not entirely accurate, as it implies the wrong order of operations. The correct equation should be written as two separate steps: dividing 72 by 8 to find the number of lemons in each bowl, and then multiplying the result by 2 to find the total number of lemons used to make lemonade.
Understanding the Importance of Order of Operations
The order of operations is a fundamental concept in mathematics that dictates the order in which mathematical operations should be performed. In this case, the correct order of operations is:
- Division
- Multiplication
By following this order, we can accurately solve the problem and find the correct answer.
Real-World Applications of Order of Operations
The order of operations is not just a theoretical concept; it has real-world applications in various fields, such as:
- Science: In scientific calculations, the order of operations is crucial in determining the accuracy of results.
- Engineering: In engineering, the order of operations is essential in designing and building complex systems.
- Finance: In finance, the order of operations is critical in calculating investments and financial returns.
Conclusion
Introduction
In our previous article, we explored the problem presented by Mrs. Robbins, who divides 72 lemons into 8 bowls and uses two of the bowls to make lemonade. We also examined Janine's equation, $72 \div 8 \times 2 = ?$, to determine if it accurately represents the problem. In this article, we will answer some frequently asked questions related to the problem.
Q: What is the correct equation to represent the problem?
A: The correct equation to represent the problem is:
This equation accurately represents the problem by first dividing 72 by 8 to find the number of lemons in each bowl, and then multiplying the result by 2 to find the total number of lemons used to make lemonade.
Q: Why is Janine's equation incorrect?
A: Janine's equation, $72 \div 8 \times 2 = ?$, is incorrect because it implies that the result of the division (9) is then multiplied by 2, which is incorrect. The correct order of operations is to first divide 72 by 8 to find the number of lemons in each bowl, and then multiply the result by 2 to find the total number of lemons used to make lemonade.
Q: What is the importance of order of operations?
A: The order of operations is a fundamental concept in mathematics that dictates the order in which mathematical operations should be performed. In this case, the correct order of operations is:
- Division
- Multiplication
By following this order, we can accurately solve the problem and find the correct answer.
Q: How does the order of operations affect real-world applications?
A: The order of operations has real-world applications in various fields, such as:
- Science: In scientific calculations, the order of operations is crucial in determining the accuracy of results.
- Engineering: In engineering, the order of operations is essential in designing and building complex systems.
- Finance: In finance, the order of operations is critical in calculating investments and financial returns.
Q: Can you provide more examples of the order of operations?
A: Here are a few more examples of the order of operations:
- Example 1: 24 ÷ 3 × 2 = ?
- First, divide 24 by 3: 24 ÷ 3 = 8
- Then, multiply the result by 2: 8 × 2 = 16
- Therefore, the correct answer is 16.
- Example 2: 48 ÷ 6 + 2 = ?
- First, divide 48 by 6: 48 ÷ 6 = 8
- Then, add 2 to the result: 8 + 2 = 10
- Therefore, the correct answer is 10.
Q: How can I practice the order of operations?
A: You can practice the order of operations by working through math problems that involve multiple operations, such as division and multiplication, or addition and subtraction. You can also try solving word problems that require you to follow the order of operations.
Conclusion
In conclusion, the problem presented by Mrs. Robbins is a simple yet intriguing math problem that requires a clear understanding of the order of operations. By following the correct order of operations, we can accurately solve the problem and find the correct answer. We hope this Q&A article has helped you understand the importance of the order of operations and how it affects real-world applications.