Hello friends! Today, you will learn about an interesting math topic which you will use throughout mathematics. Grade V of Maharashtra state board, is the basic class in which students learn lots of topics that will be used throughout their math career. Grade V is considered as the primary grade and students learn the basic of multiple things and as they move to higher classes they implement the concepts on different types of problems. In the anterior articles we have learnt different topics of the grade V that includes relationship between data, Prime and composite numbers, Variables, expressions, graphs, equations to solve problems and linear functions. In this section I make you aware with the other concepts of the algebra that includes: Solving one-step equations and Patterns and relationships. You can also take help of differential equations tutor.
First start with solving one step equations. In this you will learn how to solve equations. Afore, we move to this topic let’s have a brief idea of what equation is? Equation is the way to represent the mathematical numbers with different operators in a proper way and in this representation an equal to symbol is must which shows the equality between two mathematical statements. In the primary grade you must clear all your doubts so that in future you will not face any problem in the topics. Many students fear from this wonderful language as in early classes they don’t understand different topics properly and their concepts remain unclear. So kids try to overcome your doubts at the same time when they occur. Ok, now, come back to topic, in algebra you learn different types of equations, like linear equations, constant equations, equations with different variables, quadratic equations and many others. You will all learn all these types of equation in the antecedent article. Let’s start with the one step linear equation; a linear equation is an algebraic equation in which each term is either a constant or the product of constant and a single variable. Linear equation may possess one or more than one variable. The standard form of one step linear equation in one variable is given as: ax + b = c. the second type of linear equation is with two variables and its standard form is given as: x + by = c.
In both the equations i.e. one step linear equation with one variable and one step linear equation with two variables ‘a’,’b’, and ’c’ are defined as the constant. Whenever we perform addition, subtraction, multiplication, or division of any number on both the side of the equation, the equality symbol (=) of the equation does not change. Now, move towards the example of the one step linear equation problems and see how to solve these types of problems with easy method.
Example: x + 10 = 18,
Solution: Solution of this problem is very simple let’s see the step used while solving the problems and so feel how simple it is.
X + 10 = 18,
Now, subtract 10 on both the sides of the equation, on doing this we get,
x + 10 -10 = 18 -10,
x = 8
So, the answer is x =8. In this you see how to solve the one step equations, solving one step equation is simply the moment of the numbers and we have to perform simple operations on them.
Next example:
a – 15 = 6,
Solution: a – 15 = 6, in this simple example add 15 on both the side, you must be thinking that in above equation we subtract the number and in this we are adding the number why? We perform the addition and subtraction operation on the basis of the problem, if in problems we have negative sign after the variable then we perform addition operation and we add that numeric value which is written after the symbol on both the sides. And if the add sign is present then perform minus operation.
This is we have subtraction sign so we add 15 on both the sides, on doing this we get,
a – 15 + 15 = 6 +15,
a = 21,
Thus value of variable ‘a’ is equal to 21.
Now, a bit complex example of the same problem, perform one step solving operation on given equation:
4x = 28,
In this divide both the side with the coefficient of x, in this problem the coefficient of x is 4 so divide both sides with 4, this will give result as:
4x/4 = 28/4,
4 will get cancelled with4 on LHS and on RHS 28 is divided by 4,
x = 28/4,
x= 7
Thus variable x = 7 and this is the final answer.
Example: solve the one step linear equation for the variable a:
a/5 = -1,
In this equation, we multiply both the sides of the equation with 5 as:
(a/5) x 5 = -1 x 5,
In this, on LHS 5 will get cancel with 5 and on right hand side we will multiple 5 with -1.
a = -5, this is the final answer of the problem.
This is all about the how to solve one step equations. Using these methods you can easily solve these types of problems.
Now, we move to the next topic of today, in this part of the article we will discuss about Patterns and relationships. In mathematics we mainly deal with different types of number patterns. The patterns can be in the form of numbers or words. Math is especially useful when it helps you predict, and number patterns are all about the prediction. Let’s see few common examples of number patterns like number pattern, figure pattern, etc. Let’s have few examples of the same. 2,4,6,8,10,12? In this series each number is increasing by sequence 2 so last numbers will be 12 + 2 = 14, and the other number of the sequence can easily be determined by adding the common difference.
