Number Lines With Fractions – What They Are And Meaning

Have you ever thought that a number line can also be used to add fractions? Would you know how to do it? Do you know what the number lines with fractions are and what is their meaning? In this article we are going to explain everything to you so that you clear up your doubts once and for all. Would you like to learn how to do these lines? In that case, keep reading!

What are number lines with fractions? Its meaning

How number lines work?

Before we begin to explain how to create a number line with fractions, it is important that we understand two concepts: lines and number lines. Next we will explain both.

The straight lines

Lines are one-dimensional lines made up of many points. They are one of the elementary concepts within geometry. And they are together with the plane or the point.  When we say that a line is made up of many points, it is because, if you were to approach it with a magnifying glass, you would see that the line you are looking at is made up of many small dots.

Straight lines are characterized by being infinite and lacking a beginning and end. All the points that form the line advance infinitely towards the same place.

Many people confuse lines with segments or rays. However, they are not the same elements.

• Segments are characterized by starting at one point and ending at another. Therefore they are not infinite like lines. In fact the segments are a finite part of the lines.
• Rays, for their part, are characterized by having a beginning but no end.

This misunderstanding is usually related to the way lines are represented when they are studied. As they are normally drawn on a blackboard or paper, they are given a finite shape. However, it must be remembered that they are not finite, but infinite. In this way we will avoid messing up.

Number lines

When we talk about a number line, what we do is unite two different concepts in a single representation. On this line we will find numbers separated from each other at the same distance. The appearance of a number line is very similar to the ruler used in technical drawing. Composed of vertical lines that cross the straight line and that mark the number.

Number lines with fractions

Number lines are represented by both positive and negative whole numbers. However, fractions can also be included. In case of incorporating fractions to the line we would be talking about number lines with fractions.

How to Create a Number Line With Fractions?

The main question that arises when we work with fractions on number lines is how to place these fractions on them. We are going to explain how it is done below:

Placing a fraction on the number line.

The first thing we are going to learn is how to place a fraction on the number line. You will see that with these 5 simple steps that we are going to explain, it will be super fast for you to figure out how to do it. We go to them.

1. Know our fraction. To position the fractions on the number line we must think of a fraction. For example 3/5.
2. Look at our fraction. The fraction tells us the number of parts into which a whole is divided. Why is it like this? Because fractions are part of a whole.
3. Draw the line In this case from 0 to 1 there will be 5 parts. It is as if we had a circle divided into five little cheeses. The circle would be our whole and each cheese the fractions that make it up.
4. Divide the line. So now we have to divide the line into 5 equal parts. The parts into which we divide the line are given by the denominator of the fraction from which we started. Remember that fractions are divided into two parts. The little number on top, which is called the numerator, and the one on the bottom, which is considered the denominator. While the denominator will indicate the number of parts into which the line is divided, the numerator will indicate the exact position it occupies within it.
5. Place the line in the proper position. If our fraction is 3/5, we must advance three positions along our line. This position will be that of 3/5. That is precisely the place where our faction is located. In this case our fraction is 3/5.

Putting two fractions with different denominators on a number line

Now let’s make the example a bit more complicated of how to plot fractions on a number line. Imagine that you have two fractions with different denominators and you want to place them on the same line. How should you place them in the same integer on your number line? It’s possible? Let’s see it next.

1. Know our fractions. In this case, the fractions with which we are going to operate have different numerators and denominators. We will play with two simple fractions. ½ and 2/3.
2. Do a multiplication of fractions. To know what position they occupy within the same integer it is necessary to do a multiplication of fractions. You will see that it is very simple. Although at first glance it may not seem like it! To do this we will multiply each numerator with the other and each denominator with the other denominator. Do you know how much the total would be? Indeed!, 2/6. You can also take the least common multiple to find this number.
3. Pay attention to the denominator. Once the multiplication of fractions is done, the denominator marks the positions that our number line will have. That is, the number of equidistant separations between each number. The total is 6.
4. Find out where each of the fractions goes on the number line. Let’s get to the heart of the matter. Let’s find out what position each of our fractions occupies within the line. To know it we will have to multiply the numerator of each fraction with the denominator of the other fraction that we have. That is, we will multiply 1 with 3 and 2 with 2.
5. Position of the first fraction on the number line. By multiplying the numerator of the first fraction with the denominator of the second fraction we will obtain a total of 3. This is the number of spaces that our ½ fraction must advance along the line. And that is the position that the fraction ½ will occupy within our integer.
6. Position of the second fraction on the number line. In the same way that we have proceeded with the first fraction, we must proceed with the second to find out what position it is on the number line. In this case we will multiply the numerator of the second fraction with the denominator of the first. In total we will obtain a 4. These are the positions that we have to advance on the line. And this will be the space that the second fraction will occupy within the number line. Have you noticed that the second fraction, that of 2/3, is greater than the first, that of 1/3?

Place improper fractions

In our last example we are going to figure out how to place an improper fraction on a number line. That is, a fraction whose numerator is greater than the denominator. These fractions are known as improper fractions on the number line. Calm. You will see that it is much easier than it seems at first glance. Let’s see how to do it.

1. Look at the fraction we have. In this case, our fraction with which we are going to do the example will be the following: 5/3. If you look at the numerator of this fraction it is greater than the denominator.
2. Convert the improper fraction to a mixed number. In order to find out how to place the improper fraction we must pass it to a mixed number. Do you know how this is done? Very easy.
   1. Step 1.First we look at our fraction.
   2. Step 2.Secondly, we pass the fraction to a mixed number. The method to convert an improper fraction to a mixed number is to divide the numerator of this fraction by its denominator.
   3. Step 3. From now on the quotient of this division will represent the whole number.  When we do a division we are left with a remainder. Well, this remainder will be the numerator of the fraction. For its part, the denominator will remain the same as the one that the fraction had. That is, the divisor with which we made the division. That is to say, that the mixed number of the fraction 5/3 will be equal to 1 integer and 2/3. You can see the explanation of these three steps in the image below. You will see that in this way it is much easier for you to understand the operation.
3. Observe the mixed number. The integer that you have given us to convert the fraction into a mixed number tells us the position in which the fraction is found. And the position is in the integer 1. That is, it will be located between 1 and 2. Our number line will therefore consist of segments 1 and 2 to be able to place the fraction.
4. Divide the parts of each segment. Since our denominator of the mixed number tells us that each integer is divided into three parts, we will divide our integers with that number of parts. Now we must place the fraction from the integer 1 in position 2/3. That is, we will advance two positions from 1. This will be the place occupied by the original fraction. The one from 5/3. And we would be done. Hasn’t it been much easier than it seemed at first?