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. We multiply 9 by each value inside the bracket and then find the difference of the products. Now, let us use the distributive property of multiplication over subtraction to 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.
The formula for the distributive property of multiplication over subtraction is: a(b - c) = ab - ac. 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. In each case, the result is the same.ĭistributive Property of Multiplication Over Subtraction
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. 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. So, let us find the product of the distributed number: 7 × 9 and 7 × 3. This is called distributing the number 7 to 9 and 3, and then we add each product. However, according to the distributive property of multiplication over addition, we multiply 7 by each addend. 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. For example, let us solve the expression 7(9 + 3). This property of multiplication over addition is used when we need to multiply a number by a sum. 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. Since different variables cannot be added or subtracted, the distributive property helps in this case.ĭistributive Property of Multiplication Over Addition The answer is that the distributive property is used to solve expressions that have variables instead of numbers. Now, the question is, why do we use the distributive property if we get the same result by both the methods.
We get the same result with both the methods.
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. 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. 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. 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. What is the Distributive Property of Multiplication?