The answer to the question: Is [elementary] algebraic addition distributive over multiplication ? is generally NO of course. The word "generally" implies that the answer could be YES in certain circumstances. [The distribution of multiplication over addition may be taken as always true.]
Where the subject of this question is true, then it is found that a relationship exists between the algebraic variables. Consider the equation:
a + b.c = [a + b].[a + c] [This equation is not generally true as is found by substituting any values for a, b and c.] However multiplying out the right side gives: a + b.c = a**{2} + a.c + b.a + b.c Cancelling the term b.c enables us to solve for the variable: a in terms of the variables: b and c. We find that:
a = 1 - b - c . There are clearly an infinite number of possible values of a for pairs of b and c.
Note that if b and c are uneven integers, then a is also an uneven integer.
Check: set b = 5, c = 7, then a = - 11 from the answer given.
Now a + b.c = - 11 + 35 = 24 and [a + b] = - 6 and [a + c] = - 4 so that:
[a + b].[a + c] = [- 6].[- 4] = 24 .
A similar result can be found for the distribution of subtraction over multiplication and moreover these examples can be made much more general.
In the case of subtraction, an uneven number of factors are needed to cancel the multiplicative term b.c.d on the left, thus:
a - b.c.d = [a - b].[a - c].[a - d]
SOMeThingZ ;O
Usually the distributive property of multiplication over addition is considered:a(b+c) = ab + acHowever, since subtracting is the same as adding the additive inverse, it is valid for subtraction as well:a(b-c) = ab - ac
In mathematical operations, addition, subtraction, and multiplication are governed by the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). When addition, subtraction, and multiplication are used in a problem, multiplication is performed first, followed by addition and subtraction, which are executed from left to right. Thus, in a sequence where these operations appear together, multiplication takes priority over addition and subtraction.
a*(b ± c) = a*b ± a*c
b= brackets o= over power d= division m= multiplication a = addition s = subtraction
SOMeThingZ ;O
It means that A*(B+C) = A*B + A*C and similarly for subtraction.
Usually the distributive property of multiplication over addition is considered:a(b+c) = ab + acHowever, since subtracting is the same as adding the additive inverse, it is valid for subtraction as well:a(b-c) = ab - ac
In mathematical operations, addition, subtraction, and multiplication are governed by the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). When addition, subtraction, and multiplication are used in a problem, multiplication is performed first, followed by addition and subtraction, which are executed from left to right. Thus, in a sequence where these operations appear together, multiplication takes priority over addition and subtraction.
addition and subtraction * * * * * No. The distributive property applies to two operations, for example, to multiplication over addition or subtraction.
The three properties of operations are commutative (changing the order of numbers does not change the result), associative (changing the grouping of numbers does not change the result), and distributive (multiplication distributes over addition/subtraction).
The distributive property of multiplication OVER addition (or subtraction) states that a*(b + c) = a*b + a*c Thus, multiplication can be "distributed" over the numbers that are inside the brackets.
Addition and subtraction property of equalityMultiplication and division property of equalityDistributive property of multiplication over additionAlso,Identity property of multiplicationZero property of addition and subtraction.
a*(b ± c) = a*b ± a*c
Multiplication can be the first step when using the distributive property with subtraction. The distributive law of multiplication over subtraction is that the difference of the subtraction problem and then multiply, or multiply each individual products and then find the difference.
No, the order of operations in PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) has remained consistent over time.
b= brackets o= over power d= division m= multiplication a = addition s = subtraction