Have you ever heard the definition “number lines”? Do you know what they are and what is their meaning? If you have certain doubts about this concept, do not worry. You have come to the right place. From now on this term will no longer generate any doubts. Do you want to know more about it? In that case, keep reading!
The straight. What are they?
To understand what a number line is, it’s easiest to start by learning what lines are. The word straight comes from the Latin rictus. This term refers to a line that does not have any curved area or angles.
In geometry, when talking about straight lines, it is done by thinking of a one-dimensional line that lacks a beginning or an end. These lines are made up of dots, one after the other, and never end. They are infinite.
Lines are one of the main elements of geometry. In its composition, as we have explained a few lines above, are the points. With the points we can create portions of lines that we will call segments. Hence, it is understood that a line is composed of many segments or points.
The number lines. What are they and meaning
Now that we understand a little better the meaning of lines in geometry, it is time to understand what a number line is. This term is composed of two words.
- The word straight, which, as we have explained a little above, is an indefinite line made up of points or segments.
- The number word. When we introduce this term, what we are doing is linking that line to specific numbers or quantities.
In this way, number lines therefore combine the characteristics of lines and numbers. That is to say, it is made up of a one-dimensional line that does not have an end but that, in turn, incorporates integers. These numbers are located by creating points or sections that are equidistant from each other.
If you notice, the number line is very similar to a ruler. Since its points are numerically divided equidistantly, it is used to add and subtract elements.
Did you know that the number line is also known by another term? So that’s it. The number line is also known under the term real line. And why does it receive this name?, you will ask yourself. Well, for a very simple fact that will help you remember this concept. The number line includes the real numbers in its form. The real numbers, in turn, are divided as follows:
- Rational numbers, which are the positive and negative numbers other than zero.
- Irrational numbers, which are those numbers that cannot be defined by means of a fraction m/n.
Can the numbers on a number line be arranged in any way?
No. As we have already explained a few lines above, the numbers are placed with the same distance from each other. Furthermore, the real numbers are divided by two from the point of origin. The point of origin is marked by 0.
Negative rational numbers are positioned to the left of 0. To the right of 0, however, are the positive numbers. These numbers on the number line are known as positive real numbers and negative real numbers.
How to Create a Number Line?
Now that we know what a number line is, it will surely be much easier for us to create it. Let’s see the steps below.
- Get hold of sheets of graph paper. To make it much easier for you to create a number line, it is best to use graph paper. When you have done with a sheet the first step will consist of drawing a straight line. Help yourself with the grids on the paper to trace it. This line will be the main element of your line. Separate the line into equidistant points. To do this, you can start from one of the sides by creating a vertical line on it and protruding the same from above as from below. Then continue creating points at the same distance from each other from that first point you have marked. If you look closely, your drawing will be very similar to that of the train tracks.
- Add the numbers. Your number line can be made up of positive or negative rational numbers. It all depends on the type of problem you want to solve. If you only need positive numbers you will have to start numbering from the left side of the line. The first point will be 0, the next will be 1, 2, 3… and so on. If you want to create a number line with negative numbers, 0 will be on the right and we will begin to number from right to left in the following way: -1, -2, -3,… etc. In case we want it to have positive and negative rational numbers, we will have to place 0 in the central point. From the left of 0 we will place the negative numbers starting with -1. And from the right of 0 we will place the positive rational numbers starting with 1.
Different ways to use a number line
Now that we know what a number line is and how to create it, we are sure to realize the multiple uses that this tool has. You can use a number line to solve not too complex math problems. Mainly it will help you to subtract and add small numbers. Problems involving single negative numbers can also be solved with a number line.
Solve a problem with a number line and positive numbers
Let’s look at an example to see how to use the number line to solve a sum.
Jaimito has bought 5 apples at the supermarket in his neighborhood. When he gets home he sees that his sister Laura has brought 3 pears from him. How many fruits do they have in all?
In this case we will have to add the total number of pears and apples to know how many fruits there are in total. In order to solve this problem, the steps are as follows:
- Understand the problem. It is clear that in this case what we have to do is an addition. To make it easier we will have to position one of the numbers as the first and the other as the second. In this case we are going to look for the answer of this sum 5 + 3 with the number line. Therefore, the first number of the operation will be 5.
- Circle this number on your number line. In this way you will know that you have to start counting from position 5 of the straight line. From there you will have to start the addition.
- Move 3 more spaces on the number line to find the solution. Since we have to add 3 (pears) to 5 (apples) we will advance 3 positions in total from number 5.
- When we have advanced the total positions of number two, we will have to stop. If we look closely, after advancing 3 spaces, we will stop on the number 8 of our number line. Therefore, the solution to the problem is 8. In total, Jaimito and Laura have 8 fruits.
- Redo the calculation. Repeat the operation on the number line again to make sure you have done the calculation correctly. If you get the same answer after checking, it is clear that you have done the counting correctly.
Solve a problem with a number line and negative numbers
Adding positive numbers is very easy with the number line. But it is also if you want to subtract negative numbers. In this case we are going to give you an example so that you can see for yourself how easy this operation is also thanks to the number line.
In this case we are going to solve the following account. What would be (-7) – (-3)? To make this account we will have to carry out the following steps.
- Find position 0 on the number line. We know that if our number line has positive and negative rational numbers, 0 will be placed in the middle of the line. To the left are the negative rational numbers and to the right the positive ones. In the event that our number line only has negative numbers, 0 will be in the first position on the right of the line.
- Find the main number. As we did with the previous problem, we have to look for the main number. To make it easier, we will always place the highest negative as the main number. In this case it is -7.
- Locate the main number of the problem on the number line. Now that we know that -7 is the main number we have to locate it on the number line. Once we have located it, we will circle it in red or mark it in another way. The important thing is that we know that we have to start making the account from that number. In this case the -7.
- Begins to perform the operation. The difficulty in subtracting negative numbers is understanding that the number line in this case works the same as if we were to add positive numbers. That is, we must move to the right to find the solution. Since in this case we have started our problem from the number -7, we must move 3 positions to the right to find out what is (-7) – (-3). Once we finish advancing the 3 positions to the right we will have found the solution to the problem. In this case the answer is -4.
- Repeat the operation to make sure that the answer is correct. If you want to confirm that you have done the accounts correctly, it is best to repeat the operation again. Just like we did when we added positive numbers in the previous problem. If the answer is the same, we will have done the math correctly.