Distributive Property of Multiplication
According to the distributive property of multiplication, when we multiply a number with the sum of two or more addends, we get a result that is equal to the result that is obtained when we multiply each addend separately by the number. The distributive property of multiplication applies to the sum and the difference of two more numbers.
What is the Distributive Property of Multiplication?
The distributive property of multiplication which holds true for addition and subtraction helps to distribute the given number on the operation to solve the given equation easily. In simple words, when a number is multiplied by the sum of two numbers, then the product is the same as the product that we get when the number is distributed to the two numbers inside the brackets and multiplied by each of them separately. Let us understand this with an example. When we get an expression like 6(3 + 5), we use the order of operations by first solving the brackets and then we multiply the result with the other number in the following way: 6(3 + 5) = 6 (8) = 6 × 8 = 48.
However, when we apply the distributive property of multiplication on the same expression 6(3 + 5), we distribute the number 6 to 3 and then to 5 in the following way: (6 × 3) + (6 × 5) = 48. We get the same result with both the methods. Now, the question is, why do we use the distributive property if we get the same result by both the methods. The answer is that the distributive property is used to solve expressions that have variables instead of numbers. Since different variables cannot be added or subtracted, the distributive property helps in this case.
Distributive Property of Multiplication Formula
The formula for the distributive property of multiplication is a(b + c) = ab + ac. This formula explains that we get the same product on both sides of the equation even when we multiply 'a' with the sum of 'b' and 'c' on the left-hand-side, or, when we distribute 'a' to 'b' and then to 'c' on the right-hand-side. Observe the following formula for the distributive property of multiplication. It is to be noted that this property is applicable to addition and subtraction.
Distributive Property of Multiplication Over Addition
The distributive property of multiplication over addition states that multiplying the sum of two or more addends by a number gives the same result as multiplying each addend individually by the number and then adding or the products together. This property of multiplication over addition is used when we need to multiply a number by a sum. For example, let us solve the expression 7(9 + 3). If solve it in the usual order of operations, we will solve the brackets first and then we will multiply the number with the obtained result. 7(9 + 3) = 7(12) = 84
However, according to the distributive property of multiplication over addition, we multiply 7 by each addend. This is called distributing the number 7 to 9 and 3, and then we add each product. So, let us find the product of the distributed number: 7 × 9 and 7 × 3. This gives us: 7(9) + 7(3) = 63 + 21 = 84. This shows that we get the same product.
Observe the following equation which shows the usual method on the left-hand side and the distributive property of multiplication over addition on the right-hand side. Applying the distributive property, we distribute the number 7 to 9 and 3, then we multiply the respective numbers by 7 and add the results. In each case, the result is the same.
7(9 + 3) = 7(9) + 7(3)
7(12) = 63 + 21
84 = 84
Distributive Property of Multiplication Over Subtraction
The distributive property of multiplication over subtraction states that the multiplication of a number by the difference of two other numbers is equal to the difference of the products of the distributed number. The formula for the distributive property of multiplication over subtraction is: a(b - c) = ab - ac. For example, let us solve: 9(20 - 10).
Using the usual order of operations, we find the difference of the numbers given in brackets and then we multiply the result by 9.
9(20 -10) = 9(10) = 90
Now, let us use the distributive property of multiplication over subtraction to solve 9(20 - 10). We multiply 9 by each value inside the bracket and then find the difference of the products.
So, let us multiply: 9 × 20 and 9 × 10. This gives us: 9(20) - 9(10) = 180 - 90 = 90. The result is the same as the above.
Observe the following equation in which the usual method is shown on the left-hand side and the distributive property of multiplication is applied on the right-hand side. Applying the distributive property of multiplication over subtraction, we distribute the number 9 to 20 and 10, then we multiply the respective numbers by 9 and subtract the products. In both the cases, we get the same answer.
9(20 - 10) = 9(20) - 9(10)
9(10) = 180 - 90
90 = 90
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FAQs on the Distributive Property of Multiplication
What is the Distributive Property of Multiplication in Math?
According to the distributive property of multiplication, when we multiply a number with the sum of two or more addends, we get a result that is equal to the result that is obtained when we multiply each addend separately by the number. The distributive property of multiplication applies to the sum and the difference of two more numbers. It is used to solve expressions easily by distributing a number to the numbers given in brackets. For example, if we apply the distributive property to solve the expression: 3(2 + 4), we would solve it in the following way: 3(2 + 4) = (3 × 2) + (3 × 4) = 6 + 12 = 18.
What is the Distributive Property of Multiplication Formula?
The distributive property of the multiplication formula is applied on addition and subtraction and is expressed as:
- a(b+c) = ab + bc
- a(b-c) = ab - bc
How to Solve the Distributive Property of Multiplication Over Addition?
The distributive property of multiplication over addition is used when we multiply a value by the sum of two or more numbers. For example, let us solve the expression: 5(5 + 9). This expression can be solved by multiplying 5 by both the addends. So, 5(5) + 5(9) = 25 + 45 = 70.
How to Solve Distributive Property of Multiplication Over Subtraction?
The distributive property of multiplication over subtraction is applied when we multiply a value by the difference of two numbers. For example, let us solve the expression: 3(9 - 5). The expression can be solved by multiplying 3 by each term and then find the differences of the products. So, 3(9) - 3(5) = 27 - 15 = 12.
What does Distributive Property of Multiplication Look Like?
The distributive property of multiplication can be seen with the help of its formula which is applicable to addition and subtraction in the following way:
- Distributive property of the multiplication over addition: a(b+c) = ab + bc.
- Distributive property of the multiplication over subtraction: a(b-c) = ab - bc
Give an example of the Distributive Property of Multiplication.
The distributive property of multiplication can be understood through various examples. For example, let us solve the expression 4(7 + 3). We will distribute the number 4 to 7 and 3. This will make it 4(7) + 4(3) = 28 + 12 = 40.