Question

Multiplication is distributive over addition for whole numbers, say true or false.

Answer 1

Hint: Distributive property explains that the operation performed on numbers, available in brackets that can be distributed for each number outside the bracket. The distributive property states that when a factor is multiplied by the sum (addition) of two terms, it is essential to multiply each of the two numbers by the factor, and finally perform the addition operation. The distributive property of multiplication over addition is given as \[A \times \left( {B + C} \right) = \left( {A \times B} \right) + \left( {A \times C} \right)\].

Complete step-by-step answer:
We know that,
Natural numbers along with zero form the collection of whole numbers
The distributive property of multiplication lets you simplify expressions wherein you multiply a number by a sum or difference. According to this property, the product of a sum or difference of a number is equal to the sum or difference of the products.
In algebra, we can have the distributive property for two arithmetic operations such as:
1) Distributive Property of Multiplication
2) Distributive Property of Division
We will explain Distributive Property of Multiplication Over Addition:
The distributive property of multiplication over addition is applied when you multiply a value by a sum. The distributive property of multiplication over addition is given as \[A \times \left( {B + C} \right) = \left( {A \times B} \right) + \left( {A \times C} \right)\].

For example, you want to multiply 5 by the sum of 10 + 4.
As we have like terms, we usually first add the numbers and then multiply by 5.
\[A\left( {B + C} \right)\]
\[ = 5\left( {10 + 4} \right)\]
\[ = 5\left( {14} \right)\]
\[ = 70\]
=LHS

But, according to the property, you can first multiply every addend by 5. This is known as distributing the 5 and then you can add the products.
The multiplication of 5(10) and 5(3) will be performed before you add.
\[(A \times B) + (A \times C)\]
\[ = 5\left( {10} \right) + 5\left( 4 \right)\]
\[ = 50 + 20\]
\[ = 70\]
=RHS
Thus, LHS = RHS
The below equations describe both the methods. We have 10 and 4 on the left-hand side then multiplied by 5. This expansion is rewritten by applying the distributive property on the right-hand side where we distribute 5 then multiply by 5 and add the results. You will see that the result is similar in each case.
So, the correct answer is “TRUE”.

Note: The distributive property of multiplication can be expressed under addition and subtraction. We usually use the distributive property because the two terms inside the parentheses can’t be added because they’re not like terms. Make sure you apply the outside number to all of the terms inside the parentheses or brackets. The distributive property of multiplication over addition is applied when you multiply a value by a sum.