Vinay Pacha

Tally marks are most ordinarily used to represent the scoreboard in games and sports. The frequency of knowledge is often represented using Tally Marks. Tally Marks are also called Hash Marks. It is denoted by a single vertical bar ‘ | ‘. You may use the tally for solving addition, subtraction, or word problems. Before numbers were invented people found it difficult to stay records of their belongings and then they used to count by sticks which are further referred to as Tally Marks.

Read More: Frequency Distribution of Ungrouped and Grouped Data

Tally Marks – Definition

Tally marks are defined as a way to record or mark your counting. It is a numeral system used to make counting easier. The general way of tally marks writing may be a group or set of 5 lines, in these five lines first four lines are drawn vertically and each fifth line runs diagonally over the four vertical lines it means from the top of the first line to the bottom of the fourth line.

Tally marks are commonly used for counting the points, scores, many people like that, these tally marks will differ from country to country because each country has developed with their own system. The tally marks are expressed as shown below

Counting Tally Marks

Let us see how to use tally marks for counting numbers 1 to 10. Tally marks are the quickest way of keeping track of numbers during a group of five.

How to represent the numbers in Tally Marks?

• One is represented by ‘I’
• Two is represented by ‘II’
• Three is represented by ‘III’
• Four is represented by ‘IIII’
• Five is not represented by ‘IIIII’, it is represented as four vertical lines and one cross line (diagonal line) it means from the top of the first line to the bottom of the fourth line.
• Six is represented by a set of five lines with ‘I’
• Seven is represented by the set of five lines with ‘II’
• Eight is represented by the set of five lines with ‘III’
• Nine is represented by the set of five lines with ‘IIII’
• Ten is represented by 2 (two) sets of five lines.

Tally Mark Chart

Tally charts are used to collect the data efficiently and quickly. A Tally Mark chart or a Tally Mark graph is a graphical representation of data in statistics, so it is beneficial in scanning the data. A tally chart filling with marks is represented by numbers is quicker than writing out figures or words, then the information is collected into sub-groups, making it easy to research.

In a tally mark graph has first four numbers lines are represented by vertical lines and the fifth line is represented by a diagonal (/) line across the four vertical lines. The tally marks chart contains the number from 1 to 10 is as shown below,

Tally Marks are used for finding the frequency of the set of data values specifically for the raw data or ungrouped data. consider an example, asked to create the frequency distribution provided with raw data or random values. In this case, we may have to make either for class intervals or individual observations.

Now, we count all occurrences of a single data value or a class interval in one go, then we have to cross-check the entire list again and again for the next class interval or individual observation. Therefore this will be taking a lot of time for finishing. So, we can be reducing the complexity by making use of tally marks. The entire process can be done just by adding tally marks for each class interval or different observations.

Thus, we’ve to traverse the whole list of given data set on one occasion and then write the frequency numbers by counting the tally marks after completing the identification. So the obtained table is defined as the frequency distribution of the given data. The below example on tally marks will help you to understand the concept in a better way.

Tally Marks Examples

Example 1:

Below given the marks of 35 students on the Maths test (out of 10). Arrange those marks in tabular form using tally marks?

6, 1, 7, 8, 10, 9, 4, 2, 3, 7, 1, 8, 7, 5, 1, 4, 7, 6, 5, 2, 3, 8, 2, 4, 6, 2, 9, 3, 1, 4, 5, 7, 5, 10. Find the  

1. How many students scored more than 8 marks?
2. How many students scored less than & equal to 5?
3. What are the marks scored by the maximum students? what is the number of students?

Solution:

Given the marks of 35 students in Maths test. The frequency table of given data is as shown below

(i) Given the 35 students’ marks out of 10 in the maths test.

Now, we can find the number of students with more than 8,

The number of students with more than 8 marks is, 3 + 2 = 5

Therefore the total number of students with more than 8 marks is 5.

(ii) Given the 35 students’ marks out of 10 in the maths test.

Now, we can find the number of students who scored less than and equal to 5.

The number of students who scored less than and equal to 5 is,

= 4 + 4+ 3+ 4 + 4

= 19

Therefore, the number of students who scored less than and equal to 5 is 19.

(iii) Given the 35 students’ marks out of 10 in the maths test.

Now, we can find the maximum number of students who scored 5 marks.

The maximum number of students who scored 5 marks is 5.

The maximum number of students scored 5 marks. The number of students is 5.

FAQ’S on Tally Marks

1. What is Tally Mark Chart?

Tally Mark charts are used to collect the data efficiently and quickly. A Tally Mark chart is a graphical representation of data in statistics, so it is beneficial in scanning the data. A tally chart filling with marks is represented by numbers is faster than writing out figures or words, then the data is collected into sub-groups, making it easy to analyze.

2. Define Tally Frequency Table?

The Tally Frequency table is defined as a method of collecting the data with the tally marks, tally frequency table is also known as Tally Chart.

3. Why should Tally marks be essential?

Tally marks are very important mainly use to keep the record of a running or continuous count. These tally marks are so useful for maintaining and recording the scores in a game or a sport.

5. What are the advantages of Tally Marks?

The advantages of tally marks are

1. Enables Effortlessness in data movements
2. Fewer expenses on data collection and data transfer of files.
3. Helps for easy and fast documents access.

To learn more about the Frequency Distribution of Grouped data and Ungrouped data this is the right place to learn, and to increase more knowledge on Frequency Distribution. Statistics is the study of collecting data, organization, interpretation, analysis, and data presentation. The main purpose of statistics is to plan the collected data in terms of the experimental designs and statistical surveys.

Statistical knowledge will help to collect the data in the proper method, and samples are employed in the correct analysis process, in order to effectively produce the results. In statistics, the Frequency distribution is a table that displays the number of outcomes of a sample. In this platform, we have to learn about Frequency Distribution definition, ungrouped data, grouped data advantages, and disadvantages.

Also, Read: Terms Related to Statistics

What is Frequency Distribution?

A frequency distribution can be defined as the tabulation of the values with one or more variables. A frequency distribution is a representation, either in a graphical format or tabular format, that displays the number of observations within a given interval. The interval size will depend on the data being analyzed and the goals of the analyst. The intervals must be mutually exclusive and exhaustive.

Basically, the Frequency distribution is typically used within a statistical context. A frequency distribution can be graphed as a histogram (or) pie chart. Frequency distributions are particularly useful for normal distributions, which show the observations of probabilities divided among standard deviations.

The tabular form of Frequency Distribution of statistics is shown below

Frequency Distribution of Grouped Data

Grouped data means the data or information given in the form of class intervals. This information can also be displayed using a pictograph or a bar graph.  Grouped data plays an important role when we have to deal large information or data. Arranging the individual observations of a variable into groups, so that the frequency distribution table of these groups provides a convenient way of summarizing or analyzing the data is termed grouped data.

The advantages of Frequency distribution grouped data are:

• It improves the accuracy and efficiency of estimation.
• It helps to focus on the important subpopulations and ignores irrelevant ones.

The disadvantages of grouping data are:

• Lose some of the details in the data.
• we cannot accurately calculate statistics such as the mean or median from a grouped data of frequency table is alone

Frequency Distribution Table of Grouped Data:

The frequency distribution of grouped data is to analyze when the collected data is large, we can follow this approach to analysed it easily. It is named tally marks.

Example of Frequency Distribution Grouped Data: 

Consider the marks of 30 students of class VII obtained in an examination. The maximum marks of the exam are 50.

24, 6, 12, 17, 33, 45, 16, 7, 24, 28, 11, 31, 23, 40, 39, 16, 26, 9, 16, 20, 31, 25, 28, 18, 15, 33, 28, 47, 43, 21.

So, if we create a frequency distribution table for each and every observation, then it will form a large table. For easy understanding, we can make a table with a group of observations say that 0 – 10, 10 – 20, 20 – 30, 30 – 40,   40 – 50, and so on. We can form the data like the above table, easily understanding and faster-doing the calculation.

The distribution obtained in the above table is known as grouped data of frequency distribution. In that tabular form mention the data or marks in between 10 – 20, suppose 3 numbers will be there then the frequency is 3 like that you can counting or calculated the intervals, frequency will be noticed. But 20 will appear in both 10 to 20 and 20 to 30, 30 also will appear in both 20 to 30 and 30 to 40. But is not feasible that observation either 10 or 20 belong to two classes concurrently.

To avoid this inconsistency, we choose the rule that the general conclusion will belong to the higher class. It means that 10 belongs to the class interval 10-20 but not to 0-10, similarly 20 belongs to class interval of 20-30 but not to 10-20. This is how we create a frequency distribution table of grouped data.

Frequency Distribution of Ungrouped Data

Frequency Distribution of ungrouped data is a data given as individual data points. An ungrouped set of data is basically a list of numbers. Ungrouped data does not fall in any group, it still raw data.

The advantages of ungrouped data frequency distribution are :

• Most people can easily interpret it.
• When the sample size is small, it is easy to calculate the mean, mode and median.
• It does not require technical expertise to analyze it.

Frequency Distribution Table of Ungrouped Data

The data is raw that means it cannot sorted in to categories, classified, or otherwise grouped. An ungrouped set of data is basically a list of numbers. The ungrouped data of frequency distribution table is as shown below,

The following rules must be completed in order to create an ungrouped data frequency distribution :

1.  Set the values of data, which are called scores, in the column starting from the lowest value to the highest or vice versa.
2. Create the second column with the frequency of each data occurrence. This column is known as the tally of the scores.
3.  Create the third column, where the relative frequency of each score will be inserted. The relative frequency can be obtained as follows: fr = f/N, where f is the frequency of each score from the second column and N is the total number of scores. In order to check the correctness of calculations, the sum of fr should be calculated and should be equal to 1.
4. The next column, where the relative frequency will be performed in percentages, is to be created.
5. In the next column, known as the cumulative frequency column, the cumulative frequency for each score should be estimated. Calculation of the cumulative frequncy should be started from the lowest value of score, for which the cumulative frequency equals the value of frequency from the second column.
6. The further calculations are to be performed for each score in a sequence from lowest to highest and the cumulative frequency for each next score equals to the sum of the cumulative frequency of the previous score and frequency of this score from the second column. The cumulative frequency of the highest score should be equal to the total number of scores.
7.  The next column is called “cumulative proportion” and the values of its column are obtained as a ratio of cumulative frequency for each score and the total number of scores.
8.  The last column is the cumulative percent, where the cumulative proportion is presented as percentages.

Difference between Grouped Data and Ungrouped Data

Based on Classification, Accuracy, Summarization of grouped data and ungrouped data difference are listed below:

• Classification: Grouped data is organized into forms whereas Ungrouped data has no forms of organisation.
• Accuracy: Grouped data has higher accuracy levels when calculating mean and median, whereas ungrouped data has less accurate in determining the mean and median.
• Preference: Grouped data preferred the analyzing data whereas ungrouped data preferred the collecting data.
• Summary : Grouped data is summarised in a frequency distribution, while the ungrouped data has no summarization.
• The representation of grouped data and ungrouped data of frequency distribution is as shown below:

Statistics is a method of collecting data and summarizing the data. The study of the collection, analysis, interpretation, presentation, and organization of data is called Statistics. Now a days Statistics is very important because today we live in the information world and much of this information is determined mathematically by Statistics. The statistics concept is necessary for informing correct data. Go through the entire article to be well versed with Statistical Terms and Concepts along with Examples.

Also, Read: Real Life Statistics

Statistical Terms and Definitions

The various terms related to statistics such as Data, Mean, Mode, Raw data, Observation, Array, Range are explained clearly. Let us discuss them in detail by considering few examples.

Data

Statistical refers to the set of numerical facts collected for the purpose of an investigation is called Statistical data. There are two types of statistical data,

1. Primary Statistical data
2. Secondary Statistical data

The data can be about population, birth, death, the temperature of place during a week marks scored in the class runs scored in different matches, etc.

Primary Statistical Data: The data which are naturally obtained by the investigator himself for the first time for his own use is called Primary Statistical data. Primary data also called First Handed Data.

Secondary Statistical Data: The data which was collected by someone with the help of primary data is called secondary data, which is artificial in nature. Secondary Statistical data is also called Second Handed Data in nature. They are two types of Secondary Statistical Data,

1. Raw data (or) ungrouped data.
2. Array

Example:  

The below table is an example of statistical data, in this, the data will be regarding the number of students opting for different subjects like English, Maths, Science, Social.

Based on the above table, we can easily calculate the total numbers of the students, average of the students. Therefore the total number of students is 115. If we want to calculate two subjects total then we can add that two subjects student numbers.

Raw Data (or) Ungrouped Data

Raw data is also called ungrouped data. These types of data are obtained in their original form. When some information is randomly and presented is called Raw Data.

Example: 

The example of Raw data (or) ungrouped data is given below. The students in class VII A are 15 and marks obtained by them out of 25 in the English Test. Based on the given data we can know each student’s marks, this means a student is one data and marks is another data we are knowing the marks based on the student. In some marks will be given more students but student strength gives less at that time we are comparing both then choose the predict or collect values.

Given the marks (out of 25) obtained by 15 students of class VII A in English in a test.

16, 13, 20, 21, 15, 25, 14, 19, 10, 20, 22, 12, 18, 15, 23

Array

Generally, Arrays are the data that are put in the form of a table which is also called the presentation of data. simply, Array refers to the arrangement of data in ascending or descending of data order. If the number of times an observation occurs, then it is called frequency distribution. Array data is also called Arrayed data.

Example:

In this example, the main concept is array is putting the raw data in ascending order or descending order. The below data is given, we can arrange them in ascending order,

Given data is 12, 10, 10, 12, 8, 3, 7, 2, 17, 20, 15

The given data is arranged in ascending and represented as,

2, 3, 7, 8, 10, 10, 12, 12, 15, 17, 20

Observation

The observation is defined as every entry is collected as a numerical fact in the given data. In other words, an observation in statistics means a value of something of interest you are measuring or counting during a study or experiment ‘like a person’s height, a bank account value at a certain point in time, or a number of animals like that. The observation unit measures the same thing in the context.

For example, let’s say you are measuring how well your savings perform over the period of one year. You record one measurement that is your bank account balance for every three months for a total.

Range

Statistics Range means the difference between the highest value and the lowest value of the observation is called the range of the data. In other words, statistics the range of a set of data is the difference between the largest and smallest values. The formulae of Range is,

Range (X) = Max(X) – Min(X)

The above range formula is used for calculating the same value, the minimum range is subtracted from the maximum range value to get the Range Value. X is denoted as the value of data.

