Video: Comparing Integer Numbers with Absolute Value

Which of the following is true? [A] −|−61| < −35 [B] −|−61| > −35 [C] −|−61| = −35.


Video Transcript

Which of the following is true? A) Negative absolute value negative sixty-one is less than negative thirty-five. B) Negative absolute value, negative sixty-one is greater than negative thirty-five. Or C) negative absolute value, negative sixty-one is equal to negative thirty-five.

Before we make our decision, we first need to understand those absolute value signs. The absolute value sign makes numbers positive. Let’s take a look. We need to decide whether we are going to replace our question mark with a less than sign, a greater than sign, or an equal to sign. Let’s first simplify the left-hand side. As we said before, the absolute value makes numbers positive; so that negative sixty-one is positive sixty-one. We also need to bring down our negative sign as well as negative thirty-five. So is negative sixty-one less than negative thirty-five? Is negative sixty-one greater than negative thirty-five? Or is negative sixty-one equal to negative thirty-five? Well in order to be equal, they must be equal in value. And negative sixty-one and negative thirty-five are not equal in value. Therefore we can eliminate option C.

Let’s look at a number line to help us come to a conclusion. On a number line, numbers to the left are smaller and numbers to the right are larger. Therefore negative sixty-one must be smaller than negative thirty-five. So the sign that we would use instead of saying smaller than would be less than. So we would say negative sixty-one is less than negative thirty-five. Therefore A is true.

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