About Distributive Property Formula
Distributive Property
The distributive law of multiplication over addition and subtraction is another name for the distributive property. The operation's name implies that it involves dividing or dispersing something. Addition and subtraction are both covered by the distributive law.
What is the Distributive Property?
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 indicates that operand A is shared by the other two operands.
The formula for distributive property is: a(b+c)=ab+ac
Multiplication Over Addition Has a Distributive Property
We apply the distributive property of multiplication over addition when we need to multiply a number by the sum of two numbers.
Use the distributive property of multiplication over addition for solving the statement 7(20 + 3).
When utilising the distributive property to calculate expression 7(20 + 3), we multiply each addend by 7, known as spreading the number 7 between the two addends, after which products can be added. This signifies that addition will be performed before multiplication of 7(20) and 7(3). 7(20) + 7(3) = 140 + 21 = 161 is the result.
Multiplication Over Subtraction Has a Distributive Property
Except for operations of addition and subtraction, the distributive property of multiplication over subtraction is equivalent to the distributive property of multiplication over addition.
Example: Using the distributive property of multiplication over subtraction, solve expression 7(20 – 3).
Solution: We may solve the expression using the distributive property of multiplication as follows:
7 × (20 – 3) = (7 × 20) – (7 × 3) = 140 – 21 = 119
Verification of Distributive Property
Let us verify this property with the help of an example.
Example: Solve the expression 2(1 + 4) using the distributive law of multiplication over addition.
Solution: 2(1 + 4) = (2 × 1) + (2 × 4)
⇒ 2 + 8 = 10
When we use the BODMAS law to solve the expression, we get the following result. To begin, add the numbers in brackets, then multiply the sum by the number outside the brackets. As a result, 2(1 + 4) = 2 × 5 = 10 is obtained. As a result, the results of both operations are identical.
Solved example of Distributive Property Formula
Example: Solve the expression 2(4 - 1) using the distributive law of multiplication over subtraction.
Sol: 2(4 - 1) = (2 × 4) - (2 × 1)
⇒ 8 - 2 = 6
Distributive Property of Division
We can show the division of larger numbers using the distributive property by breaking the larger number into two or smaller factors. Let us understand this with an example.
Example: Divide 24 by 6 using the distributive property of division.
Sol: 24 can be written as 18 + 6.
24 ÷ 6 Equals (18 + 6) ÷ 6
Let's now distribute the division operation for each of the bracket's factors (18 and 6).
⇒ (18 ÷ 6) + (6 ÷ 6) ⇒ 3 + 1
As a result, the answer is 4.
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