Captionless Image
Addition Property of Equality
Subtraction Property of Equality
Multiplication Property of Equality
Division Property of Equality
Distributive Property
Substitution Property
Reflexive Property
Symmetric Property
Transitive Property
This image represents a series of mathematical properties that are applied in equations. The properties displayed are the addition property of equality, subtraction property of equality, multiplication property of equality, division property of equality, distributive property, substitution property, reflexive property, symmetric property, and transitive property.
The addition property of equality states that if you add the same number to both sides of an equation, the equality is preserved. The subtraction property of equality is similar, but with subtraction. The multiplication property of equality states that if you multiply both sides of an equation by the same number, the equality remains true. The division property of equality is similar, but with division.
The distributive property states that if you multiply a number by a sum, you can distribute that multiplication to each term within the sum. The substitution property allows you to substitute one value for another in an equation, as long as the equality remains true.
The reflexive property states that any value is equal to itself. The symmetric property states that if a equals b, then b equals a. The transitive property states that if a equals b and b equals c, then a equals c.
Overall, these properties help us manipulate and solve equations, providing a solid foundation for mathematical reasoning and problem-solving.
I'm sorry, but as an AI text-based bot, I am unable to view or analyze images. However, I can provide step-by-step explanations for the properties you listed:
1. Addition Property of Equality: This property states that if you add the same number to both sides of an equation, the equation remains true. For example, if you have the equation x + 5 = 10, you can apply the addition property of equality by adding 5 to both sides of the equation, resulting in x = 5.
2. Subtraction Property of Equality: This property states that if you subtract the same number from both sides of an equation, the equation remains true. For example, if you have the equation y - 3 = 8, you can apply the subtraction property of equality by subtracting 3 from both sides of the equation, resulting in y = 11.
3. Multiplication Property of Equality: This property states that if you multiply both sides of an equation by the same number, the equation remains true. For example, if you have the equation 2x = 10, you can apply the multiplication property of equality by multiplying both sides of the equation by 2, resulting in 4x = 20.
4. Division Property of Equality: This property states that if you divide both sides of an equation by the same non-zero number, the equation remains true. For example, if you have the equation 6y = 24, you can apply the division property of equality by dividing both sides of the equation by 6, resulting in y = 4.
5. Distributive Property: This property is used to simplify expressions involving multiplication and addition or subtraction. It states that when you multiply a number by a set of parentheses, you can distribute the multiplication to each term inside the parentheses. For example, if you have the expression 3(a + b), you can apply the distributive property by multiplying 3 to both terms inside the parentheses, resulting in 3a + 3b.
6. Substitution Property: This property allows you to replace a variable with its corresponding value in an equation or expression. For example, if you have the equation x + 2 = 8 and you know that x = 6, you can apply the substitution property by replacing x with 6, resulting in 6 + 2 = 8.
7. Reflexive Property: This property states that any quantity is equal to itself. For example, for any number x, x = x.
8. Symmetric Property: This property states that if a=b, then b=a. In other words, if two quantities are equal to each other, then the order can be reversed. For example, if you have the equation 4x = 20, you can apply the symmetric property to write it as 20 = 4x.
9. Transitive Property: This property states that if a=b and b=c, then a=c. In other words, if two quantities are equal to each other and the second quantity is also equal to a third quantity, then the first quantity is also equal to the third quantity. For example, if you have the equations x + 3 = 8 and 8 = 2y, you can apply the transitive property to conclude that x + 3 = 2y.
Please let me know if you need any further explanation!
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Addition Property of Equality:
The Addition Property of Equality states that if you add or subtract the same value from both sides of an equation, the equation remains true.
For example, if you have an equation: 5x + 3 = 8, you can apply the Addition Property of Equality by subtracting 3 from both sides: 5x + 3 - 3 = 8 - 3, which simplifies to 5x = 5. By doing so, you are keeping the equation balanced and maintaining its truth.
Subtraction Property of Equality:
The Subtraction Property of Equality is similar to the Addition Property but involves subtraction instead. It states that if you subtract or add the same value from both sides of an equation, the equation remains true.
Using the same example as before: 5x + 3 = 8, you can apply the Subtraction Property of Equality by subtracting 3 from both sides: 5x + 3 - 3 = 8 - 3, which simplifies to 5x = 5.
Multiplication Property of Equality:
The Multiplication Property of Equality states that if you multiply or divide both sides of an equation by the same non-zero value, the equation remains true.
For example, if you have the equation: 2x = 10, you can apply the Multiplication Property of Equality by multiplying both sides by 5: 2x * 5 = 10 * 5, which simplifies to 10x = 50.
Division Property of Equality:
The Division Property of Equality is similar to the Multiplication Property but involves division instead. It states that if you divide or multiply both sides of an equation by the same non-zero value, the equation remains true.
Using the same example as before: 2x = 10, you can apply the Division Property of Equality by dividing both sides by 2: 2x / 2 = 10 / 2, which simplifies to x = 5.
Distributive Property:
The Distributive Property is a property of numbers or variables that allows you to multiply a number or variable by a sum or difference of other numbers or variables.
For example, if you have the expression: 3(x + 2), you can apply the Distributive Property by multiplying 3 with each term inside the parentheses: 3 * x + 3 * 2, which simplifies to 3x + 6.
Substitution Property:
The Substitution Property states that if two quantities are equal, then they can be substituted for each other in an equation or expression without changing the value or truth of the equation.
For example, if you have the equation: x + 4 = 9, you know that x must be equal to 5. You can then substitute x with 5 in any other equation or expression where x appears.
Reflexive Property:
The Reflexive Property is a property of equality that states that any quantity is equal to itself. It is a basic and evident property.
For example, the reflexive property can be applied to the equation: x = x, where x represents any number or variable.
Symmetric Property:
The Symmetric Property is a property of equality that states that if two quantities are equal, then switching or swapping their places in an equation or expression does not change the value or truth of the equation.
For example, if you have the equation: 2x + 5 = 15, you can apply the Symmetric Property by rearranging the terms: 15 = 2x + 5. The equation's truth remains the same even after rearranging the terms.
Transitive Property:
The Transitive Property is a property of equality that states that if two quantities are equal to a third quantity, then they are also equal to each other.
For example, if you have the equations: x + 2 = 8 and x + 8 = 14, you can use the Transitive Property to conclude that x + 2 = x + 8. This property allows you to establish connections and relationships between various equations.