Example:

In an exam, the highest marks obtained are 20 and the lowest marks are 5 then what is the range?

Highest marks obtained = 20

Lowest marks obtained = 4

Range (X) = Max(X) – Min(X)

Therefore, range = highest marks – lowest marks = 20 – 5 = 16

Another example is, in {4, 6, 9, 3, 7} the lowest value is 3, and the highest is 9, so the range is 9 − 3 = 6.
The range can also mean all the output values of a function.

Mean

Mean and mode is used to measure the central tendency. Mean is defined as the average or the most common value in a collection of numbers. The mean or average of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.

If x, x₁, x₃, ……… x_n are n observations then
Arithmetic mean = (x₁ + x₂ + x_n, ……………. x_n)/n = (∑x_i)/n.
∑ is the Greek letter sigma and is used to denote summation.

Mode

In Statistics, the mode is the value that appears most frequently in a data set. A set of data may have one mode, more than one mode, or no mode at all. The mode can be the same value as the mean and/or median, but this is usually not the case.

A Mode in statistics is defined as the value that has a higher frequency in a given set of data. It is the value that appears the most number of times.  Two modes in a given set of data, such values are called Bimodal. A set of numbers with three modes is called Trimodal, and any set of numbers with more than one mode is called Multimodal.

The advantages of mode in statistics are below,

• The mode is equal to understand and calculate.
• The mode is not affected by extreme values.
• The mode is easy to identify in a data set and in a discrete frequency distribution
• The mode is useful for Qualitative data.
• The mode can be located graphically.
• The mode can be computed in an open- Ended frequency table.

Example:

In the following list of numbers, 12 is the mode since it appears more times in the set than any other numbers:

3, 3, 4, 5, 5, 6, 8, 9, 12, 12, 12, 24, 27, 37

Solving Problems on Statistical Terms

Example 1:

The height of 12 girls was measured in cm and the results are as follows:

149, 144, 126, 138, 145, 130, 145, 150, 133 ,129, 131, 151

(i) What is the height of the tallest girl?

(ii) What is the Height of the shortest girl?

(iii) What is the range of data?

Solution:

Given the 12 girls heights in cm

To finding the tallest girl height and shortest height and range.

(i) The height of the tallest girl is 151 cm

(ii) The height of the shortest girl is 126

(iii) We know the Range Formula,

Range (X) = Max (X) – Min (X )

Substitute the given values in above formula, we get

Range = 151 cm – 126 cm

= 25 cm

Therefore, Range = 25 cm.

Example 2:

Find the Mean of the given data

5, 6, 9, 10, 15, 17, 19, 20, 25, 30

Solution :

Given the data is 5, 6, 9, 10, 15, 17, 19, 20, 25, 30

Now, we can calculate the Mean

Mean = Total sum / no. of terms

Mean = 156 / 10 = 15. 6

Therefore, the Mean of a given data is 15.6

Example 3:

Find the Mode of a given data.

3, 3, 5, 6, 13, 15, 15, 19, 20 , 15

Solution:

Given the data is 3, 3, 5, 6, 13, 15, 15, 19, 20, 15

Now, we are finding the Mode of a given data.

Mode means the value that has the higher frequency in a given set of data.

In this given data the higher frequency data is 15.

Therefore the Mode of a given data is 15.

Statistics is more important because nowadays we live in the information world and much of this information is determined mathematically by statistics. It helps to use the proper methods to collect the data, employ the correct analyses, and effectively present the results. Basically, statistics is a mathematical discipline to collect data and summarize the data. The study of statistics is the collection, analysis, interpretation, presentation, and organization of data. Check out Statistics Definition, Types, Advantages, Applications, and Examples in the later sections.

Statistics Definition

The main purpose of statistics is to plan the collected data in terms of the experimental designs and statistical surveys. The study of the collection, analysis, interpretation, presentation, and organization of data is called statistics. It will be collecting the data and summarizing the data. If it is studying the population of the country or its economy statistics are used for all such data analysis. Statistics has many applications from small scale to large scale.

Statistics basics including the measure of central tendency and the measure of dispersion. Mean, Median and Mode are central tendencies whereas dispersion comprises variance and standard deviation. Statistics used in many sectors such as psychology, geology, sociology, weather forecasting, probability, and much more. The scope of statistics helps in economic planning, business management, administrations, and research.

Characteristics of Statistics

• Statistics are aggregate facts.
• Statistics are numerically expressed.
• Statistics are collected in a systematic manner.
• Statistics for a predefined purpose.
• Statistics are enumerated or estimated according to reasonable standards of Accuracy.
• Statistics are capable of being placed in relation to each other.

Types of Statistics

Statistics are of two types

1. Descriptive Statistics
2. Inferential Statistics

Descriptive Statistics: It provides the tool to define our data in a most understandable and appropriate way, the collection of data is described in summary. Descriptive statistics are used on a large scale.

Inferential Statistics: It is about using the data from the sample and then making inferences about the larger population from which the sample is drawn. Inferential statistics are used to explain the descriptive one, it will also be used on a large scale.

Descriptive statistics are transitioned into inferential statistics, it is one more type of statistics.

Representation of Statistics Data

Bar charts, histograms, pie charts, and box plots (box and whiskers plots). Two common types of graphic displays are bar charts and histograms. Both bar charts and histograms use vertical or horizontal bars to represent the number of data points in each category or interval.

Some of the methods involve collecting, summarizing, analyzing, interpreting variables of numerical data. The methods are provided below for representing statistics data.

• Data Collection
• Data Summarization
• Statistical Analysis

In this, the data is a collection of facts, such as numbers, words, measurements, observations, etc. Data are two types is Qualitative data and the second one is Quantitative data. Descriptive data is called Qualitative data whereas Numerical data is Quantitative data, again it has two types.

1. Discrete data
2. Continuous data.

Discrete data is in form of digital that means zero’s and ones, it has a particular fixed value. so, discrete data can be counted whereas continuous data is not counted because it won’t have a particular fixed value but continuous data has a range of data, so it can be measured.

The representation of statistics data as follow :

Pie Chart: Pie charts are used in data handling and are circular charts divided up into segments that each represent a value. Pie charts are divided into sections or slices to represent a value of different sizes. The pie chart has different parts are Title, Legend, Source, and data. The title offers a short explanation of what is in your graph and legend tells what each slice represents, source explains where you found the information that is in your graph.

Bar Graph: A bar graph is a chart that plots data using rectangular bars or columns called bins, that represents the total amount of observations in the data for that category. Bar graphs are commonly used in financial analysis for displaying data. In other words, Bar graphs are used to compare things between different groups or to track changes over time.

Bar Graphs are three types :

1. Horizontal Bar Graphs
2. Vertical Bar Graphs
3. Line Graph

Bar Graphs have different parts such as Title, Source, X-Axis, Y-Axis, Data, and Legend.

Line Graph: Line graphs or line charts are used to track variations over time, which may be long-term or short-term. We can also use line graphs to compare changes over the same period for more than one group. There are 3 main types of line graphs in statistics namely, a simple line graph, multiple line graph, and a compound line graph. Each of these graph types has different uses depending on the kind of data that is being evaluated.