Solve the following problem of mathematical pattern given below. Look the following number of sequence and calculate the value of unknowns?
Example: 15 22 29 36 43 X 57 64 71 78 85 Y
Solution: 15 22 29 36 43 X 57 64 71 78 85 Y
In this sequence number is increasing by +7 or there is a difference of 7 in all the terms,
The previous number of X is 43 so X will be 43+7, X=50
The previous number of Y is 85 so Y will be 85+7, Y=92.
In this way we see how to determine the number pattern.
Example: determine the number pattern and find the value of A and B?
85 79 73 67 61 55 49 43 A 31 25 B
Solution: 85 79 73 67 61 55 49 43 A 31 25 B
In this sequence numbers are decreasing by 6. To calculate the value of of A and B simply subtract 6 from the previous number of A and so on.
The previous number of A is 43 so A will be 43-6, A=37
The previous number of B is 25 so B will be 25-6,B=19
Now, we see the example of intermediate pattern, in this you learn how to understand that the given problem has intermediate pattern and how to solve them.
Example: The given information value of the table below explains numbers positioned into groups I, II, III, IV, V and VI. In which grouping would the following numbers belong?
a) 32
b) 33
c) 34
Solution: In this pattern the remains when the number is divided by 6 determine the collection.
Now, here is an example of advance pattern. A number of students were at a networking meeting. Every student exchanges his record with each additional student who were there.
If there were 11students, how many students’ records were exchanged?
Solution: 10+9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 55 exchanges
55 × 2 = 110 records
If there were 11students, 110 records were exchanged.
In this way you can easily understand the different mathematical patterns present in different forms. Apart from this you will also deal with even number pattern, odd number, prime number, skip number patterns, before and after patterns and many more. Pattern is the simple topic which only needs concentration to solve the problem once you understand the type of the pattern you can easily calculate the value of unknowns or nth terms. If you do practice of different types of number patterns then you can easily differentiate the type of patterns simply by analyzing the problem.
In next post we will talk on Equations in Grade V. For more information on standard deviation calculator, you can visit our website
First start with solving one step equations. In this you will learn how to solve equations. Afore, we move to this topic let’s have a brief idea of what equation is? Equation is the way to represent the mathematical numbers with different operators in a proper way and in this representation an equal to symbol is must which shows the equality between two mathematical statements. In the primary grade you must clear all your doubts so that in future you will not face any problem in the topics. Many students fear from this wonderful language as in early classes they don’t understand different topics properly and their concepts remain unclear. So kids try to overcome your doubts at the same time when they occur. Ok, now, come back to topic, in algebra you learn different types of equations, like linear equations, constant equations, equations with different variables, quadratic equations and many others. You will all learn all these types of equation in the antecedent article. Let’s start with the one step linear equation; a linear equation is an algebraic equation in which each term is either a constant or the product of constant and a single variable. Linear equation may possess one or more than one variable. The standard form of one step linear equation in one variable is given as: ax + b = c. the second type of linear equation is with two variables and its standard form is given as: x + by = c.
In both the equations i.e. one step linear equation with one variable and one step linear equation with two variables ‘a’,’b’, and ’c’ are defined as the constant. Whenever we perform addition, subtraction, multiplication, or division of any number on both the side of the equation, the equality symbol (=) of the equation does not change. Now, move towards the example of the one step linear equation problems and see how to solve these types of problems with easy method.
Example: x + 10 = 18,
Solution: Solution of this problem is very simple let’s see the step used while solving the problems and so feel how simple it is.
X + 10 = 18,
Now, subtract 10 on both the sides of the equation, on doing this we get,
x + 10 -10 = 18 -10,
x = 8
So, the answer is x =8. In this you see how to solve the one step equations, solving one step equation is simply the moment of the numbers and we have to perform simple operations on them.
Next example:
a – 15 = 6,
Solution: a – 15 = 6, in this simple example add 15 on both the side, you must be thinking that in above equation we subtract the number and in this we are adding the number why? We perform the addition and subtraction operation on the basis of the problem, if in problems we have negative sign after the variable then we perform addition operation and we add that numeric value which is written after the symbol on both the sides. And if the add sign is present then perform minus operation.
