Maths is a subject that a lot of students face problems in and find it difficult to score, but if you get the logic and reasons behind the usage of different formulas, it becomes really easy and a high scoring subject. Fractions are a really important concept of mathematics so it is really important to know it in and out.
Basics of fractions:
We all know that fractions are simply part of a whole that has a numerator or upper number and a denominator or bottom number. Fractions are of many types and plotting of fractions forms the basics of some important concepts of mathematics like linear equations, number line, and slope in algebra. If you find it difficult to work with numbers then here are some free Number Tips and Tricks offered by Cuemaths which helps you in solving fractions and other number questions easily and a little quickly.
Types of fractions:
- Proper fraction: In this type of fraction, a numerator is always less than the denominator like ⅔, ⅗, and ⅚.
- Improper fractions: In this type of fractions, a numerator is always greater than or equal to the denominator like in the case of 1, 3/2, and 4/3.
- Mixed fractions: It is a type of fraction which is basically an improper fraction but is a combination of a whole number and proper fraction. For example 2⅓ and 3¾. Mixed fractions can always be converted back into normal improper fractions by multiplying the whole number with a denominator and adding the numerator which now becomes the new numerator. Like 2⅔ can be converted by multiplying 3 by 2 and then adding 2 which is the numerator now, the new numerator is 8 and fraction will be 8/3.
How to plot fractions on graphs?
What are different ways of plotting fractions?
What are the steps of plotting fractions?
These questions must be in your mind and it is important to answer them now. By the end of this blog, you should be able to:
- Plot fractions on graph
- Use different ways of plotting fractions
- Use different tips and tricks to graph fractions easily
What are different ways of plotting fractions?
Plotting of fractions can be done in 3 different ways:
- Graphing fractions on Number Line
- Graphing coordinates that have fractional values
- Graphing fractions using slope
These 3 ways can be used to graph fractions and if you know basic plotting of numbers on graphs then plotting fractions will be very easy. Following are the steps and tips to graph fractions using these 3 ways.
Graphing Fractions On Number Line:
Graphing fractions on the number line is the simplest method of plotting fractions. It is very similar to plotting whole numbers. Steps of graphing fractions on the number line are:
Locate The Nearest Whole Numbers: The first step is to find the nearest whole numbers of the fraction. For example, the fraction is ⅖ so the nearest whole numbers are number before ⅖ that is 0 and number after ⅖ that is 1.
Make Subdivisions Between The Located Whole Numbers: Make subdivisions on the basis of denominator or a bottom number of the fraction. So if the fraction is ⅖ then the denominator is 5 and 5 subdivisions are made between 0 and 1.
Mark The Fraction: Note the numerator of the fraction and start counting from the lower whole number to find the numerator subdivision. In the above case as the numerator is 2, start counting subdivisions from 0 and mark the fraction at the 2nd subdivision. The marked point is fraction ⅖.
Example: Plot fraction 4/6 on a number line.
- This fraction is not in the lowest form so it is important to convert the fraction into the lowest form by dividing both numerator and denominator by 2. So, now the fraction is ⅔ which is the lowest form possible.
- Locate closest whole numbers or integers that are 0 and 1.
- Make 3 subdivisions as the denominator is 3.
- Count 2 units starting from 1st integer or whole number that is 0.
- Mark that point and label it as A.
- You have successfully plotted fraction ⅔ as point A.
Tips and Tricks:
- Always reduce the fraction to the lowest form as this will save a lot of time and effort.
- Don’t forget to label the fraction for further use.
Graphing coordinates that have fractional value:
The previous method was to graph fractions on a single number line, while this method involves graphing fractions on 2-dimensional graphs, which consists of 2 perpendicular number lines X-axis and Y-axis. Following are the steps of plotting fractions using this method:
Reduce The Fraction To Lowest Form: This step forms the first step of any method otherwise graphing without reducing a fraction to the lowest form will take a lot of time and might lead to some mistakes.
Label The Coordinates And Form A Scale: In this method of graphing, you are provided with coordinates like (1, ⅓) where coordinates are always in format (X-axis, Y-axis). The scale has to be formed keeping in mind the denominator of a fraction, if there are 2 different denominators then the common denominator is used as a scale.
Plot The Coordinates: Plotting has to be done like in the previous method by counting the subdivisions and matching it with the numerator of the fractions.
Tips and Tricks:
- If there are 2 fractional coordinates with different denominators then the common denominator has to be used which is the LCM of the denominators. For example fractional coordinates are (⅔, ½) then common the denominator will be LCM of denominators 2 and 3 that is 6 and new coordinates will be (4/6, 3/6).
- It is always advisable to make the scale of the axis large enough to even plot some extreme set of fractional coordinate values.
Graphing Using Fractional Slope:
The slope is not a new concept for algebra students, but for those who are hearing slopes for the first time, it is simply a fraction that tells by what amount of change a line is tilting.. It is expressed in fraction where numerator shows the change in y coordinate and denominator depicts the change in x coordinate.
Mark the point online: Coordinates of at least one point of the line is given. Locate that point on the given slope and mark that point as the starting point.
Count Up or down: From the point, you just graphed, count the number units up or down on the basis of the numerator of the fraction. If the numerator is positive as in the case of ⅔ then count 2 units up while if the numerator is negative as in the case of -⅔ then count 2 units down.
Count across right or left: From the point, you ended while counting up or down, now start counting across on the basis of the denominator of the fraction. If the denominator is positive as in case of ⅘ then count 5 number units to right of that point and if denominator is negative as in case of 4/(-5) then count 5 units to left of that point.
Mark the point of line: The point that you are now on is the fraction asked in the question. This fraction must be on your line.
Tips and Tricks:
- Reduce the fraction to lowest form.
- Always check for the sign twice as a single mistake in the sign will make the whole plotting of the fraction wrong.
Now that you know the different ways and methods of plotting fractions on graphs, you will be feeling more confident in classes. Best way to learn graphing of the fractions is to practice as much as possible. You can double check your plotting by graphing using one method and then matching it with graphing done by using the second method. Then you can opt for the method which you find easier but if you want to increase your speed further then you can look forward to Number Tips and Tricks that is provided by Cuemaths for free which will help you in increasing your calculation speed with some amazing tips and tricks.
Frequently Asked Questions (FAQs):
How to decide which method to use while plotting fractions?
If a single fraction is asked to plot then the 1st method that is the number line method is the best and easiest way of solving, but if you are asked to plot fractional coordinates then any of the other 2 methods should work which are coordinate method and slope method.
Are these methods of plotting acceptable in board or school examinations?
Yes, these methods are acceptable in school and board examinations. These methods do exist in NCERT books and are often part of school curriculum.
Can plotting be done without graphs?
Yes, plotting can be done without a graph, but use of graphs allows you to plot the fraction properly without much mistakes.
For any queries or questions related to plotting of fractions on graph, you can submit it in the given comment section, which will be answered by experts from Cuemaths as soon as possible.