How to use operations on integers?

Sample Solution

I'm glad you want to learn about operations on integers! While memorization techniques can be helpful, true understanding comes from comprehending the underlying concepts. Here's a breakdown of the four basic operations on integers:

Addition:

• Imagine a number line with positive integers to the right of zero and negative integers to the left.
• Adding two positive integers means moving the same number of steps to the right on the number line. (Example: 5 + 3 = 8)
• Adding a negative integer means moving that many steps to the left. (Example: 5 - 2 = 3)
• Adding two negative integers means moving the combined number of steps to the left. (Example: -5 + (-2) = -7)

Subtraction:

• Think of subtraction as the opposite of addition. You can visualize it as moving steps in the opposite direction on the number line.
• Subtracting a positive integer is the same as adding its negative counterpart. (Example: 5 - 3 = 5 + (-3) = 2)
• Subtracting a negative integer is like adding its positive counterpart. (Example: 5 - (-2) = 5 + 2 = 7)

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Multiplication:

• Multiplication of integers can be seen as repeated addition.
• Multiplying by a positive integer means adding that number to itself the specified number of times. (Example: 3 x 4 = 4 + 4 + 4 = 12)
• Multiplying by a negative integer means adding the opposite (positive version) of that number the specified number of times with a negative sign. (Example: 3 x (-2) = (-2) + (-2) + (-2) = -6)

Division:

• Division is the opposite of multiplication. It asks, "How many times does one number go into another?"
• Dividing by a positive integer means splitting the first number into equal groups with that size. (Example: 12 / 3 = 4, as 4 groups of 3 make 12)
• Dividing by a negative integer means splitting the first number into equal groups with the opposite size (absolute value) and making the result negative. (Example: 12 / (-3) = -4, as 4 groups of -3 make -12)

Remember, practice is key to solidifying your understanding. Try working out various examples for each operation to solidify these concepts!