Pictogram:  A Pictogram is one of the simplest and most popular forms of data visualization out there. Also known as “pictographs”, “icon charts”, “picture charts”, and “pictorial unit charts”, pictograms use a series of repeated icons to visualize simple data.

Histogram: A histogram is a display that indicates the frequency of specified ranges of continuous data values on a graph in the form of immediately adjacent bars. Interval is a range of data in a data set. The different types of a histogram are uniform histogram, symmetric histogram, bimodal histogram, probability histogram.

Frequency Distribution: Frequency distribution in statistics is a graph or data set organized to show the frequency of occurrence of each possible outcome of a repeatable event observed many times. The frequency of a data value is represented by ‘f’. There are three types of frequency distributions:

1. Grouped Frequency distribution.
2. Ungrouped Frequency distribution.
3. Cumulative Frequency distribution.
4. Relative Frequency distribution.
5. Relative cumulative Frequency distribution.

FAQ’s on Real Life Statistics

1. What are the applications of Statistics?

A. Some of the applications of Statistic are listed below :

1. Statistics applied to Theoretical Statistics and Mathematical Statistics
2. Statistics in society
3. Statistical computing
4. Machine learning and data mining.

2. How many types of Statistics, namely?

Statistics are two types, namely

1. Descriptive Statistics
2. Inferential Statistics

3. What is Statistics?

The study of the collection, analysis, interpretation, presentation, and organization of data is called statistics.

4. What are the types of Bar Graphs?

Bar graphs are commonly used in financial analysis for displaying data. Bar graphs are used to compare things between different groups or to track changes over time. There are 3 types of bar graphs namely:

1. Horizontal Bar Graphs
2. Vertical Bar Graphs
3. Line Graph

5. How to represent data on Statistics?

In Statistics, the data can be represented by using pie charts, bar graphs, histograms, pictograms, line graph,s and frequency distribution. Data will be two types one is qualitative and another one is quantitative. Descriptive data is called Qualitative data whereas Numerical data is Quantitative data. Again quantitative data has two types those are discrete and continuous.

If we want to learn a Multiplication Chart of 8 with whole numbers, this is the right place to learn because you will get complete knowledge on 8 Times Table with whole numbers. Some students may feel the 8 Times Multiplication Chart difficult. To help such students we have mentioned the Table of 8 up to 20 both in the image and tabular format for your convenience. Math Tables are necessary at the time of primary schooling, it develops memory skills at your learning stages.

8 Times Table Multiplication Chart

If we want to practice daily the Multiplication Chart of 8 Times Table, you can download an image format, here we will have the image of 8 Times Table. Learn Tips & Tricks to memorize the Table of 8 and here know how to read and write the Table of Eight. You can download the Multiplication Table of Eight images for free and prepare, then you can easily and fastly solve more basic multiplications, division problems.

How to Read Multiplication of 8?

One time Eight is 8.

Two times Eight is 16.

Three times Eight is 24.

Four times Eight is 32.

Fives times Eight is 40.

Six times Eight is 48.

Seven times Eight is 56.

Eight times Eight is 64.

Nine times Eight is 72.

Ten times Eight is 80.

Table of 8 | Multiplication Table of 8 up to 20

Get the 8 Times Table Multiplication Chart in the tabular form is shown in the below sections and now you get the idea of how to write the 8 table or Multiplication Table of 8. We have given the first 20 multiples of 8 here. This Multiplication Table of 8 Chart is used to perform the arithmetic operations quickly.

Why should learn Multiplication Table of 8?

Learning a Multiplication Chart of Eight will help to enhance skills and do the calculation quickly. Solving the mathematical problems will increase the mental arithmetic skills. The Multiplication Tables are the basics or fundamentals in learning Maths.

• 8 Times Table Multiplication Chart helps to understand the patterns easily.
• Table of 8 makes you perfect in performing the quick calculations.
• Learning the Multiplication Table of 8, you can easily solve all the mathematical problems like Multiplications, Divisions.

Get More Math Table Multiplication Charts

Tips & Tricks to memorize Table of Eight

The below tips and tricks are memorize Multiplication of 8 Times Table, mentioned here

• Multiplication of 8 Times Table is simple and easy to memorize. However, there is a pattern for every five multiples of 8 i.e., 8, 16, 24, 32, 40, 48, 56, 64, 72, 80.
• You can identify the multiplication sequence being followed by successive multiples of 8.
• Multiplying any two numbers, the order does not matter the answer should be always the same (if we multiply the first number with a second number or the second number with the first number). Example, 3 x 4 = 12 or 4 x 3 = 12
• The patterns will help to remember the product of two numbers.
• Learning the Table of 8 helps you solve mathematical problems easily.
• Multiples of 8 are multiples of both 2 and 4.
• If you multiply an even number with 8 the result will be the same even number in the unit digit i.e 8 x 2 = 16, 8 x 6 = 48, 8 x 8 = 64 and so on.

Solved Examples on 8 Times Table

Example 1:

What does 8 x 7 mean?

Solution:

8 x 7 means multiply 8 with 7 or 8 times 7

8 x 7 = 56

In other words, Seven times Eight is 56.

Therefore, 56 is equal to 8 times 7.

Example 2:

A person eats 3 mangoes per day. How many Mangoes will he eat in 8 days?

Solution:

Given that,

The number of mangoes A person eats in a day is 3

The number of mangoes A person eats in 8days is,

8 days = 8 x 3 = 24 ( three times eight is 24)

Therefore, A person eats 24 mangoes in 8 days.

Example 3:

Sunny planned to attend 8 hours of online classes for 4 days. Unfortunately, he wasn’t able to attend one session for 3hours on one particular day. Using the table of 8 find how many hours of sessions has he attended in total classes?

Solution:

Given that,

Plan to attending classes is 8 hours for 4days

Not attended session hours is 3

now, write  the given statement in the form of a mathematical expression, that is

= 8 x 4 =32

Next, 32 – 3 = 29

Therefore, sunny totally attended online classes is 29 hours.

Example 4:

Find the value of 8 times 6 minus 4 plus 3?

Solution:

Given that, the finding value is 8 times 6 minus 4 plus 3

now, finding

= 8 x 6 = 48

next, minus 4 into the above value

48 – 4 = 44

next, add 3 to the above value

44 + 3 = 47

Therefore the value is 47.

FAQ’s on 8 Times Multiplication Table

1. What is Multiplication Table?

Multiplication tables are the list of multiples of the number. In other words, it defines the multiplication operation of the two given numbers.

2. How to remember the maths tables up to 20?

Create a maths tables chart from 2 to 20 and read the chart every day and practice from basic to remember it.

First, identify the pattern and then product the first number with the second number or the second number with the first number. You just read it and remember, otherwise there are no other special tricks for 8 Times Table Multiplication. If the multiplying number is an even number then the unit digit of the remains the same that is even number.

4. What is the importance of the Multiplication Table?

The Multiplication Table helps to keep the information at the fingertips to use it whenever required. It helps to enhance skills and increases memory power and calculation speed.

5. What are the factors of 8?

The number which divides the original number evenly is called a factor of 8. When a pair of numbers are multiplied together to produce 8, then they are called pair factors. When 8 is divided by its factor, it results in zero remainders. The factors are 1, 2, 4, and 8.

