## Distributive Property

Distributive property explains that the operation performed on numbers, available in brackets that can be allocated for each number outside the bracket. It is one of the most often used mathematical properties. The commutative and associative properties are the other two main properties.

Multiplying the sum of two or more addends by a number produces the same effect as multiplying each addend separately by the number and then adding the components together, according to the distributive property.

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### Commutative Property

The commutative property states that the numbers we operate with can be moved or swapped from their original positions without affecting the result. The property applies to addition and multiplication, but not subtraction or division.

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### Associative Property

The associative property states that no matter how the numbers are arranged, they can be added or multiplied. We mean 'how you use parentheses' when we say 'grouped.' In other words, it doesn't matter where you place the parentheses whether you're adding or multiplying.

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### Definition of the Distributive Property

The Distributive Property is an algebraic property that makes you multiply two or more values within a set of parenthesis.

When a factor is multiplied by the sum/addition of two terms, the distributive property states that it is necessary to multiply each of the two numbers by the factor before performing the addition operation.

The formula of distributive property is,

A (B + C) = AB + AC

Where, A, B and C are three different variables.

### Distributive Property Formula

The formula of distributive property is,

A (B + C) = AB + AC

Let’s discuss the left and right distributive property.

Given set S and two binary operators + and * on S.

The operator * is a left distributive operation concerning +. If any given element x, y, and z follow set S. Left distributive property can be stated symbolically as:

x * (y + z) = (x * y) + (x * z)

The operator * is a right distributive operation concerning +. If any given element x, y, and z follow set S. Right distributive property can be stated symbolically as:

(y + z) * x = (y * x) + (z * x)

### Distributive Property Examples

Ex.1. Solve 6(4 + 5) by Distributive Property Formula.

Solution:

To find the value of 6(4 + 5) using the distributive property.

Using the distributive property formula,

a × (b + c) = a × b + a × c

Now, multiplying the outside term by all terms within the parenthesis:

= (6 × 4) + (6 × 5)

= 24 + 30

= 54

Answer: The value of 6(4 +5) = 54.

Ex.2. Solve (7 + 2)(4 + 3) by Distributive Property Formula.

Solution:

To find the solution of (7 + 2)(4 + 3).

Using distributive property formula,

(a+b)(c+d) = ac + ad + bc + bd

Now, multiplying the outside term by all terms within the parenthesis:

= (7 + 2) × 4 + (7 + 2) × 3

= 7 × 4 + 2 × 4 + 7 × 3 + 2 × 3

= 28 + 8 + 21 + 6

= 63

Answer: The solution of (7 + 2)(4 + 3) is 63.

Ex.3. Solve (4 + 7)8 by Distributive Property Formula.

Solution:

To find the value of (4 + 7)8 using the distributive property.

Using the distributive property formula,

(b + c) × a = b × a + c × a

Now, multiplying the outside term by all terms within the parenthesis:

= (4 × 8) + (7 × 8)

= 32 + 56

= 88

Answer: The value of (4 +7)8 = 88.

1. What Distributive Means?

Answer: The simple meaning of distributive is a sharing of something to each member of the group with a definite rule.

2. What is the Distributive Property of Integers?

Answer: The distributive property of integers is that the product of an integer with the number of two integers contained in parentheses equals the sum of the products of the integers separately. If a, b, and c are integers, then a(b + c) = ab + bc is the distributive property of multiplication over the addition of integers.

3. What is the Distributive Property of 3x6?

Answer: With Dr D, the distributive doctor, students will claim they are surgeons “breaking apart” arrays. They will start to see that 3x6 is equal to the (3 x 2)+(3 x 4) or 3 x (2 + 4) because of the distributive property of multiplication.