The Distributive Property: Multiplication Facts, Arrays, and Applications

The Distributive Property    

What is Distributive Property?

To ‘distribute’ means to divide something or give a share or part of something.

The distributive property says that a multiplication fact can be broken apart into the sum of two other multiplication facts.

Example:  6 x 2 = (4 x 2) +(2 x 2)

= 8 +4

= 12

The below image provides a pictorial representation of distributive property.

What is an Array?

An arrangement of objects, pictures, or numbers in rows and columns is called an array.

A real-life example of an array.

From the above array

Rows = 3

Columns = 5

Multiply 3 x 5 =15

Example1:

Maria and her father went to a school art competition. They saw 5 rows of pictures displayed on a wall. Each row had 9 pictures. How many pictures are there on the wall?

Solution:

Step 1: Break apart 5 rows into 3+2.

Step 2: Multiply  5 x 9 =( 3 x 9 )+ (2 x 9)

Step 3: Add   27 + 18

5 x 9 = 45

So,  5 x 9 = 45.

A total of 45 pictures are arranged on a wall.

Example2:

Ria arranged  8 rows of chocolates in a box. Each row has 5 chocolates. How many chocolates has she arranged in the box?

Solution:

Step 1: Break apart 8 rows into 4 + 4.

Step 2: Multiply  8 x 5 =( 4 x 5 )+ (4 x 5)

Step 3: Add  = 20 + 20

8 x 5 = 40

So,  8 x 5 = 40.

She arranged 40 chocolates in the box.

Example3:

A father and his son went to a shop. The shopkeeper had arranged fruit drinks in 7 rows. Each row had 4 drinks. What is the total number of drinks that he arranged?

Solution:

Step 1: Break apart 7 rows into 4 + 3.

Step 2: Multiply  7 x 4 =( 4 x 4 )+ (3 x 4)

Step 3: Add  = 16 + 12

7 x 4 = 28

So,  7 x 4 = 28.

The shopkeeper arranged 28 fruit drinks in a shop.

Concept Map:

Exercise:

1. How many rows and columns are there in the below array?

2. Separate the rows in the large array into two small arrays.

3. Separate the rows in the large array into two small arrays. Write the new facts.

4. Use the smaller arrays and distributive property to find the missing factor. You may use counters to help.

            ______ x 6 = (_____ x 6) +(3 x 6)

5. Separate the rows in the large array into two small arrays. Write the new facts.

6. Match the following:

7. Use the distributive property to find the missing factor. Use counters and arrays to help.

8 x 6 = (4 x ____) +(4 x 6)

7 x 4 = (___ x 4) +( 3 x 4)

8 x ____ = (6 x ___) +(2 x5)

8. Steffen watches 4 spiders on the playground. Each spider made 5 webs. How many spider webs are there in all?

9. Easton is organizing his bug collection. He put the bugs in 5 rows with 6 bugs in each row. How many bugs are there in total?

10. Maria broke upon array for 4 x 3 into two new arrays. Both of her new arrays are the same. What were the two new arrays?

What Have We Learned:

• Understand distributive property.
• Understand an array.
• Understand how to separate large arrays into two small arrays.
• Understand break apart unknown facts into known facts and solve multiplication problems.