Solving 28 ÷ 7 + 2 × 3 A Step-by-Step Guide
Mathematical equations can often seem daunting, but by breaking them down into smaller, manageable steps, even complex problems become solvable. In this comprehensive guide, we will tackle the equation 28 ÷ 7 + 2 × 3 using the fundamental principles of order of operations. Our goal is to provide a clear, step-by-step solution that not only answers the question but also enhances your understanding of basic arithmetic operations. Whether you are a student looking to improve your math skills or someone who enjoys problem-solving, this guide will equip you with the knowledge and confidence to tackle similar equations. Let’s dive into the world of numbers and unravel the solution together!
Understanding the Order of Operations: PEMDAS/BODMAS
Before we dive into solving the equation 28 ÷ 7 + 2 × 3, it is crucial to understand the order of operations. This is a set of rules that dictate the sequence in which mathematical operations should be performed to ensure consistency and accuracy in calculations. The most commonly used acronyms to remember this order are PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) and BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction). Both acronyms essentially convey the same sequence, with slight variations in terminology.
In our context, PEMDAS/BODMAS tells us that we should first address any Parentheses or Brackets, followed by Exponents or Orders (powers and square roots), then Multiplication and Division (from left to right), and finally, Addition and Subtraction (from left to right). This order is not arbitrary; it is a convention that ensures everyone arrives at the same answer when solving an equation. Without a standardized order, mathematical expressions could have multiple interpretations, leading to confusion and errors. By adhering to PEMDAS/BODMAS, we establish a universal language for mathematics, enabling clear and precise communication of mathematical ideas.
Step 1: Division - 28 ÷ 7
Our equation, 28 ÷ 7 + 2 × 3, includes division, addition, and multiplication. According to the order of operations (PEMDAS/BODMAS), we must first address division and multiplication before we can proceed with addition. Between division and multiplication, we perform the operations from left to right. Therefore, the first step in solving this equation is to perform the division operation: 28 ÷ 7. This simple division asks us how many times 7 fits into 28. The answer is 4, because 7 multiplied by 4 equals 28. So, we can rewrite the equation, replacing 28 ÷ 7 with 4. Our equation now looks like this: 4 + 2 × 3. This simplification is a crucial step in making the equation more manageable and sets the stage for the next operation.
Division is a fundamental arithmetic operation that plays a critical role in various mathematical and real-world applications. It is the inverse operation of multiplication and helps us to split a quantity into equal parts or groups. In the context of problem-solving, understanding division allows us to tackle a wide range of scenarios, from dividing resources fairly among a group to calculating rates and ratios. By mastering division, we build a solid foundation for more advanced mathematical concepts and enhance our ability to solve practical problems efficiently.
Step 2: Multiplication - 2 × 3
Now that we have simplified the equation to 4 + 2 × 3, the next step according to PEMDAS/BODMAS is to perform the multiplication. We need to calculate 2 × 3, which means multiplying 2 by 3. This operation is straightforward: 2 multiplied by 3 equals 6. We can now replace 2 × 3 in the equation with 6, further simplifying the expression. Our equation now reads 4 + 6. This step is crucial because it reduces the equation to a simple addition problem, making it very easy to solve. Multiplication, like division, is a fundamental arithmetic operation that is essential in many areas of mathematics and real-life applications. It helps us to find the product of two or more numbers, which is the total when the numbers are combined multiplicatively.
Multiplication is also the foundation for more complex mathematical concepts such as exponents, polynomials, and algebra. By understanding multiplication, we can solve problems involving scaling, grouping, and combining quantities. In the context of problem-solving, mastering multiplication enables us to tackle various scenarios, from calculating areas and volumes to determining costs and revenues. By practicing multiplication, we not only enhance our arithmetic skills but also improve our overall mathematical reasoning and problem-solving abilities.
Step 3: Addition - 4 + 6
With the equation simplified to 4 + 6, the final step is to perform the addition. We simply need to add 4 and 6 together. The sum of 4 and 6 is 10. Therefore, the final result of the equation 28 ÷ 7 + 2 × 3 is 10. This completes our step-by-step solution. Addition is one of the basic arithmetic operations and is the foundation for more complex mathematical concepts. It involves combining two or more numbers to find their total, which is known as the sum.
Addition is used in countless everyday scenarios, from calculating the total cost of items at a store to determining the total distance traveled on a trip. In mathematics, addition is a fundamental operation that is used in various areas, including algebra, calculus, and statistics. By mastering addition, we develop a strong foundation for understanding and solving mathematical problems. In the context of our equation, the addition step is the final step that leads us to the solution, demonstrating the importance of understanding and applying basic arithmetic operations in the correct order.
Final Answer: 10
After carefully following the order of operations (PEMDAS/BODMAS), we have successfully solved the equation 28 ÷ 7 + 2 × 3. We first performed the division, 28 ÷ 7, which gave us 4. Then, we carried out the multiplication, 2 × 3, resulting in 6. Finally, we added the two results together, 4 + 6, which equals 10. Therefore, the final answer to the equation 28 ÷ 7 + 2 × 3 is 10. This result aligns with option A in the given choices, confirming that our step-by-step solution is accurate and complete.
Understanding the process of solving mathematical equations is not just about arriving at the correct answer; it is also about developing critical thinking and problem-solving skills. By breaking down complex problems into smaller, more manageable steps, we can tackle a wide range of mathematical challenges with confidence. In this case, we have demonstrated how applying the order of operations can lead to a clear and precise solution. The final answer of 10 not only answers the specific question but also reinforces the importance of following a systematic approach in mathematics. By mastering these fundamental principles, we pave the way for more advanced mathematical learning and problem-solving in various fields.
Conclusion
In conclusion, we have successfully solved the equation 28 ÷ 7 + 2 × 3 by carefully adhering to the order of operations (PEMDAS/BODMAS). Our step-by-step approach involved first performing the division (28 ÷ 7 = 4), then the multiplication (2 × 3 = 6), and finally the addition (4 + 6 = 10). This process not only led us to the correct answer of 10 but also reinforced the importance of following a systematic methodology in mathematical problem-solving. The order of operations is a fundamental principle that ensures consistency and accuracy in calculations, and mastering it is crucial for success in mathematics and related fields.
By breaking down complex equations into smaller, manageable steps, we can demystify mathematical challenges and approach them with confidence. The solution to this equation demonstrates the power of understanding and applying basic arithmetic operations in the correct sequence. Whether you are a student learning the fundamentals or someone looking to refresh your math skills, this guide provides a clear and concise example of how to tackle mathematical equations effectively. As we have shown, with a solid understanding of PEMDAS/BODMAS and a step-by-step approach, even seemingly complex problems can be solved with ease and precision. The final answer of 10 underscores the value of mathematical literacy and its practical applications in everyday life.
