**What Is Distributive Property In Math** – The distributive property is also known as the distributive law of multiplication over addition and subtraction. The name itself indicates that the action involves dividing or distributing something. The distributive law applies to addition and subtraction. Let’s learn more about the distribution property on this page.

The distributive property states that an expression given in the form A (B + C) can be solved as A × (B + C) = AB + AC. This distributive law also applies to subtraction and is expressed thus, A (B – C) = AB – AC. This means that operand A is distributed between the other two operands.

## What Is Distributive Property In Math

The division property of multiplication by addition is applied when we need to multiply a number by the sum of two numbers. For example, let’s multiply 7 times the sum of 20 + 3. Mathematically we can represent this as 7(20 + 3).

#### Distributive Property — Definition, Uses & Examples

Solution: When we solve the expression 7(20 + 3) using the distributive property, we first multiply each addition by 7. This is known as dividing the number 7 between the two compounds and then we can add the products. This means that the multiplication of 7(20) and 7(3) will be done before addition. This leads to 7(20) + 7(3) = 140 + 21 = 161.

The distributive property of multiplication over subtraction is similar to the distributive property of multiplication over addition except for the addition and subtraction operations. Let’s consider an example of the distributive property of multiplication over subtraction.

Solution: Using the distributive property of multiplication, we can solve the expression as follows: 7 × (20 – 3) = (7 × 20) – (7 × 3) = 140 – 21 = 119

Let’s try to justify how the distributive property works for different operations. We will apply the distributive law to the two basic operations one after the other, namely, addition and subtraction.

## Math Properties: Solve By Distributive Property, Free Pdf Download

Distributive property of addition: The distributive property of multiplication by addition is expressed as A × (B + C) = AB + AC. Let’s verify this property with an example.

Now, if we try to solve the expression using the BODMAS law, we can solve it as follows. First, we’ll add the numbers in the parentheses, and then multiply that sum by the number given outside the parentheses. This means, 2(1 + 4) ⇒ 2 × 5 = 10. Therefore, both methods result in the same answer.

Distributive property of subtraction: The distributive law of multiplication over subtraction is expressed as A × (B – C) = AB – AC. Let’s verify this with an example.

Now, if we try to solve the expression using the order of operations, we will solve it as follows. First, we subtract the numbers given in parentheses, and then multiply that difference by the number given outside the parentheses. This means that 2(4 – 1) ⇒ 2 × 3 = 6. Since both methods result in the same answer, this law of distributive subtraction is proven.

## Teaching The Distributive Property

We can demonstrate the division of larger numbers using the distributive property by dividing the larger number by two or more smaller factors. Let us understand this with the help of an example.

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The distributive property is also known as the distributive multiplication law. This distributive property of multiplication applies to addition and subtraction. The formula of the distributive property is expressed like this, a × (b + c) = (a × b) + (a × c).

The formula of the distributive property is expressed like this, a × (b + c) = (a × b) + (a × c); where, a, b and c are the operands. Here, the number outside the parentheses is multiplied by each term inside the parentheses and then the products are added.

#### Question Video: Solving Word Problems Involving Decimals Using The Distributive Property Of Multiplication

When we use the distributive property formula, we multiply the outer term by the terms inside the parentheses and then add the terms to get the solution. For example, let’s solve 15(4 + 3). First, we multiply 15 by 4, then multiply 15 by 3, and then add the products to get the answer. This means that 15 × (4 + 3) = (15 × 4) + (15 × 3) = 60 + 45 = 105.

Using the distributive property formula, a × (b + c) = (a × b) + (a × c), we multiply the outer term by the two terms inside the brackets. This means that 2(m + 2) = 22 ⇒ 2m + 4 = 22. Now, the value of ‘m’ can be calculated. That is, 2m = 22 – 4 which can be further solved as, m = 9.

The distributive property of multiplication is used when we need to multiply a number with the sum of two or more additions. The distributive property of multiplication applies to the addition and subtraction of two or more numbers. It is used to easily solve expressions by dividing a number by the numbers in parentheses. For example, if we apply the distributive property of multiplication to solve the expression: 4(2 + 4), we will solve it in the following way: 4(2 + 4) = (4 × 2) + (4 × 4) = 8 + 16 = 24 .

The distributive property states, if p, q and r are three rational numbers, then the relationship between the three is given as p × (q + r) = (p × q) + (p × r). For example, 1/3(1/2 + 1/5) = (1/3 × 1/2) + (1/3 × 1/5) = 7/30.

#### Multiplying Decimals Using Distributive Property

The distributive property is used while adding, subtracting, multiplying and dividing large numbers. By grouping numbers we can form smaller parts regardless of order to solve larger equations. This makes calculations easier and faster.

The distributive property applies to variables in the same way as to numbers. For example, let’s find the value of ‘x’ in the equation -4(x – 3) = 8 using the distributive property. First we multiply -4 by x and then by 3. That is, -4(x – 3) = 8 ⇒ -4x + 12 = 8. So, the value of x = 1.

The distributive property applies to fractions in the same way that it applies to numbers and variables. For example, let’s solve the expression, 1/3(2/6 + 4/6) using the distributive property. Let’s first multiply 1/3 by 2/6 and then by 4/6. That is, 1/3(2/6 + 4/6) ⇒ (1/3 × 2/6) + (1/3 × 4/6) = 2/18 + 4/18 = 6/18 = 1/ 3 .

The distributive property of addition is another name for the distributive property of multiplication by addition. This is expressed as, a × (b + c) = (a × b) + (a × c). In math, the distributive property means that the sum of two or more additions times a number gives you the same division answer. The multiplier, multiplying each addition separately and combining the products.

#### Zero & Distributive Property

The distributive property is one of the most common properties in mathematics. It is used to simplify and solve multiplication equations by dividing the multiplier by each number in parentheses and then adding those products together to get your answer.

You can use the distributive property to turn a complex multiplication equation into two simpler multiplication problems, then add or subtract the two answers as needed.

The distributive property is the same as the distributive property of multiplication, and can be used in addition or subtraction.

The distributive property does not apply to division as it applies to multiplication, but rather the idea of division or “decomposition”

### Distributive Property. To Multiply A Sum By The Same Factor…

The distributive law of division can be used to simplify division problems by factoring or dividing the numerator into smaller values to make solving division problems easier.

, you can use the distributive law of division to simplify the numerator and turn this one problem into three smaller, easier division problems that you can solve more easily.

In basic operations, the distributive property applies to the multiplication of the product of all terms within the parentheses. This is true whether you add or subtract terms:

You can use properties of the distributive property to “break down” something hard to do like mental math:

## How To Teach Distributive Property In Your Middle School Math Classroom

In algebra, the distributive property is used to help you simplify algebraic expressions, combine like terms, and find the value of variables. This works with monomials and when multiplying two binomials:

The distributive property works on all real numbers, including positive and negative integers. In algebra especially, you need to pay attention to negative signs in expressions.

We can express this distribution of negative sign using two generic formulas, one for addition and one for subtraction:

We can apply the distributive property to geometry when working with problems involving the area of rectangles. Although algebra may seem unrelated to geometry, the two fields are closely related.

#### Multiplying By Parts(distributive Property) Worksheets

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