Learning the 3 Times Table Multiplication Chart helps you to keep a track of odd numbers, knowing the table helps students to save a lot of time, mainly in the time-based examination it will be easy to solve any type of mathematical problems. Multiplication Table of 3 is important for the students to memorize the table, it will helps to do a fast and quick calculation. Math Tables have a strong foundation for learning such as Multiplication, Division and Fractions, etc. In this article, you will learn how to read and write the Multiplication Table of Three, Tips & Tricks to memorize the table.

3 Times Table Multiplication Chart

If we learn the 3 Times Table Multiplication Chart simply and easily, you can download the Table of 3 in image format with free pay for a better understanding of students and solving the basic mathematical problems like multiplication, divisions, LCM, etc, so here we can easily download the 3 Times Table Multiplication Chart and try to memorize it, it helps in competitive exams for doing fast calculations.

Multiplication Table of 3 up to 20 | How to write Table of 3?

Here given the first 20 multiples of 3 for your comfort. You can remember the 3 Times Table Multiplication Chart output to make your math problems solving easily. You can improve your math skills to gave speed answering the math problems in exams. The below section is a tabular form of a 3 Times Table Multiplication Chart, it will help to perform the arithmetic operations quickly.

How to read Table of 3 in words?

One time three is 3

Two times three is 6

Three times three is 9

Four times three is 12

Five times three is 15

Six times three is 18

Seven times three is 21

Nine times three is 27

Ten times three is 30

Eleven times three is 33

Twelve times three is 36

Thirteen times three is 39

Fourteen times three is 42

Fifteen times three is 45

Sixteen times three is 48

seventeen times three is 51

Eighteen times three is 54

Nineteen times three is 57

Twenty times three is 60

Why should one learn a 3 Times Multiplication Table?

Learning of 3 Times Table is very important and has some advantages also for doing mathematical problems. There are many aspects of mathematics that require time tables to spend less time for solving.

• Multiplication Table Chart saves your time while performing multiplications, divisions, LCM, Fractions etc.
• Learning tables helps to solve the mathematical problems easily and quickly.
• The pattern will be easily understands for learning 3 Times Table Multiplication Chart.
• 3 Times Multiplication Table makes you perfect in performing the quick calculations.

Get More Multiplication Tables

Tips & Tricks to remember Table of 3

Memorize of 3 Times Table Multiplication Chart Tips & Tricks are listed below.

1. To Remembering the 3 Times Multiplication Table, first you have to know how many numbers are increased to get each resultant.
2. Learning the 3 Times Table Multiplication Chart using skip counting process.
3. The patterns will help to remember the product of two numbers.
4. Learning the Table of 3 Times helps to solve mathematical problems easily
5. Practice each table until you get perfect on it and also practice the number of multiplication facts.
6. The last digit of these 3 multiples will always repeat. You can remember these digits to memorize the multiples of 3 easily.

Solved Examples on 3 Times Table

Example 1:

Calculate the value of 3 plus 3 times of 7 minus 4, using the 3 Times Table?

Solution:

Given, calculate the value using 3 Times Table

First, we have to write down the given statement 3 plus 3 times of 7 minus 4

Now, solving the above expression by using 3 Times Table Multiplication Chart,

3 plus 3 times 7 minus 4 = 3 + 3 x 7 – 4

= 3 + 21 – 4

= 3 + 17

= 20

Therefore the value of 3 plus 3 times of 7 minus 4 is 20.

Example 2:

There are 3 dogs, each dog has 15 biscuits. How many biscuits are there in total?

Solution:

Given that,

The number of dogs is 3

Number of biscuits per each dog has 15 biscuits.

Now, find the total number of biscuits

According to law of multiplication ,we can finding the total number of biscuits

By using 3 times table,

The total number of biscuits = 3 x 15 = 45

so , all the dogs have totally 45 biscuits.

Therefore, the total biscuits are 45.

Example 3:

John has 6 cards with numbers 7, 13, 15, 18 ,20, 24, 28 written on them. Take help from the table of 3, and assist john in identifying the cards which are 3 times any number?

Solution:

Given 8 cards numbers are 7, 13, 15, 18, 20, 24, 28

From the table of 3 multiples, the first 10 multiples of whole numbers are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30.

Therefore, among the 7 cards only 3 multiple cards are 15, 18, 24. These 3 card numbers are the only table of 3 multiples, so john has 3 card numbers of 3 multiples.

Example 4:

By using the 3 Times Table find the (i) 3 times 12 (ii) 3 times 3 plus 7 (iii) 3 times 4 minus 3 (iv) 3 times 2 multiple of 5?

Solution:

(i) Given, find the value of 3 times 12

By using the 3 times table, to solve the given expression

3 Times 12 in mathematical expression is equal to 3 X 12 = 36.

So, the value of  3 times 12 is equal to 36.

(ii) Given, to find the value of  3 times 3 plus 7

By using the 3 Times table, to solve the given expression

3 times 3 plus 7 can be written in mathematical expression as,

3 x 3 +7

9+ 7 = 16

so, the value of 3 x 3 + 7 is equal to 16.

(iii) Given, finding the value of 3 times 4 minus 3

By using the 3 times table, to solve the given expression

We can write the given expression in mathematical form as 3 x 4 – 3

3 x 4 -3 = 12 – 3 = 9

so, the value of 3 x 4 – 3 is 9.

(iv) Given, finding the value of 3 times 2 multiple of 5

By using the 3 times table, to solve the given expression

We can write the given expression in mathematical form as,

3 x 2 x 5 = 6 x 5 = 30

So,the value of 3 times 2 multiples of 5 is equal to 30.

Before we learn about the Order of a Matrix let us know What is a Matrix. Matrices are defined as a rectangular array of numbers or functions. It is a rectangular array and two- dimensional. A Matrix is a rectangular array of numbers or symbols which are generally arranged in rows and columns. The plural of matrix is matrices. The entries are the numbers in the matrix and each number is known as an element.

Order a Matrix – Definition

Basically, a two-dimensional matrix consists of the number of rows and the number of columns. The order of the matrix is defined as the number of rows and columns. The number of rows is represented by ‘m’ and the number of columns is represented by ‘n’. Therefore the order of the matrix is equal to m x n, and it is also called as ‘m by n’.

The size of the matrix is written as m x n, where m is the number of rows and n is the number of columns. For example, we have a 3 x 2 matrix, the number of rows is equal to 3, and the number of columns is equal to 2.

Different Types of Matrices

There are different types of matrices, basically categorized on the basis of the value of their elements, their order,  number of rows and number of columns, etc. Now, using different conditions, the various matrix types are categorized along with their definition.

1. Row Matrix
2. Column Matrix
3. Null Matrix
4.  Square Matrix
5. Diagonal Matrix
6. Upper Triangular Matrix
7. Lower Triangular Matrix
8. Symmetric Matrix
9. Anti- Symmetric Matrix
10. Equal Matrix
11. Singular Matrix
12. Non Singular Matrix
13. Horizontal Matrix
14. Vertical Matrix
15. Unity or identity Matrix.

Row Matrix: A Matrix having only one row is called a Row Matrix. A= [a_ij]_mxn  is a row matrix , if m=1 then row matrix is represented as A= [a_ij]_1xn . It has only one row and the order of a matrix will be 1 x n. For example, A= [1 2 4 5] is row matrix of order 1 x 4.

