Video: Comparing Two Numbers Involving Absolute Value

State whether the following is true or false: −4 1/4 is equal to the absolute value of 4 1/4.

02:25

Video Transcript

State whether the following is true or false. Minus four and a quarter is equal to the absolute value of four and a quarter.

Now we know that the absolute value of a number is how far away from zero it is. So if we draw a number line, we can find where four and a quarter belongs. We can label it. And we can see straightaway that the distance from zero to our number is four and a quarter.

In maths, we can write absolute value as a number in between two vertical lines. So this says the absolute value of four and a quarter equals four and a quarter. In other words, the number four and a quarter is four and a quarter away from zero.

Let’s have a look at our statement because the way it’s being written, we have to be very careful about how we answer it. Now we’ve already calculated the absolute value of four and a quarter as four and a quarter. So really, we could read the statement as minus four and a quarter is equal to four and a quarter. Is this true? Is minus four and a quarter the same as four and a quarter? No, the statement is false.

Before we finish the video, it might be worth pointing out that the statement was slightly different. It would give us a different answer. If we mark minus four and a quarter on our number line, we can see that this value is also four and a quarter away from zero. So the absolute value of minus four and a quarter is equal to the absolute value of four and a quarter. But our problem doesn’t ask this. Our problem just asks whether minus four and a quarter is equal to the absolute value of four and a quarter.

We know that the absolute value of four and a quarter is four and a quarter. And so the two are not equal. So by reading the question carefully, we’ve avoided the mistake, and we can say the statement is false.

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