Distributive Property of Whole Numbers With Examples

The Distributive Property is a fundamental property of multiplication in arithmetic. It states that multiplying a number by a sum is the same as multiplying the number by each addend separately and then adding the results. In algebraic terms, this can be expressed as:

a×(b+c)=(a×b)+(a×c)

Let’s break this down with some detailed examples:

Example 1: Using Small Whole Numbers

Suppose we want to multiply 3 by the sum of 4 and 5:

3×(4+5)

Using the Distributive Property, we can break this down as follows:

3×(4+5)=(3×4)+(3×5)

Now, we calculate each multiplication separately:

3×4=12

3×5=15

Then, we add the results together:

12+15=27

So,

3×(4+5)=27

To confirm, let’s calculate the original multiplication directly:

4+5=9

3×9=27

Both methods give us the same result,

demonstrating the Distributive Property.

Example 2: Using Larger Whole Numbers

Let’s use the property with larger numbers, say 6 and 13:

6×(10+3)

Applying the Distributive Property, we get:

6×(10+3)=(6×10)+(6×3)

Now, we calculate each multiplication separately:

6×10=60

6×3=18

Then, we add the results together:

60+18=78

So,

6×(10+3)=78

Again, let’s verify by calculating the original multiplication directly:

10+3=13

6×13=78

Both methods give the same result.

Example 3: Using Variables and Whole Numbers

Consider a more general example with a variable x:

x×(7+2)

Applying the Distributive Property:

x×(7+2)=(x×7)+(x×2)

This shows that no matter what value x takes, multiplying x by the sum of 7 and 2 is the same as multiplying x by 7 and then by 2 and adding the results.

Real-World Example

Imagine you have 5 bags, each containing 3 apples and 4 oranges. To find the total number of fruits, you can use the Distributive Property:

5×(3+4)

Breaking it down using the property:

5×(3+4)=(5×3)+(5×4)

Calculate each part:

5×3=15

5×4=20

Add the results:

15+20=35

So, there are 35 fruits in total.

Summary

The Distributive Property helps simplify multiplication, especially when dealing with larger numbers or sums. It breaks down complex multiplications into simpler parts, making calculations easier and more intuitive. This property is a powerful tool in arithmetic and algebra, providing a foundational understanding for more advanced mathematical concepts.