help me remember the rules for adding and subtracting integers like (-7) - 3 =

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Welcome! Today we'll master the rules for adding and subtracting integers using visual methods. Let's start with the example negative seven minus three. We'll use a number line to see exactly how this works step by step. The first step is understanding that subtraction is the same as adding the opposite. When we subtract three, it's exactly the same as adding negative three. So our problem negative seven minus three becomes negative seven plus negative three. This conversion is crucial for solving integer problems correctly. Now we apply the rule for adding numbers with the same sign. Both negative seven and negative three are negative, so we add their absolute values: seven plus three equals ten. Since both numbers were negative, we keep the negative sign. The result is negative ten. On the number line, we start at negative seven and move three more spaces to the left, landing at negative ten. Let's practice with more examples to reinforce these rules. First, negative five minus two becomes negative five plus negative two, which equals negative seven. Second, eight minus twelve becomes eight plus negative twelve, which equals negative four. Third, negative three minus negative six becomes negative three plus positive six, which equals positive three. Remember, the key is always converting subtraction to addition of the opposite! Excellent work! Let's summarize what we've learned. The key rules are: subtraction equals adding the opposite, when signs are the same we add absolute values and keep the common sign, and when signs are different we subtract absolute values and keep the sign of the larger number. Our original problem negative seven minus three equals negative ten. You now have the tools to solve any integer addition or subtraction problem!