91Ó°ÊÓ

When you add integers, it’s crucial to consider their signs. Integers can be positive or negative. Here are some key points to remember when adding integers:
* If both integers are positive, you simply add the values. For example, \(5 + 7 = 12\).
* If both integers are negative, you add their absolute values and give the result a negative sign. For example, \((-4) + (-6) = -10\).
* If one integer is positive and the other one is negative, subtract the smaller absolute value from the larger absolute value. The result takes the sign of the integer with the larger absolute value. For example, \(8 + (-3) = 5\).
In the exercise, we see \(64 + (-17)\). Here, 64 is positive and -17 is negative. Following the rule above, we subtract 17 from 64, giving us 47.

Understanding these basic rules helps in simplifying expressions accurately.

Subtracting integers also involves key rules. Think of subtraction as the addition of a negative value. Let’s break it down:
* If you subtract a positive integer, this means you move left on the number line. For example, \(10 - 3 = 7\).
* Subtracting a negative integer is like adding a positive integer. For example, \(-5 - (-2) = -5 + 2\) yields -3.
* Another helpful rule is that subtracting an integer is the same as adding its opposite. So, \(a - b = a + (-b)\).
In our exercise, we need to subtract 9 from 47. This means moving 9 units left from 47, resulting in \(47 - 9 = 38\).
Understanding subtraction this way simplifies using subtraction in expressions.

When simplifying expressions, always follow the Order of Operations, often remembered by the acronym PEMDAS:
* P: Parentheses first
* E: Exponents (i.e. powers and roots, etc.)
* MD: Multiplication and Division (left to right)
* AS: Addition and Subtraction (left to right)
In our exercise, we see only addition and subtraction. According to PEMDAS, we process these from left to right. Therefore, we first handle the addition \(64 + (-17)\), and then move to the subtraction \(47 - 9\).
Consistently applying this order ensures the accuracy of your simplified expressions.