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Negative numbers can be a bit tricky at first, but once you get the hang of it, they're not so bad. Negative numbers are simply the numbers less than zero. Think of them as the opposite of positive numbers. They are usually represented with a negative sign in front of a number, like

• -1, -2, -3, ... all the way to negative infinity!

Negative numbers are useful in many areas, such as describing temperatures below zero, bank overdrafts, or depths below sea level. One important thing to remember is that if you add a negative number, it's the same as subtracting its positive counterpart. When multiplying or dividing two numbers:

• If both numbers have the same sign (both positive or both negative), the result is positive.
• If the numbers have different signs (one positive, one negative), the result is negative.

With practice, understanding negative numbers becomes second nature. The key is to remember their interaction with positive numbers and zero.

Multiplication is one of the fundamental arithmetic operations, which involves adding a number to itself a certain number of times. For example, when you multiply 3 by 4, it means you add 3 four times: 3 + 3 + 3 + 3 = 12. The numbers being multiplied are called factors, and the result is called the product.In our expression \[ -9 \times 3 \]we multiply the negative number \(-9\) by the positive number \(3\). The important rule to remember here is:

• Multiplying numbers with different signs results in a negative product.

To do this, multiply the absolute values. Here, the absolute values are 9 and 3, which give us:\[ 9 \times 3 = 27 \]Since the original multiplication had a negative sign, the result becomes -27. This consistent rule makes multiplication predictable and simpler with practice.

Absolute value is a concept that indicates the distance of a number from zero on a number line, regardless of direction. Basically, it's the positive version of any number. You can think of it as "how far this number is from zero," ignoring any negative signs.For example:

• The absolute value of -9 is 9, written as \( |-9| = 9 \).
• Similarly, the absolute value of 3 is 3, which is \( |3| = 3 \).

When dealing with operations like multiplication, it’s often helpful to first consider the absolute values of the numbers involved. This way, you can determine the magnitude of the result and then apply the correct sign based on the multiplication rules you know.Absolute values are particularly useful when you need to determine the size of numbers regardless of their sign, like when finding distances or comparing numbers.