# Distributive Property Formula

## Distributive Property Formula

The Distributive Property Formula describes the operation performed on numbers that are available in brackets and can be distributed for each number outside the bracket. The Distributive Property Formula is one of the most commonly used properties in Mathematics. The commutative and associative qualities are the other two major features.

The Distributive Property Formula is simple to recall. Mathematics has a lot of qualities that can help students reduce not only arithmetic computations but also algebraic expressions. This article will teach students about distributive property, formulas, and solved instances.

The Distributive Property Formula is sometimes referred to as the distributive law of addition and subtraction. The name suggests that the operation entails dividing or dispersing something. The distributive law governs addition and subtraction.

What is the Distributive Property?

The Distributive Property Formula is an algebraic property used to multiply a single value by two or more values enclosed by parenthesis. The Distributive Property Formula states that when a factor is multiplied by the sum/addition of two terms, each of the two numbers must be multiplied by the factor before performing the addition operation. The Distributive Property Formula can be expressed symbolically as follows:

A (B+ C) = AB + AC

Where A, B, and C represent three distinct values.

### Distributive Property Formula

Due to the fact that the two values inside the parenthesis cannot be added because they are not like words, they cannot be simplified further. Students require a different approach, which is where Distributive Property Formula becomes relevant.

When students use the Distributive Property Formula,

6× 2 + 6 × 4x

The parenthesis is gone, and each term is multiplied by 6.

Students can now simplify multiplication for individual terms.

12 + 24x

Multiplication’s Distributive Property Formula allows students to simplify phrases in which students multiply an integer by a sum or difference. This property states that the product of a sum or difference of two numbers is equal to the sum or difference of the products.

### Distributive Property of Multiplication Over Addition

Multiplication’s Distributive Property Formula can be represented using addition and subtraction. That is, the operation exists inside the bracket, i.e. addition or subtraction between the integers inside the bracket.

According to the distributive property, an expression of the form A (B + C) can be solved as A (B + C) = AB + AC. This distributive property applies to subtraction as well and is written as A (B – C) = AB – AC. This signifies that operand A is shared by the other two operands. When students multiply a value by a sum, the distributive property of multiplication over addition is used. For instance, suppose students want to multiply 5 by the sum of 10 + 3.

When students have similar phrases, students normally sum the numbers and then multiply by 5.

5(10 + 3) = 5(13) = 65

However, the property states that students must first multiply each addend by 5. This is referred to as spreading the 5, after which students can add the products.

Before students add, the multiplication of 5(10) and 5(3) will be performed.

5(10) + 5(3) = 50 + 15 = 65

As students can see, the outcome is the same as before.

Students most likely employ this strategy without even realising it.

The equations below describe both strategies. Students have 10 and 3 on the left, which students multiply by 5. This expansion is redone by using the Distributive Property Formula on the right side, in which students distribute 5, multiply by 5, and then sum the results. Students see that the outcome is consistent in each scenario.

5(10 + 3) = 5(10) + 5(3) (3)

5(13) = 50 + 15

65 = 65

### Distributive Property of Multiplication Over Subtraction

Except for the operation of addition and subtraction, the Distributive Property Formula of multiplication over subtraction is analogous to the Distributive Property Formula of multiplication over addition. Consider the Distributive Property Formula of multiplication over subtraction as an example.

Addition and subtraction’s distributive features can be used to modify expressions for various purposes. Students can add and multiply when multiplying a number by a sum. Students can also multiply each addend separately before adding the products. This also applies to subtraction. In each case, students change the outer multiplier for each value in the parenthesis so that multiplication occurs before addition or subtraction.

Students must now consider an example of a Distributive Property Formula of multiplication over subtraction.

Assume students need to multiply 6 by 13 and 5, resulting in (13 – 5).

This can be done in two ways.

Case 1: 6 × (13 – 5) = 6 × 8 = 48

Case 2: 6 × (13 – 5) = (6 × 13) – (6 × 5) = 78 – 30 = 48

Whatever approach is used, the end effect will be the same in both circumstances.

### Verification of Distributive Property

Distributive Property Formula of addition: A (B + C) = AB + AC expresses the distributive property of multiplication over addition.

Example: Using the Distributive Property Formula of multiplication over addition, solve the expression 2(1 + 4).

Solution: 2(1+4) = (2 1) + (2 4) 2 + 8 = 10

Now, if students try to solve the expression using the law of BODMAS, students get the following result. students will first add the numbers in the brackets and then multiply this total by the number outside the brackets. This means that 2(1 + 4) 2 5 Equals 10. As a result, both procedures get the same response.

Subtraction Distributive Property: Distributive Property Formula of multiplication over subtraction is represented as A (B – C) = AB – AC.

Example: Using the Distributive Property Formula of multiplication over subtraction, solve the expression 2(4 – 1).

Solution: 2(4-1) = (2 4) – (2 1) 8 – 2 = 6

Now, if students try to solve the expression using the order of operations, students get the following result. Students start by subtracting the numbers in brackets, and then multiplying the difference by the number outside the brackets. This equals 2(4 – 1) 2 3 = 6. Because both procedures yield the same result, this Distributive Property Formula of subtraction is proven.

### Distributive Property of Division

Although the Distributive Property Formula does not apply to division in the same way that it applies to multiplication, the concept of distributing or “splitting apart” can be applied to division.

To make division problems easier to solve, the Distributive Property Formula of division can be utilised to split apart or distribute the numerator into smaller amounts.

Instead of attempting to solve 125/5, students can utilise the distributive property of division to reduce the numerator and divide this one problem into three smaller, easier division problems.

### Distributive Property Examples

When students need to multiply a given number by the sum of two numbers, students apply the Distributive Property Formula. In such circumstances, the rule of order of operations dictates that students add the numbers first, and then multiply them by the provided number. For example, if students need to multiply the number 5 by the total of 10 + 5, students can write it as 5(10 + 5). Now, according to the law of order of operation, students must first find the sum of 10 + 5, which is 15, and then multiply 15 by the number 5. The entire solution could look like this,

5(10 + 5)

= 5(15) (15)

= 75

However, in the distributive law of multiplication, what students have to do is distribute the sum first and then multiply the same with the given number, and then students have to add the results of both. Take the same example once again, which was 5(10 + 5), What students have to do now is first multiply 5 by 10, which is 50, and then multiply the 5 with the 5, the answer is 25, now add 50 and 25 together, students 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:

One thing to remember is that the Distributive Property Formula of multiplication remains constant even when the variables within the sum bracket increase. That is, if the question is 5(10 + 5 + 5), the rule remains the same; it is 5(10) + 5(5) + 5(5), which equals 50 + 25 + 25, and the total is 100.

### Practice Questions on Distributive Property

It is always preferable to have a summary of the processes for a better understanding of the distributive law of Multiplication, hence the steps are as follows.

• The first step in using the Distributive property is to multiply the number outside the bracket or parentheses by the number given inside the parenthesis.
• Now multiply the number shown outside the parentheses by the number shown inside the parenthesis.
• Finally, students must add both of the results.