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Distributive Property of Maths Explained
Multiplication is one of the four operational functions of mathematics, the other three are, Addition, Subtraction, and Division. And the students of Maths need to understand all the aspects of this operational function. Now, coming to the properties, there are three main types of properties of Number, Commutative, which can be achieved with the addition and multiplication operations, then there is Associative Property, which deals with the binary functions of the number, and then there is distributive property also known as distributive law of multiplication. Understanding the Distributive PropertyThe Distributive property is used when you have to multiply the given number by the sum of the two numbers. In such cases what you generally do by following the rule of order of operations, is to first add the numbers, and then multiply them by the given number. For example, if you have to multiply the number 5 with the sum of 10 + 5, then you can represent it in this manner, 5(10 + 5), now according to the rule of order of operation, you first have to find the sum of 10 + 5, which becomes 15, and then you have to multiply 15 with the 5. The whole solution may look like, 5(10 + 5) = 5(15) = 75 But in the distributive law of multiplication, what you have to do is to distribute the sum first and then multiply the same with the given number, and then you have to add the results of both. Take the same example once again, which was 5(10 + 5), What you have to do now is first multiply 5 with the 10, which is 50, and then multiply the 5 with the 5, the answer is 25, now add 50 and 25 together, you have got 75. The whole solution looks like this: 5(10 + 5) = 5(10) + 5(5) = 50 + 25 = 75 The distributive property can be present in the equation form as: One thing you must keep in mind, that the distributive law of multiplication remains the same, even when the variables inside the sum bracket increase. That is to say, if the question is 5(10 + 5 + 5) then the rule still remains the same, it goes like this, 5(10) + 5(5) + 5(5), which becomes 50 + 25 + 25, and the total becomes 100. Steps to Follow in the Distributive PropertyIt is always better to have a summarization of the steps, for an even better understanding of the distributive law of Multiplication, and hence following are the steps of the same.
Types of Distributive PropertyThere are three properties of numbers most widely used. They are commutative, associative and distributive property. The distributive property is also known as the distributive law of multiplication. The distributive property is the most frequently used property in mathematics. Distribute means the name itself implies that to divide something. Distributive property means dividing the given operations on the numbers so that the equation becomes easier to solve. So let us study distributive property definition, distributive property formula, distributive property example and distributive property with variables Distributive Property DefinitionThe distributive property applies to the multiplication of a number with the sum or difference of two numbers i.e., the distributive property holds true for multiplication over addition and subtraction. The distributive property definition simply states that “multiplication distributed over addition.” For instance, take the equation
Distributive Property Formula(Image will be uploaded Soon) Let us understand this concept with distributive property examples For example 3( 2 + 4) = 3 (6) = 18 or By distributive law \[3( 2 + 4) = 3 \times 2 + 3 \times 4\] = 6 + 12 = 18 Here we are distributing the process of multiplying 3 evenly between 2 and 4. We observe that whether we follow the order of the operation or distributive law the result is the same. Distributive Property with VariablesThe distributive property law can also be used when multiplying or dividing algebraic expressions that include real numbers and variables that are called distributive property with variables. The expression can be monomial, binomial or polynomial. You can multiply a polynomial by a monomial by using distributive law in the following ways
For example consider x (2x + 8) = \[(x \times 2x) + (x \times 8)\] = 2 x2+ 8x You can use the distributive property law to find the product of binomials too. For example consider (x + y)(x + 5y) (x + y)(x + 5y) =x( x + 5y) + y (x + 5y) = \[x^{2} + 5xy + xy + 5y^{2}\] = \[x^{2} + 6xy + 5y^{2}\] The distributive property also allows us to simplify the algebraic equation and find the values of unknown variables. Using distributive property finding the values of unknown variables
For example : 4( x + 3) = 20 4(x) + 4(3) = 20 4x + 12 = 20 4x = 20 - 12 4x = 8 x = 8/4 x = 2 In Mathematics distributive property is applied to various operations such as
Distributive Property of AdditionWe add two or more numbers to get their total. The distributive property tells us that the sum of two numbers multiplied by the third number is equal to the sum of each addition multiplied by the third number. Distributive property of addition is represented as \[(p + q) \times r = (p \times q) + (p \times q)\] Distributive Property of SubtractionThe distributive property of subtraction is the same as the distributive property of addition. And is represented as: \[(p - q) \times r = (p \times q) - (p \times q)\] Distributive Property of MultiplicationWhen we want to multiply any number with the sum of a number we usually first add the numbers and then multiply it by the number. For instance 6( 2+ 3) = 6(5) = 30 But by the law of distributive property of multiplication, we first multiply the number by every addend and then perform the addition on the products. As, 6 ( 2 + 3) = \[6 \times 2 + 6 \times 3\] =12 + 18 = 30 We observe that the results for the operations are the same. Distributive Property of DivisionDividing large numbers is a bit time consuming, hence distributive property allows us to make it easier by breaking those numbers into smaller factors and then distributing the divide operation between them. For example, divide 96 8 Solution: we can write 96 = 80 + 16 (80 + 16) 8 Now distributing division operation for each value in the bracket we get, ( 80 ÷ 8) + (16 ÷ 8) =10 + 2 = 12 In this way, we can make the division operations easier. Let us understand this concept with more distributive property examples. Solved Examples1. 4(8x + 4) Solution: 4(8x + 4) = \[(4 \times 8x) + ( 4 \times 4)\] = 32x + 16 2. 9a(5a + 2b) Solution: 9a(5a + 2b) = \[(9a \times 5a) + (9a \times 2b)\] = \[45a^{2} + 18ab\] Quiz TimeApplying distributive law solve
How do you do the distributive property step by step?Distributive property with variables. Multiply, or distribute, the outer term to the inner terms.. Combine like terms.. Arrange terms so constants and variables are on opposite sides of the equals sign.. Solve the equation and simplify, if needed.. How do you do distributive property in math?According to this property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.
What is distributive property formula?The formula for the distributive property is expressed as, a × (b + c) = (a × b) + (a × c); where, a, b, and c are the operands. Here, the number outside the brackets is multiplied with each term inside the brackets and then the products are added.
What is the distributive property of 3x6?Remember that there are several ways to write multiplication. 3 x 6 = 3(6) = 3 • 6. 3 • (2 + 4) = 3 • 6 = 18. The distributive property of multiplication over addition can be used when you multiply a number by a sum.
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