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.
![Distributive property](https://www.turito.com/learn-internal/wp-content/uploads/2023/07/Distributive-property.png)
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.
![An Array](https://www.turito.com/learn-internal/wp-content/uploads/2023/07/An-Array.png)
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?
![Pictures displayed on a wall](https://www.turito.com/learn-internal/wp-content/uploads/2023/07/Pictures-displayed-on-a-wall-1-1024x734.png)
Solution:
Step 1: Break apart 5 rows into 3+2.
![5 Rows](https://www.turito.com/learn-internal/wp-content/uploads/2023/07/5-Rows-1024x510.png)
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.
![Hint on Distributive Property](https://www.turito.com/learn-internal/wp-content/uploads/2023/07/Hint-on-Distributive-Property-1024x146.png)
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?
![8 rows of chocolets](https://www.turito.com/learn-internal/wp-content/uploads/2023/07/8-rows-of-chocolets.jpg)
Solution:
Step 1: Break apart 8 rows into 4 + 4.
![8 rows into 4 + 4](https://www.turito.com/learn-internal/wp-content/uploads/2023/07/8-rows-into-4-4.png)
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.
![The Distributive Property](https://www.turito.com/learn-internal/wp-content/uploads/2023/07/The-Distributive-Property-1-1024x146.png)
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?
![Each row had 4 drinks](https://www.turito.com/learn-internal/wp-content/uploads/2023/07/Each-row-had-4-drinks.png)
Solution:
Step 1: Break apart 7 rows into 4 + 3.
![7 rows into 4 + 3](https://www.turito.com/learn-internal/wp-content/uploads/2023/07/7-rows-into-4-3.png)
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.
![The Distributive Property](https://www.turito.com/learn-internal/wp-content/uploads/2023/07/The-Distributive-Property-2-1024x146.png)
Concept Map:
![Concept Map](https://www.turito.com/learn-internal/wp-content/uploads/2023/07/Concept-Map-26-1024x657.png)
Exercise:
- How many rows and columns are there in the below array?
![Rows and columns](https://www.turito.com/learn-internal/wp-content/uploads/2023/07/Rows-and-Columns-2.png)
2. Separate the rows in the large array into two small arrays.
![Separate-large array into two small arrays](https://www.turito.com/learn-internal/wp-content/uploads/2023/07/Separate_large-array-into-two-small-arrays.png)
3. Separate the rows in the large array into two small arrays. Write the new facts.
![The rows in the large array](https://www.turito.com/learn-internal/wp-content/uploads/2023/07/The-rows-in-the-large-array.png)
4. Use the smaller arrays and distributive property to find the missing factor. You may use counters to help.
![distributive property](https://www.turito.com/learn-internal/wp-content/uploads/2023/07/Distributive-property-1-1024x651.png)
______ x 6 = (_____ x 6) +(3 x 6)
5. Separate the rows in the large array into two small arrays. Write the new facts.
![Separate-The large array into two small arrays](https://www.turito.com/learn-internal/wp-content/uploads/2023/07/Separate-The-large-array-into-two-small-arrays-1024x355.png)
6. Match the following:
![Match the following](https://www.turito.com/learn-internal/wp-content/uploads/2023/07/Match-the-following-1024x371.png)
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.
![Distributive Property](/_next/image?url=https%3A%2F%2Fwww.turito.com%2Flearn-internal%2Fwp-content%2Fuploads%2F2023%2F07%2FThe-Distributive-Property.png&w=1920&q=50)
Related topics
Addition and Multiplication Using Counters & Bar-Diagrams
Introduction: We can find the solution to the word problem by solving it. Here, in this topic, we can use 3 methods to find the solution. 1. Add using counters 2. Use factors to get the product 3. Write equations to find the unknown. Addition Equation: 8+8+8 =? Multiplication equation: 3×8=? Example 1: Andrew has […]
Read More >>Dilation: Definitions, Characteristics, and Similarities
Understanding Dilation A dilation is a transformation that produces an image that is of the same shape and different sizes. Dilation that creates a larger image is called enlargement. Describing Dilation Dilation of Scale Factor 2 The following figure undergoes a dilation with a scale factor of 2 giving an image A’ (2, 4), B’ […]
Read More >>How to Write and Interpret Numerical Expressions?
Write numerical expressions What is the Meaning of Numerical Expression? A numerical expression is a combination of numbers and integers using basic operations such as addition, subtraction, multiplication, or division. The word PEMDAS stands for: P → Parentheses E → Exponents M → Multiplication D → Division A → Addition S → Subtraction Some examples […]
Read More >>System of Linear Inequalities and Equations
Introduction: Systems of Linear Inequalities: A system of linear inequalities is a set of two or more linear inequalities in the same variables. The following example illustrates this, y < x + 2…………..Inequality 1 y ≥ 2x − 1…………Inequality 2 Solution of a System of Linear Inequalities: A solution of a system of linear inequalities […]
Read More >>Other topics
![demo](https://a.storyblok.com/f/128066/544x376/641160f2e6/learn_toast.webp)
Comments: