Multiplication Property Of Equality Example
Properties of Equality
We have mainly nine backdrop of equality, namely improver belongings, subtraction property, multiplication property, sectionalisation property, reflexive property, symmetric property, transitive property, substitution property, and square root property of equality. Backdrop of equality give the relation between two quantities that are equal and how the equation remains counterbalanced after applying an operation. When an operation (addition, subtraction, multiplication, and sectionalisation) is practical on both sides of an equation, the equation still holds truthful.
In this article, we will explore the concept of the properties of equality with explanations and examples. We will list the various properties of equality forth with examples for a amend understanding of the concept. Nosotros shall also talk over the applications of these properties and provide a summary of the properties in a table for a quick review.
| one. | What are Properties of Equality? |
| 2. | Listing of Backdrop of Equality |
| 3. | Properties of Equality Table |
| 4. | Applications of Properties of Equality |
| v. | FAQs on Properties of Equality |
What are Properties of Equality?
Properties of equality draw the relation between 2 equal quantities and if an operation is applied on one side of the equation, so it must exist applied on the other side to keep the equation balanced. We have mainly nine properties of equality - addition, subtraction, multiplication, division, reflexive, symmetric, transitive, commutation, and square root backdrop. The addition, subtraction, multiplication, and sectionalisation properties of equality help to solve algebraic equations involving real numbers. The reflexive, symmetric, and transitive properties of equality together define the equivalence relation.
Properties of Equality Definition
The properties that do non change the truth value of an equation, that is, the properties that do non impact the equality of two or more quantities are called the properties of equality. Such properties of equality aid us to solve various algebraic equations and define an equivalence relation.
List of Properties of Equality
We will focus on nine properties of equality. Permit us list them below and ascertain each 1 of them to empathize these backdrop:
- Addition Property of Equality
- Subtraction Property of Equality
- Multiplication Property of Equality
- Partition Holding of Equality
- Reflexive Property of Equality
- Symmetric Property of Equality
- Transitive Property of Equality
- Substitution Property of Equality
- Foursquare Root Property of Equality
We volition now become through each of these properties in detail to sympathize them better.
Addition Property of Equality
The addition belongings of equality is defined every bit "When the aforementioned amount is added to both sides of an equation, the equation yet holds true". We tin can express this belongings mathematically equally, for existent numbers a, b, and c, if a = b, then a + c = b + c. This property can exist used in arithmetic and algebraic equations.
Subtraction Property of Equality
The subtraction belongings of equality states that if the same existent number is subtracted from both sides of an equation, so the equation nonetheless holds true. The formula for this property tin be written as, for existent numbers a, b, c, if a = b, so a - c = b - c. Nosotros can use this property to solve algebraic equations.
Multiplication Property of Equality
According to the multiplication property of equality, when the same real number is multiplied past both sides of an equation, then the two sides of the equation remain equal. We can express the formula for this property as, for real numbers a, b, and c, if a = b, so a × c = b × c.
Division Belongings of Equality
The division holding of equality states that when both sides of an equation are divided by the same existent number, and then equality yet holds. Mathematically, we tin write this property equally, for real numbers a, b, and c, if a = b, then a/c = b/c. This property is used to find the unknown variable in an algebraic equation.
Reflexive Property of Equality
Co-ordinate to the reflexive belongings of equality, every real number is equal to itself. We can express it mathematically every bit, for an arbitrary real number x, nosotros have ten = x.
Symmetric Property of Equality
The symmetric property of equality states that, when a real number ten is equal to a real number y, then we tin say that y is equal to ten. This holding can be expressed as, if x = y, then y = x.
Transitive Property of Equality
The transitive property of equality is divers as, for real numbers x, y, and x, when x is equal to y and y is equal to z, so we tin say that x is equal to z. Mathematically, we can limited this holding of equality as, for real numbers x, y, and 10, if x = y and y = z, so we have 10 = z.
Substitution Holding of Equality
According to the substitution property of equality, for real numbers x and y, if nosotros take ten = y, then we tin substitute y in place of x in whatsoever algebraic expression. In other words, we can say that if x = y, so y can exist substituted for x in any algebraic expression to notice the value of the unknown variable. We tin can express the substitution property as, for real numbers x, y, and z, if x = y and 10 = z, then we tin can write y = z
Square Root Property of Equality
The square root holding of equality states that if a real number x is equal to a real number y, then the square root of ten is equal to the square root of y. We can write this property mathematically equally, for existent numbers x and y, if x = y, and so √x = √y.