This is we have subtraction sign so we add 15 on both the sides, on doing this we get,
a – 15 + 15 = 6 +15,
a = 21,
Thus value of variable ‘a’ is equal to 21.
Now, a bit complex example of the same problem, perform one step solving operation on given equation:
4x = 28,
In this divide both the side with the coefficient of x, in this problem the coefficient of x is 4 so divide both sides with 4, this will give result as:
4x/4 = 28/4,
4 will get cancelled with4 on LHS and on RHS 28 is divided by 4,
x = 28/4,
x= 7
Thus variable x = 7 and this is the final answer.
Example: solve the one step linear equation for the variable a:
a/5 = -1,
In this equation, we multiply both the sides of the equation with 5 as:
(a/5) x 5 = -1 x 5,
In this, on LHS 5 will get cancel with 5 and on right hand side we will multiple 5 with -1.
a = -5, this is the final answer of the problem.
This is all about the how to solve one step equations. Using these methods you can easily solve these types of problems.
Now, we move to the next topic of today, in this part of the article we will discuss about Patterns and relationships. In mathematics we mainly deal with different types of number patterns. The patterns can be in the form of numbers or words. Math is especially useful when it helps you predict, and number patterns are all about the prediction. Let’s see few common examples of number patterns like number pattern, figure pattern, etc. Let’s have few examples of the same. 2,4,6,8,10,12? In this series each number is increasing by sequence 2 so last numbers will be 12 + 2 = 14, and the other number of the sequence can easily be determined by adding the common difference.
Solve the following problem of mathematical pattern given below. Look the following number of sequence and calculate the value of unknowns?
Example: 15 22 29 36 43 X 57 64 71 78 85 Y
Solution: 15 22 29 36 43 X 57 64 71 78 85 Y
In this sequence number is increasing by +7 or there is a difference of 7 in all the terms,
The previous number of X is 43 so X will be 43+7, X=50
The previous number of Y is 85 so Y will be 85+7, Y=92.
In this way we see how to determine the number pattern.
Example: determine the number pattern and find the value of A and B?
85 79 73 67 61 55 49 43 A 31 25 B
Solution: 85 79 73 67 61 55 49 43 A 31 25 B
In this sequence numbers are decreasing by 6. To calculate the value of of A and B simply subtract 6 from the previous number of A and so on.
The previous number of A is 43 so A will be 43-6, A=37
The previous number of B is 25 so B will be 25-6,B=19
Now, we see the example of intermediate pattern, in this you learn how to understand that the given problem has intermediate pattern and how to solve them.
Example: The given information value of the table below explains numbers positioned into groups I, II, III, IV, V and VI. In which grouping would the following numbers belong?
a) 32
b) 33
c) 34
| I | 1 | 7 | 13 | 19 | 25 |
| II | 2 | 8 | 14 | 20 | 26 |
| III | 3 | 9 | 15 | 21 | 27 |
| IV | 4 | 10 | 16 | 22 | 28 |
| V | 5 | 11 | 17 | 23 | 29 |
| VI | 6 | 12 | 18 | 24 | 30 |
-
26 + 6 = 32 remainder 3 (Group II)
b) 27 + 6 = 33 remainder 3 (Group III)
c) 28+ 6 = 34 remainder 5 (Group IV)
Now, here is an example of advance pattern. A number of students were at a networking meeting. Every student exchanges his record with each additional student who were there.
If there were 11students, how many students’ records were exchanged?
Solution: 10+9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 55 exchanges
55 × 2 = 110 records
If there were 11students, 110 records were exchanged.
In this way you can easily understand the different mathematical patterns present in different forms. Apart from this you will also deal with even number pattern, odd number, prime number, skip number patterns, before and after patterns and many more. Pattern is the simple topic which only needs concentration to solve the problem once you understand the type of the pattern you can easily calculate the value of unknowns or nth terms. If you do practice of different types of number patterns then you can easily differentiate the type of patterns simply by analyzing the problem.
In next post we will talk on Equations in Grade V. For more information on standard deviation calculator, you can visit our website
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