Column Matrix: A Matrix having only one column is called a Column Matrix. A= [a_ij]_mxn  is a column matrix, if n=1 then column matrix is represented as A= [a_ij]_mx1 . It has only one column and the order of a matrix will be m x 1. Just like row matrices had only one row, column matrices have only one column. Thus the value of the column matrix will be 1.

Null Matrix: Null Matrix is also called Zero Matrix. In a matrix all the elements are zero then it is called a Zero Matrix or Null Matrix and it is generally denoted by 0. Thus, A = [a_ij]_mxn is a Zero or Null Matrix.

Unity or Identity Matrix: If a square matrix has all elements 0 and each diagonal element is non-zero, it is called an identity matrix. It is denoted by I.

Equal Matrix: If two matrices are said to be equal if they are same order if their corresponding elements are equal to the square matrix.

Square Matrix: If the number of rows and the number of columns in a matrix are equal, then it is called Square Matrix.

How to find Order of a Matrix?

A Two- Dimensional matrix consists of the number of rows (m) and a number of columns (n). The order of the matrix is equal to m x n (also pronounced as ‘m by n’).

Order of Matrix = Number of Rows x Number of Columns.

In the above, you can see, the matrix has 2 rows and 4 columns. Therefore, the order of the matrix is 2 x 4.

How will you Determine the Order of Matrix?

If a matrix has m number of rows and n number of columns, now let’s know how to find the order of the matrix.

Here few examples, how to find the order of a matrix,

[1  2  3] is an example, in this, the order of the matrix is (1 x 3), which means the number of rows (m) is 1 and the number of columns (n) is 3.

[7  5] is an example of (1 x 2) matrix, in this number of rows are (m) is 1 and number of columns (n) is 2.
\( A =\left[
\begin{matrix}
6 & 2 & 3\cr
12 & 15 & 35 \cr
\end{matrix}
\right]
\)

The order of the above matrix is (2 x 3), in this number of rows is (m) is 2, and the number of columns (n) is 3.

A matrix of the order m x n has mn elements. Hence we say that if the number of elements in a matrix is prime, then it must have one row or one column. Usually, we denote a matrix by using capital letters such as A, B, C, D, M, N, X, Y, Z, etc.

The product of m and n can be obtained in more than one ways, some of the ways are,

1. mn x 1
2. 1 x mn
3. m x n
4. n x m

Number of Elements in Matrix

Suppose, A is the order of 2 x 3. Therefore, the number of elements present in a matrix will also be 2 times 3, i.e 6.

Similarly, the other matrix order is 4 x 3, thus the number of elements will be 12 i.e. 4 times 3. If we know the order of a matrix, we can easily determine the total number of elements that the matrix has,

If a matrix is of m x n order, it will have mn element.

Order of a Matrix Examples

Example 1.

If matrix A has an 8 number of elements, then determine the order of the matrix.

Solution:

We know that number of elements is 8

Let’s write all the possible factors of the number 8

8 = 1 x 8

8 = 4 x 2

8 = 2 x 4

8 = 8 x 1

we can get the number 8 is four ways.

Therefore, there are four possible ways or orders of the matrix with 8 number of elements are 1 x 8, 2 x 4, 4 x 2, and 8 x 1.

Example 2.

If a matrix X has 7 number of elements, find the order of the matrix.

Solution:

We know that number of elements is 7

Let’s write all the possible factors of the number 7

7 = 1 x 7

7= 7 x 1

we can get the number 7 in two ways.

Therefore, there are two possible ways or orders of the matrix with 7 number of elements are 1 x 7, 7 x 1.

Example 3.

What is the order of a matrix given below?

Solution:

The number of rows in a given matrix is A = 2

The number of columns in a given matrix is A = 3

Therefore, the order of matrix is  2 x 3.

Example 4.

What is the order of a matrix given below?

Solution:

The number of rows in a given matrix is A = 3

The number of columns in a given matrix is A = 3

Therefore, the order of the matrix is 3 x 3.

FAQ’s on Order of Matrix

1. What is Matrix and Types?

A Matrix can be defined as a rectangular array of numbers or functions. A matrix consists of rows (m) and columns (n) that is m x n. Types of Matrices are :

1. Row Matrix
2. Column Matrix
3. Null Matrix
4. Equal Matrix
5. Unity or Identity Matrix
6. Square Matrix
7. Rectangular Matrix
8. Horizontal Matrix
9. Vertical Matrix
10. Scalar Matrix

2. What is the Null Matrix?

Null Matrix is also called Zero Matrix. In a matrix all the elements are zero then it is called a Zero Matrix or Null Matrix and it is generally denoted by 0. Thus, A = [a_ij]_mxn is a Zero or Null Matrix.

3. What is another name of Unity Matrix?

Another name of the unity matrix is Identity Matrix. If a square matrix has all elements 0 and each diagonal element is non-zero, it is called an Identity Matrix. It is denoted by I.

4. What is the order of Square Matrix?

A Matrix that has a number of rows is equal to a number of columns is called Square Matrix. In this matrix, all the elements are arranged in m number of rows and n number of columns . So the order of the matrix is denoted by mxn.

5. Explain a Scalar Matrix?

Scalar Matrix is similar to a square matrix. In the scalar matrix, all off-diagonal elements are equal to zero and all on diagonal elements happen to be equal. In other words, the Scalar Matrix is an identity matrices multiple.

Symmetry can be split into two mirror-image halves. Suppose you can fold any picture, in it half you see both sides match, it is called Symmetrical. The word “symmetry” comes from a Greek word that implies measuring together. The two objects are claimed to be symmetrical if they have an identical size and shape with one object having a different orientation from the first. You are already acquainted with the term symmetry which is a balanced and proportionate similarity found in two halves of an object, one – half is the mirror image of the other half.

Line of Symmetry – Introduction

Line of symmetry means, it is the line that passes through the center of the object or any shape and it is considered as the imaginary or axis line of the object. Another name of line symmetry is “Reflection symmetry”, one half is the reflection of the other half. Reflection symmetry sometimes called line symmetry or Mirror symmetry.  The line of symmetry can be in any direction.

For example, if we cut an equilateral triangle into two equal halves, then the two triangles are formed after the intersection is the right-angled triangles. Take one more example, if we cut an orange into two equal halves, then one of the pieces is said to be in symmetry with another. Rectangle, circle, square are also considered examples of line symmetry.

Line of Symmetry – Definition

Line of symmetry is defined as, a line that cuts a shape exactly in half, if you fold the shape or figure along the line, both halves would match exactly that is symmetrical halves. It is also termed as Axis of symmetry.  The line symmetry also called a reflection symmetry or mirror symmetry because it presents two reflections of an image that can coincide.

A line of symmetry may be one or more lines of symmetry. Symmetry has many types such as

1. Infinite lines of symmetry
2. One line of symmetry
3. Two lines of symmetry
4. Multiple lines of symmetry (more than two lines is called multiple lines)
5. No line of symmetry means the figure is asymmetrical.

