Video: Finding and Positioning Rational Numbers on a Horizontal or Vertical Number Line Diagram

Which of the numbers ๐‘Ž, ๐‘, ๐‘, and ๐‘‘ is โˆ’0.25?


Video Transcript

Which of the numbers ๐‘Ž, ๐‘, ๐‘, and ๐‘‘ is negative 0.25?

So youโ€™ve got a number line here. And it goes from negative two up to two. And you can see on it, weโ€™ve got ๐‘Ž, ๐‘, ๐‘, and ๐‘‘. So the first thing weโ€™re gonna do is work out what each of these values is. But before I can do that, I need to work out how much each one of our little gaps is worth.

Well, we can see that between each of our units, so each of our integers, we have four spaces. Therefore, we can say that four spaces equals one unit. So if you want to work out what one of the spaces equals, then what weโ€™re gonna do is divide it by four. So therefore, we can say that one space is equal to a quarter of a unit, which equals 0.25 as a decimal because weโ€™re gonna look at dealing with decimals. Okay, great.

Well, I said that weโ€™d want to work out what each of the values are, but we can rule out ๐‘ and ๐‘‘ straightaway. And thatโ€™s because weโ€™re looking to find negative 0.25. So we want to find the position of negative 0.25. Well, if itโ€™s negative, it means itโ€™s going to be to the left of our zero point. However, ๐‘ and ๐‘‘ are to the right of it. So theyโ€™re both positive. So we can ignore ๐‘ and ๐‘‘ and take a look at ๐‘Ž first of all.

Well, ๐‘Ž is equal to negative one then add 0.25. And itโ€™s add 0.25 because weโ€™re going to the right. And we know if we go right up on our number line, weโ€™re adding on. If you go to the left, then weโ€™re subtracting. In case, weโ€™ve got ๐‘Ž equals negative one plus 0.25. And this gives us negative 0.75. And thatโ€™s because if weโ€™re adding on 0.25, weโ€™re gonna become less negative. And so, therefore, itโ€™s the same as saying negative one add a quarter. So a quarter away from one is three-quarters, which is 0.75. So the answer is ๐‘Ž is equal to negative 0.75. So thatโ€™s our answer for ๐‘Ž. Well, this is not negative 0.25. So therefore, we can rule out ๐‘Ž. So it looks like that ๐‘ is gonna be the correct number. But Iโ€™m gonna double-check.

Well, this time, weโ€™ve got ๐‘ is equal to zero minus 0.25. And thatโ€™s because weโ€™re going left down the number line. So therefore, weโ€™re subtracting. Well therefore, ๐‘ is equal to negative 0.25. And thatโ€™s because if you subtract 0.25 from zero, it gives us negative 0.25. So therefore, this is what weโ€™re looking for. So we can say that ๐‘ represents the number on the number line that is negative 0.25.

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