what property is ab=cd
what property is ab+bc=BC+CD
what property is ac=ab+bc
what property is bd=bc+cd
what property is ac=bd
1. The property that describes the equation ab = cd is the property of equality (multiplicative property of equality), which states that if two equal quantities are multiplied by the same non-zero number, the products are still equal.
2. The property that describes the equation ab + bc = BC + CD is the property of equality (additive property of equality), which states that if two equal quantities are added to the same quantity, the sums are still equal.
3. The property that describes the equation ac = ab + bc is the distributive property, which states that for any real numbers a, b, and c, the equation a(c + d) = ac + ad holds true.
4. The property that describes the equation bd = bc + cd is the commutative property (additive commutative property), which states that for any real numbers a and b, a + b = b + a.
5. There isn't a specific property that describes the equation ac = bd.
To determine which property is being used in each equation, we need to understand the properties and operations in mathematics. Here are explanations for each equation and the properties used:
1. ab = cd:
This equation represents the property of multiplication known as the Multiplication Property of Equality. According to this property, if two products are equal, then the factors or numbers being multiplied must be equal. So, in this case, ab = cd implies that a = c and b = d.
2. ab + bc = BC + CD:
This equation involves addition and is using the Property of Equality, specifically the Addition Property of Equality. According to this property, if two sums are equal, then we can add or subtract the same quantity from both sides of the equation. Therefore, ab + bc = BC + CD implies that we can subtract bc from both sides of the equation to get ab = BC + CD - bc.
3. ac = ab + bc:
This equation represents the Distributive Property of Multiplication over Addition. According to this property, when a number is multiplied by the sum of two other numbers, we can distribute the multiplication to each term individually. Therefore, ac = ab + bc implies that ac = ab + ac - ab, and by subtracting ab from both sides, we get ac - ab = ac - ab + bc, which simplifies to 0 = bc.
4. bd = bc + cd:
This equation also involves addition and is using the Reflexive Property of Equality. According to this property, any quantity is equal to itself. Therefore, bd = bc + cd implies that bd = bd + 0, where 0 represents the additive identity (the element that does not change the value when added).
5. ac = bd:
This equation does not involve any special properties, but it suggests that the values of a, b, c, and d are unknown or depend on the specific problem or context. Hence, ac = bd represents a simple equality between two variables.
Remember, math properties are general rules or characteristics that help us solve equations and manipulate numbers. They provide a framework for solving problems and making logical deductions.