Understanding the Expression 1 5 × 5 / 5 and Mastering Order of Operations

The expression 1 5 × 5 / 5 is a fundamental example used to explain the significance of the order of operations in mathematics. Proper understanding of this sequence ensures accurate and consistent results in numerical expressions. The rules of PEMDAS or BEDMAS can be applied effectively to obtain the correct answer.

What is PEMDAS and BEDMAS?

PEMDAS and BEDMAS both represent the order of operations in mathematics, which ensure that mathematical expressions are evaluated in a consistent and standardized manner. The acronym PEMDAS stands for:

Parentheses Exponents (Orders) Multiplication and Division (from left to right) Addition and Subtraction (from left to right)

Similarly, BEDMAS uses the terms:

Brackets Exponents (Orders) Multiplication and Division (from left to right) Addition and Subtraction (from left to right)

Evaluating the Expression 1 5 × 5 / 5

Let's break down the expression 1 5 × 5 / 5 step by step using the order of operations.

Step-by-Step Solution

Identify operations: The expression contains multiplication (×) and division (/). Apply the Order of Operations: There are no parentheses or brackets in this expression, so we move on to the next step. Next, we perform the multiplication and division from left to right. Perform the multiplication first:

5 × 5 25

Next, perform the division:

25 / 5 5

Finally, perform the addition:

1 5 6

Therefore, the final answer to the expression 1 5 × 5 / 5 is 6.
Now, let's verify the different methods and expressions provided in your reference text.

Method 1: Using 15 × 5 / 5

Another interpretation of the expression could be 15 × 5 / 5. Here, we follow the order of operations as well:

Identify operations: The expression contains multiplication and division. Apply the Order of Operations: There are no parentheses or brackets in this expression, so we move on to the next step. Next, we perform the multiplication and division from left to right. Perform the multiplication first:

15 × 5 75

Next, perform the division:

75 / 5 15

Therefore, the final answer to the expression 15 × 5 / 5 is 15.

Method 2: Using 1 5 × 5 / 5

To further illustrate, let's break down another expression 1 5 × 5 / 5:

Identify operations: The expression contains multiplication, division, and addition. Apply the Order of Operations: There are no parentheses or brackets in this expression, so we move on to the next step. Next, we perform the multiplication and division from left to right. Perform the multiplication first:

5 × 5 25

Next, perform the division:

25 / 5 5

Finally, perform the addition:

1 5 6

Therefore, the final answer to the expression 1 5 × 5 / 5 is 6.

Conclusion

Understanding the order of operations is crucial for evaluating mathematical expressions accurately. Whether your expression is 15 × 5 / 5 or 1 5 × 5 / 5, the correct application of PEMDAS or BEDMAS will always yield the right result. This method ensures that operations are performed in the correct sequence, leading to consistent and reliable answers in mathematical computations.

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