Order of operations is a crucial concept in mathematics that helps us solve complex mathematical problems accurately. It helps avoid errors and ensures consistency in the answers obtained. However, sometimes figuring out how to perform the calculations in the correct order can be a daunting task. In this article, we will explore the secret to solving a tricky mathematical problem: 6-6×6+6.
The answer to this problem seems to vary depending on who you ask. Some people say the answer is 42, while others argue that it is 0. So, what is the correct answer? The answer is actually 0, and in this article, we will unpack why.
The secret to solving 6-6×6+6 lies in understanding the order of operations. The order of operations is a set of rules that dictate the sequence in which mathematical operations should be performed to obtain the correct answer. The common acronym used to remember the order of operations is PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. It is important to remember that multiplication and division are given equal priority and should be performed from left to right, whichever comes first.
Now, let’s apply the order of operations to solve the problem 6-6×6+6. First, we need to perform the multiplication, which gives us 6×6=36. Next, we perform the addition and subtraction operations from left to right, giving us 6-36+6. As subtraction comes before addition, we calculate 6-36 first, giving us -30. Finally, we add 6 to -30, which gives us a final answer of -24.
However, this answer is incorrect. Why? Because we have not taken into account the parentheses in the original problem. Without parentheses to indicate the order of operations, multiplication and division should be performed before addition and subtraction. It means that we need to treat the entire expression as a set of parentheses and solve the calculation inside the parentheses first.
When we apply the order of operations to the original problem with parentheses, the correct answer emerges. The problem is 6-(6×6)+6, or 6-36+6. First, we need to solve the equation inside the parentheses, which gives us 6×6=36. Next, we subtract 36 from 6, giving us -30. Finally, we add 6 to -30, which gives us a final answer of -24.
Therefore, the secret to solving 6-6×6+6 is to understand the order of operations and apply them correctly. Always remember that multiplication and division take priority over addition and subtraction unless the problem is explicitly written with parentheses to indicate a different order.
In conclusion, a thorough understanding of the order of operations allows us to avoid errors and obtain accurate solutions to complex mathematical problems. By applying the rules of PEMDAS and taking into account parentheses, we can solve even the trickiest of calculations.
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