Absolute Value - Example 1

In mathematics, the absolute value or modulus |x| of a real number x is its numerical value without regard to its sign. The absolute value of a number may be thought of as its distance from zero along a number line; this interpretation is analogous to the distance function assigned to a real number in the real number system. For example, the absolute value of ?4 is 4, and the absolute value of 4 is 4, both without regard to sign.

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Video Transcript

we're being asked to find the opposite for each number. So remember, the opposite means it's a number that's the same distance from zero on the number line. Just it appears on the opposite side of the number line. So in other words, if it's positive, if the original numbers positive, he ever has to be negative. And if the original numbers negative, the upper will have to be positive. So let's start with Part A. We have positive five, so we have to think of what number would be five minutes away. But in the negative side of our number line. Well, that would be negative. Five. So notice the opposite really just means you need the opposite sign. So for Part B, we have negative 16. So we have to think of what number is 16 units away from zero on the positive side of the number one? Well, that would be positive. 16. So notice the opposite of a positive is a negative, and the opposite negative is a positive well part. See, we have a decimal value, so we have negative 9.8. But just because it's a decimal doesn't mean it changes anything so the number that would be 9.8 units away. On the positive side would just be positive. 9.8. And lastly, we have a fraction We have one half. So we have to think of a number that is one half unit away from zero, but on the opposite side of the number line. Well, that would simply just be negative one half. So again, notice to find the opposite of a number. All you're doing is changing the sign. If it starts positive, it will become negative. And if it starts negative, it will become positive.