How to Represent Integers on a Number Line

TenMarks teaches you how to represent and compare integers on a number line.

How to Represent Integers on a Number Line Integers on a number line, so in the first problem it asked to what number is the arrow pointing. So before we begin and answer this question let’s talk about integers on a number line. So negative and positive whole numbers are called integers. Integers are negative and positive whole numbers. They are the numbers that can be written without a fractional or a decimal component. So if for example, 65, 7 and -765 are integers. So these are examples of integers, 1.6, 1 ½, these are not integers. So in other words, integers are the numbers one can count with items such apples or finger and they are negatives as well as zero. So the numbers greater than zero are called positive integers so positive integers are the numbers that are greater than zero. So for example, +7 is a positive integer and it is read as positive 7 or 7. Numbers that are less than zero are negative integers so negative integers are less than zero. So for example, -7 is a negative integer and it is read as negative seven. Also please note that zero is not positive nor is it negative. So, to what number is this arrow pointing to? So if we look at our tick marks on the number line they have equal distance among them. So each tick mark is equal distance throughout the entire number line. So here is zero and remember zero is neither positive nor negative and when you move to the right of the number line from zero to the right you're moving positive and if you move to the left of zero you go to your negative. If we count by ones starting at zero, we see that our count matches the numbers labeled on the number line. So if I go 1, 2, 3, 4, 5, it matches the five on the number line. I can continue to 6, 7, 8, 9, 10 and so forth. So the arrow is pointing to this line right here. So if I count 1, 2, the arrow points to the number that is 2 greater than zero. We know numbers greater than zero are positive. They are to the right of the zero. It’s positive so two is greater than zero. Therefore the arrow is pointing at positive two. Let’s take a look at number two in our problem. Let’s give some room here. What is the opposite of -80o Fahrenheit? So opposite of an integer is a number which is the same distance from zero as the original number on the number line but in the opposite direction. So negative 80, here is zero. So -80 is going to be to the left of our number line and -80 is right here on our number line. So the opposite of -80 would be the same distance from zero, 80 units but in the opposite direction to the right. So if we start at zero and we go to the right or go in the positive direction. So if we went 80 to the left starting at zero then we’re going to start at zero and go 80 to the right. So if I go 80 to the right, I'm right here. So the opposite of -80 will be the same distance from the zero, 80 units. So the opposite of -80 will be 80 units to the right of the zero which is a positive 80. What is the opposite of -80o Fahrenheit? It’s +80o Fahrenheit. Let’s move on to number three. So it says compare right to greater than or less than. Use the number line to solve. We have two is either greater than or less than -7. We can use our number line to help us compare two numbers. So to compare 2 and -7 using the number line we first need to make our number line. I went ahead and made our number line and then we put our tick marks on our number line keeping an equal distance between the marks. Since I'm comparing negative and positive I'm going to put my zero in the middle and I'm going to go to negative and I'm going to go to positive and notice how I went to 8 on both sides. The reason is because I have a 7 here so I just want to make sure I'm incorporating -7 on both sides. Now we need to locate the positions of -7 and 2 on our number line. Let’s locate 2 so note that 2 is a positive 2 because there is no negative sign so any time you write a positive number it’s just the regular number 2, 3, 4, those are considered positive. So I know positive is to the right of zero so I'm going to start at zero and I'm going to move two tick marks to the right and I see my positive 2. So I'm just going to put my mark there. Now let’s go and find -7 so -7 is a negative number. Remember negative integers are to the left of zero so I'm going to start at zero and I move down to my 7 tick mark and I'm going to mark my tick there. I mark my dot there. Now let’s remember that 2 is to the right of -7 on the number line. So -7 is here and please note that 2 is to the right. We know that if any two numbers on a number line, the number to the left is always less than the number to the right. So that means that -7 is less than +2. So we know that -7 is less than 2 because 7 is to the left of the 2 and any time you move to the left you're going to the negative integers. You're getting smaller. Anything to the right is larger. It’s positive. So that means if -7 is less than +2 then 2 is greater than -7. Things to keep in mind, please note that negative and positive whole numbers are called integers. For example 65, 7, -765 are all integers. Numbers such as 1.6 or 1 ½ are not integers. An integer on the right is always greater than an integer on the left of the number line. Integers that are on the right of zero on the number line are called positive integers. They are greater than zero. Integers that are on the left side of zero on a number line are called negative integers. Negative integers are less than zero. Also keep in mind that zero is neither positive nor a negative integer.