Properties of Equality Table
Now, nosotros have understood the various properties of equality in the previous department. Permit u.s. now summarize these properties in a table given below along with their meanings for a quick review.
| Belongings of Equality | Meaning |
|---|---|
| Addition Property | For real numbers x, y, and z, If ten = y, then 10 + z = y + z |
| Subtraction Property | For real numbers x, y, and z, If x = y, and so x - z = y - z |
| Multiplication Property | For real numbers ten, y, and z, If ten = y, then x × z = y × z |
| Division Holding | For real numbers x, y, and z, If x = y, then ten ÷ z = y ÷ z |
| Reflexive Property | Every real number is equal to itself. For a real number x, x = x, |
| Symmetric Property | Society of equality does not matter. For real numbers ten and y, If x = y, then y = 10 |
| Transitive Property | Numbers equal to the same number are equal to each other. For real numbers x, y, and z, If 10 = y and y = z, and then x = z |
| Substitution Belongings | Whatever two real numbers equal to each other can exist substituted for one some other in any expression. For real numbers 10 and y, If x = y, then y can be substituted for x. |
| Foursquare Root Belongings | Square Roots of Equal Numbers are equal. For real numbers x and y, If 10 = y, so √x = √y |
Applications of Properties of Equality
Now that we have understood the significant of the dissimilar properties of equality, let us at present solve a few examples based on these properties to sympathize the awarding of the properties.
Case 1: Solve 10 - 3 = 8
Solution: To find the value of x, we will use the addition property of equality.
Add 3 to both sides of the equation. So, we have
x - 3 = 8
⇒ 10 - 3 + iii = 8 + 3
⇒ 10 = 8 + three
⇒ x = 11
Example 2: Detect the value of the expression xii + 3x - 4 if x = 2.
Solution: To find the value of the given expression, we will use the substitution property of equality. Since 10 = 2, we will substitute 2 in place of x in the expression x2 + 3x - 4.
x2 + 3x - four
= iiii + 3(2) - 4
= 4 + half dozen - iv
= six
Then, the value of the expression x2 + 3x - iv is equal to vi when x = two.
Important Notes on Properties of Equality
- We have mainly 9 properties of equality:
- Add-on Property of Equality
- Subtraction Holding of Equality
- Multiplication Property of Equality
- Partition Property of Equality
- Reflexive Property of Equality
- Symmetric Property of Equality
- Transitive Property of Equality
- Exchange Belongings of Equality
- Square Root Property of Equality
- These properties help in solving algebraic equations, finding the value of expressions, and defining the equivalence relation.
☛ Related Topics:
- Inequalities
- Equal To
- Linear Inequalities
Backdrop of Equality Examples
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Properties of Equality Questions
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FAQs on Backdrop of Equality
What are the Properties of Equality in Algebra?
Properties of equality describe the relation between two equal quantities and if an performance is applied on one side of the equation, then it must be applied on the other side to keep the equation balanced.
How Many Properties of Equality Are In that location?
We have mainly nine properties of equality:
- Addition Property of Equality
- Subtraction Property of Equality
- Multiplication Belongings of Equality
- Division Property of Equality
- Reflexive Property of Equality
- Symmetric Property of Equality
- Transitive Property of Equality
- Substitution Property of Equality
- Square Root Property of Equality
What is the Difference Between Backdrop of Equality and Properties of Inequality?
The main difference between the properties of equality and the backdrop of inequality is that if we multiply or divide both sides of an equation past the same negative real number, the equation remains the same, but if we multiply or split both sides of an inequality by the aforementioned existent negative number, the inequality reverses.
How to Solve an Equation Using the Properties of Equality?
Nosotros can solve an equation using the four properties of equality - Improver, Subtraction, Multiplication, and Segmentation. We can simply add, decrease, multiply or divide both sides of an equation to find the value of the unknown variable.
What is the Difference Between the Backdrop of Equality and the Properties of Congruence?
The primary deviation between the properties of equality and the properties of congruence is that the properties of equality are based on algebra whereas the properties of congruence are based on geometry.
What is the Distributive Property of Equality?
According to the distributive property of equality, for real numbers a, b, and c, nosotros have (a + b)c = ab + bc.
Why Do Nosotros Use Properties of Equality?
We use the properties of equality to solve different algebraic equations and find the value of the unknown variable. We can besides use these properties to define the equivalence relation.
Multiplication Property Of Equality Example,
Source: https://www.cuemath.com/algebra/properties-of-equality/
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