Section 1: Introduction to Algebra for Class 6
Algebra is a branch of mathematics, and it plays important role in solving mathematics problems. To solve algebra problems, numbers, symbols, and their relations are used. Without learning algebra, no one can have a strong grip on mathematics. Algebra starts from class 6 itself. In this article, we will see which topics of algebra are to be covered in algebra for class 6. For basic understanding of algebra, you can also read our the introduction to the algebra.
Table of Contents
Section 2: Basic Elements of Algebra for Class 6
It is necessary for us we should start learning its basic elements before going into the depths of algebra. We will begin learning its rules, formulas, and problem-solving techniques in algebra for class 6.
1. Constants
Constants are values that never change. Like 4, 5, 0.
2. Variables
Variables are called unknown values. They are represented by letters. Like x,y,z.
3. Terms
The terms can be numbers, they can be variables, or the product of these two. Like 4x, 5y.
4. Coefficients
The number by which the variable is multiplied is called the coefficient
. Like 4x, here 4 is a coefficient.
5. Like and Unlike Terms
Like terms: Have the same variable with the same power.
Example: 5x and 2x are like terms.
Unlike terms: Have different variables or powers.
Example: 3x and 4y are unlike terms.
Section 3: Algebraic Expressions class 6 (Types and Examples)
An algebraic expression is a combination of variables, a coefficient, and operations applied to them.
Types of Algebraic Expressions
1. Monomial:
An expression with only one term.
Example: 7x
2. Binomial:
An expression with two terms.
Example: x+5
3. Trinomial:
An expression with three terms.
Example: x2+3x+2
4. Polynomial:
An expression in which two or more terms are included.
Importance of Algebraic Expressions for algebra for class 6
- Formulas in mathematics are dependent on them.
- With its help, we can solve problems to get the values of variables.
- They are the base for forming equations.
Section 4: Fundamental Rules and Properties for Class 6
By following the rules and properties in Mathematics, it becomes easy to understand its operations. With their help, we can easily solve simple problems related to algebra for class 6. So, we try to understand these properties one by one.
1. Commutative Property
According to this property, if we change the order of numbers but the operation remains the same, then there will be no effect on the result.
For example
For Addition:
a+b=b+a
For Multiplication:
a×b=b×a
Applying to numbers:
3+5=5+3=8
3*5=5*3=15
⚠ Note: This applies only to additions and multiplication.
2. Associative Property
If we arrange the numbers in the given order, then their result will remain the same. This is also for addition and multiplication.
· For Addition: (a+b)+c=a+(b+c)
Example: (2+2)+4=2+(2+4)
4+4=2+6
8=8
For Multiplication: (a×b)×c=a×(b×c)
Example: (2×2)×4=2×(2×4)
4×4=2×8
16=16
3. Distributive Property
Addition and subtraction are spread out over multiplication.
Formula: a×(b+c)=a×b+a×c
Example: 3×(4+5)=(3×4)+(3×5)
3×9=12+15
27=27
Formula: a×(b-c)=a×b-a×c
Example: 3×(4-5)=(3×4)-(3×5)=12+15=27
3×-1=12-15
-3=-3
4. Simplifying Algebraic Expressions for algebra for class 6
The first step is to simplify the algebraic expressions. First of all, we will analyze the like and unlike terms and then separate the like terms. After that, we will apply operations and use suitable properties.
Example:
Simplify 3x+5y−2y+4x
(3x+4x)+(5y-2y)=7x+3y
Section 5: Equations in Algebra for Class 6
When two algebraic expressions are equated, then an equation is formed.
For example
3x+5=11
For more detail, you can analyze our topic algebraic equations.
1. Linear Equations
A linear equation is an equation in which the highest power of all variables is 1. Example: 2x+y-3=7
2. Solving Equations Step-by-Step
In algebra for class 6, you will start solving equations step by step. This is the start in the algebra field.
Example 1: Solve y-5+3y=10
Combine like terms
(y+3y)-5=10
4y-5=10
Add 5 on both sides
4y-5+5=10+5
4y=15
Y=15/4
Example 2: Solve 3x+6=12
Subtract 6 from both sides
3x+6-6=12-6
3x=6
Divide both sides by 3: 3x/3=6/3
x=2
3. Rules for solving Algebraic Equations
- Apply the same operation on both sides.
- Keep the Equation balanced.
- BODMAS RULE:
In this rule, firstly solve the bracket, then division, multiplication, addition, and subtraction.
Section 6: Algebra Formulas for Class 6
Formulas for class 6 students are based on cooked dishes. Simply analyze problems and insert variables into formulas to get the desired value.
1. What Is an Algebra Formula?
An algebra formula is a mathematical rule written using variables, constants, and operations.
2. Important Algebra Formulas for Class 6
For numbers:
Sum: a+b
Difference: a−b
Product: a×b
For the square of numbers:
(a+b)2=a2+2ab+b2
(a-b)2=a2-2ab+b2
(a+b)(a−b)=a2-b2
For geometry:
Area of rectangle: A=l×b
Area of square: A=l×l
Perimeter of square: P=4s
Area of triangle: A=1/2×b×h
Section 7: Practice Examples
- Simplify: 3x+7x-10y+2y-5
Sol:
Combining like terms:
(3+7)x+(-10+2)y-5
10x+(-8)y-5
10x-8y-5
2. Evaluate 4y−5 when y=5.
Sol:
Put the value of y in the given expression:
=4(5)-5
=20-5
=15
3. Evaluate 4y−2x+5 when x=5,y=10.
Sol:
By putting the given values:
=4(10)-2(5)+5
=40-10+5
=35
4. Simplify 3-5+10÷5
Sol:
By BODMAS RULE
=3-5+2
=3-3
=0
5. Find the area of a square where l=15cm.
Sol:
As we know:
A=l×l
A=15×15
A=225 cm2
6. Find the perimeter of a square where l=15cm.
Sol:
As we know:
P=4l
P=4(15)
P=60 cm
7. simplify
44-(33÷11-4+20)
Sol:
By BODMAS RULE
=44-(3-4+20)
=44-(3+16)
=44-(19)
=44-19
=25
Section 8. Quick Tips for Learning Algebra
Understand deeply:
Algebra for class 6, students should understand all concepts and formulas by heart, not just memorize them.
Apply the rules carefully:
Apply suitable rules with care while problem-solving.
Do substitution:
Put the values of variables in the given equation. If it becomes equal to your answer, then your answer is right.
Practice daily:
When you practice different problems daily, your grip becomes strong.
Section 9. Conclusion:
The conclusion of this article is that after understanding and memorizing these key concepts, algebra for class 6 students become capable of solving problems easily. After understanding properties, they can solve problems easily. After regular practice, every student becomes so capable that they gain a grip on algebra.
Remember, algebra is not just something that you learn, but it becomes a strength for a student in the field of mathematics.
A student who gives proper time to this in his student life can use it as a weapon in any field of mathematics or any problem in mathematics. Algebra should not be taught as a subject, but should be taught with passion.
if your concepts are clear now about algebra for class 6 then you are able to practice algebra problems for class 6 and algebra word problems for class 6.