There are many shapes that are irregular and cannot be divided into equal parts. Such shapes are termed asymmetrical shapes. Hence, in such cases, line symmetry is not applicable. Line of symmetry are two types:

1. Vertical line of symmetry
2. Horizontal line of symmetry

Also, Read:

• Types of Symmetry 
• Lines of symmetry 

Types of Line of Symmetry

Basically, the line of symmetry is of two types. The line or axes may be any combination of Vertical, Horizontal, and Diagonal. Two types of lines of symmetry are

• Vertical line of symmetry
• Horizontal line of symmetry

Vertical Line of Symmetry

A vertical line of symmetry refers to one which runs down an image or figure and divides into two identical halves. The mirror image of the other half of the shape can be seen in a vertical or straight standing position. A, H, M, O, U, V, W, T, Y are some of the alphabets that can be divided vertically in symmetry. The trapezoid has only the vertical line of symmetry.

Horizontal Line of Symmetry

The Horizontal line of symmetry is a line or axis of a shape which runs across the image, it divides into two identical halves is known as the Horizontal Line of Symmetry. B, C, H, E, are some of the alphabets that can be divided horizontally in symmetry.

Some other types of lines of symmetries are there. Those are three lines of symmetry, four lines of symmetry, five lines of symmetry, six lines of symmetry, and infinite lines of symmetry.

Three Lines of Symmetry

An Equilateral Triangle has about three lines of symmetry. It is symmetrical along its three medians.

Some other patterns also have three lines of symmetry.

Four Lines of Symmetry

A square has four lines of symmetry. It can be folded in half over either diagonal, the horizontal segment which cuts the square in half, and the vertical segment which cuts the square in half. so, the square has four lines of symmetry.

A square is symmetrical along four lines of symmetry, two along the diagonals and two along with the midpoints of the opposite sides. some other patterns also have four lines of symmetry.

Five Lines of Symmetry

A regular pentagon has around five lines of symmetry. The lines joining a vertex to the mid-point of the opposite side divide the figure into ten symmetrical halves. Some other patterns also have five lines of symmetry.

Six Lines of Symmetry

A regular polygon with N sides has N lines of symmetry. Hexagon is said to have six lines of symmetry, 3 joining the opposite vertices and 3 joining the midpoints of the opposite sides.

Infinite Lines of Symmetry

A circle has its diameter as the line of symmetry, and a circle can have an infinite number of diameters. It is symmetrical along all its diameters.

Examples of Lines of Symmetry

Line of Symmetry has different figures and we have outlined few examples

1. A Triangle is said to have 3, 1 number lines of symmetry
2. A quadrilateral has 4 or 2 number lines of symmetry
3. An Equilateral Triangle has 3- lines of symmetry
4. A Regular Pentagon has 5lines of symmetry
5. A Regular Heptagon has 7 lines of symmetry
6. A circle has an infinite number of lines of symmetry

Real-Life Examples of Lines of Symmetry

• Reflection of trees in clear water.
• Reflection of mountains in a lake.
• Most butterflies’ wings are identical on the left and right sides.
• Some human faces are the same on the left and right.
• People can also have a symmetrical mustache.

FAQ’s on Line of Symmetry

1. How many lines of symmetry does a circle have?

A circle has infinite lines of symmetry.

2. What is the figure of reflection symmetry on a vertical mirror?

A rectangle is the figure of reflection symmetry on a vertical mirror.

3. Define Line of Symmetry?

The imaginary line or axis along which you can fold a figure to obtain the symmetrical halves is called the line of symmetry. It is also termed the axis of symmetry. The other names of Line of Symmetry are Reflection Symmetry or Mirror Symmetry.

4. What are the types of Lines of Symmetry?

Lines of Symmetry are of two types, the first one is the Vertical line of symmetry and the second one is the Horizontal line of symmetry.

5. Define Vertical Line of Symmetry?

The axis of the shape or object or figure which divides the shape into two identical halves Vertically is called a Vertical line of symmetry.

6. Define Horizontal Line of Symmetry?

The axis of the shape or figure or object that divides the shape into two identical halves Horizontally is called a horizontal line of symmetry.

Worksheet on Area and Perimeter of Rectangle Problems will help the students to explore their knowledge of Rectangle word Problems. Solve all the Problems to learn the formula of Area of Rectangle and Perimeter of a Rectangle. To know the definition, properties, derivation, Problems with Solutions, Formulas of Rectangle you can visit our website. We have given the complete Rectangle concept along with examples. Check out the Area and Perimeter of Rectangle Problems Worksheet and know the various strategies to solve problems in an easy and understandable way.

Also Read :

• Perimeter and Area of Rectangle
• Practice Test on Area and Perimeter of Rectangle

Perimeter and Area of a Rectangle – Definitions

A Rectangle is a quadrilateral with two equal sides and two parallel lines and four right angles. Four right angles vertices are equal to 90 degrees, it is also called an equiangular quadrilateral.

The perimeter of the rectangle is defined as the sum of all the sides of the rectangle.  Rectangle has two lengths and breadths, it is denoted by P, it is measured in units. For finding the perimeter of the rectangle we have to add the length and breadth.

Perimeter of the Rectangle, P = 2(l + b)

The area of the rectangle is defined as to calculate the length and breadth of the two- dimensional closed figure. For finding the area of the rectangle we have to multiply the length and breadth, it is denoted by A, measured in square units.

Area of the rectangle , A = l x b

Problems on Area and Perimeter of the Rectangle

1. Find the Area and Perimeter of the following rectangles whose dimensions are :

(i) length = 15 cm             breadth = 12 cm

(ii) length = 7.9 m            breadth = 6.2 m

(iii) length = 4 m              breadth = 36 cm

(iv) length = 2 m              breadth = 6 dm

2. The perimeter of the rectangle is  140 cm. If the length of the rectangle is 30 cm, find its breadth and area of the rectangle?

3. The area of a rectangle is 78 cm². If the breadth of the rectangle is 6 cm, find its length and perimeter?

4. How many boxes whose length and breadth are 9 cm and 5 cm respectively are needed to cover a rectangular region whose length and breadth are 420 cm and 90 cm?

5. If it costs $500 to fence a rectangular park of length 40 m at the rate of $25 per m², find the breadth of the park and its perimeter. Also, find the area of the field?

6. A rectangular tile has a length equals to 20 cm and a perimeter equals 70 cm. Find its width?

7. Find the area of a rectangle, Perimeter of a rectangle, and diagonal of a rectangle whose length and breadth 12 cm and 16 cm respectively.

8. Find the cost of tiling a rectangular plot of land 200 m long and 120 m wide at the rate of $6 per hundred square m?

9. The length of a rectangular board is thrice its width. If the width of the board is 140 cm, find the cost of framing it at the rate of $5 for 30 cm.

10. The Perimeter of a rectangular pool is 46 meters. If the length of the pool is 16 meters, then find its width. Here the perimeter and length of the rectangular pool are given. we have to find the width of the pool.

11. The sides of a rectangle are in the ratio of 4: 5 and its perimeter is 90 cm. Find the dimensions of the rectangle and hence its area.

In the metric system of measurement, the meter is the basic unit of length, a gram is the basic unit of mass and liter is the basic unit of capacity.  We can use a centimeter(cm) to measure the length. Centimeter and Millimeter are very small units to measure the length, so we use another unit called meters.

Learn completely about the Units of a Measurement- Definition, Units Conversion, Prefix for Length, Time, Weight, and Volume or Capacity. Get to know the Importance of SI Units, Solved Examples on How to Convert one unit to another, etc.

