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Video: Evaluating Expressions with Integers and Absolute Values

Bethani Gasparine

Calculate −7 × (−|−64|) = _.

03:11

Video Transcript

Calculate negative seven times negative absolute value of negative sixty-four.

First, it’s important that we know where to begin in our equation. Do we multiply? Do we simplify what’s in the absolute value? Do we look at the parentheses first? Well the way that we know, is by the order of operations. Looking at our equation left to right, first you take care of the parentheses, then any exponents, then multiplication, then division, then addition, and then finally subtraction. So first, we need to take care of any parentheses.

We have a pair of parentheses. But inside those parentheses, there’s a multiplication. There’s a negative times our absolute value sign. So we need to take care of that absolute value sign, because it acts as another set of parentheses essentially to that negative sixty-four.

So first, we need to take care of the absolute value of negative sixty-four, then we will multiply by the negative sign in front of the absolute value bars. And then we will finally multiply by the negative seven. Again, we will take care of the parentheses before we multiply.

So let’s rewrite our equation. Since the absolute value is what we were looking at first, we need to understand what does the absolute value sign do. The absolute value sign makes numbers turn positive. So if a number is already positive, it will stay positive. However, if the number is negative, like this example, negative sixty-four, it will turn into a positive sixty-four. So now we have negative seven times negative sixty-four. The reason why the sixty-four is negative right now, it’s because of that negative sign we have to bring down. And essentially, we’re taking that negative sign, which is like a negative one times sixty-four. So right now in the parentheses, we have a negative sixty-four.

In our last steps, we will be taking seven times the sixty-four. However, we need to pay attention to our sign. We have a negative number times a negative number. So what will our final answer be, in terms of its sign? Will it be positive or negative? Two negative numbers multiplied together will result in a positive number as an answer.

Two other rules to take note of, is a negative number times a positive number, which you could switch that order, will turn into an answer that is negative. And then finally, if you multiply two positive numbers, it will result in a positive answer.

Therefore, negative seven times negative sixty-four equals four hundred and forty-eight.