Metric System – Introduction

The French are widely credited with originating the metric system of measurement, the system is officially adopted in 1795. It was originated in the year 1799. Metric System is basically a system used for measuring distance, length, volume, weight, and temperature. The term metric system is used as another word for SI or the international system of units.  Based on three basic units we can measure almost everything in the world, those are M- Meter, used to measure the length, Kg- Kilogram, used to measure the mass, and S- Second, used to measure time.

Units of Measurement – Definition

The SI system, also called the metric system, is used around the world. SI units stand for standard International System of the units. Seven basic units in the SI  system, give proper definitions for meter, kilogram, and the second. It also specifies and defines remaining four different  units:

1. Kelvin(K)- used to measure the Temperature

2. Ampere(A)- used to measure the Electric current

3. Candela(cd)- used to measure the Luminous Intensity

4. Mole(mol)- used to measure  the Material Quantity

Also, Read:

• Units of Length Conversion Charts
• Math Conversion Chart

Units of Measurement Conversion

To convert among units in the metric system, identify the unit that you have, the unit that you want to convert to, and then count the number of units between them. Some units are connected with each other by the following relation:

1 Kilometer (km) = 1000 meter (m)

1 meter (m) = 100 centimeter (cm)

1 centimeter (cm) =  10 millimeter (mm)

Metric Units Prefix

A metric prefix is a unit prefix that precedes a basic unit of measure to indicate a multiple or submultiple of the unit. To convert from one unit to another within the metric system usually means moving a decimal point. you can convert within the metric system relatively easily by simply multiplying or dividing the number by the value of prefix.

In order to remember the proper movements of units, arrange the prefixes from the largest to the smallest.

Now, let us discuss some of the units for length, weight, volume, time.

Units of Measurement Length

The most common unit used to measure the length are as follows. Centimeters and millimeters are very small to measure the length so, we use another unit that is the meter (m). Even meter is too small when we measure the distance between two cities, we use kilometers (km).

An Area is a space or a region occupied by any shape. Square is a two-dimensional figure with four sides, it is also known as a quadrilateral. The area of a square is defined as the number of square units needed to fill a square. In other words, a square is a product of two sides, length, and breadth that are equal. In the square, all four angles are also equal. Square has four equal sides and four vertices. The diagonals of the square are equal and bisect each other at 90 degrees, angles of the square are equal to 90 degrees. If a square is cut by a plane from the center, then both halves are symmetrical.

Learn completely about the Area of a Square Definition, Formula, and Units. Get to know the Properties of a Square, Solved Examples on How to Calculate the Area of a Square, etc.

Do Read: Practice Test on Area and Perimeter of Square

Area of a Square – Definition

The area of a square is defined as the total number of unit squares in the shape of a square. A Square is a rectangle whose length and breadth are equal which means all four sides are equal.

Area of a Square Formula

The area of a square formula is used for calculating the occupied region. It is measured in square units.

Area of a square=side x side

Perimeter of a Square Formula

The perimeter of the square is equal to the sum of all its four sides. The unit of the perimeter remains the same as that of the side-length of a square.

Perimeter=side+side+side+side=4side unit

Perimeter =4 x side of the square = 4a unit

Where ‘a’ is the length of the side of the square.

Also, Read: Perimeter of a Square

Length of Diagonal of a Square

The length of the diagonals of the square is equal to s√2, where s is the side of the square. The length of the diagonals is equal to each other. By Pythagoras theorem, diagonal is the hypotenuse and the two sides of the triangle formed by the diagonal of the square, are perpendicular and base. Hypotenuse²=Base² + Perpendicular²

Hence,Diagonal²=side² + side²

Diagonal=√2side², d=s√2

where d is the length of the diagonal of a square and s is the side of the square.

Diagonal of Square

It is a line segment that connects two opposite vertices of the square. Suppose we have four vertices, thus we can have two diagonals within a square. The diagonal of a square is always greater than its sides.

The relation between Diagonal ‘d’ and Side ‘a’ of a square is, d=a√2

The relation between Diagonal ‘d’ and Area ‘A’ of a square is, d=√(2A)

The relation between Diagonal ‘d’ and Perimeter ‘P’ of a square is,d=p/2√2

Area of Square Units

Usually, the Area of the Square is measured in the Square Units since each side of the square is the same. Some of the Common Units of Measurement and their equivalent are expressed below.

• 1 m=100 cm
• 1 sq.m=10,000 sq.cm
• 1 km=1000 m
• 1 sq.km=1,000,000 sq.m

Properties of a Square

Have a glance at the Properties of Square and get an idea of them so that you might find them useful while solving related problems. They are as follows

1. The square has 4 vertices and 4 sides.
2. All four interior angles are equal to 90⁰.
3. The opposite sides of the square are parallel to each other.
4. The two diagonals of the square are equal to each other.
5. The length of diagonals is greater than the sides of the square.

Solved Problems on Area of a Square

1. Find the Area of a square of the Side 2.5 cm?

Solution:

Given, Area of a square of the side is  2.5 cm

Area of a square = length x length

Substitute the given value in the above formula,

= 2.5 x  2.5 sq. cm

= 6. 25 sq. cm

2. Find the area of a square of side 49 m?

Solution: 

Given, Area of a square of the side is 49 m

Area of a square  = length  x  length

Substitute the given value in the above formula,

= 49  x  49 sq. m.

= 2401 sq. m.

3. Let a square has a side equal to 3 cm. Find out its area, length of diagonal, and perimeter?

Solution:

Given, side of the square, s= 3 cm

Area of a square= s²

Therefore, by substituting the value of the side, we get,

3² = 9 cm²

Length of the diagonal of  square = s√2

By substituting the value, we get,

3 x 1.414 = 4.242

The perimeter of the square = 4 xs

substituting the value in the above formula, we get,

4 x 3= 12 cm.

4. Find the area of a square clipboard whose side measures 120 cm?

Solution:

Given, side of the clipboard  = 140 cm = 1.4 m

Area of the clipboard  = side x side

substituting the value in the above formula, we get,

Area of the clipboard  = 140 cm x 140 cm

= 19,600 sq . cm

= 1.96 sq . m

5. A wall that is 40 m long and 30 m wide is to be covered by square tiles. The side of each tile is  2 m. Find the number of tiles required to cover the wall?

Solution: 

Given, Length of the wall = 40 m

The breadth of the wall = 30 m

Area of the wall = Length x breadth

substituting the length and breadth values, we get

Area of the wall= 40 m x 30 m = 1200 sq. m

side of one tile = 2 m

Area of one tile = side x side

substitute the value in the above formula, we get

Area of one tile =2 m x 2 m= 4 sq. m

No. of tiles required = Area of wall/ Area of a tile

substitute the value, we get

No.of tiles required = 1200/ 4 = 300 tiles

FAQ’s on Area of a Square

 1. What is the Area of a Square Formula?

The area of a square can be calculated by using a formula side x side square units.

2. Define Perimeter and Area of a Square?

 The perimeter of a square is the sum of all the four sides of a square, whereas the Area of a square is defined as the region or the space occupied by a square in the two-dimensional space.

3. How is a Square different from a Rectangle?

A square has all its sides are equal in length whereas a rectangle has only its opposite sides are equal in length.

4. What are the real-life examples of a Square?

Some of the real-life examples of a  square are Carrom Board, Square tiles, Square shaped tables, Cubes, Chess Board, etc.