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Lesson 5: Distributive property

# Properties and patterns for multiplication

Sal changes the order of numbers or decomposes numbers to simplify multiplication problems.    Created by Sal Khan.

## Want to join the conversation?

• why arent you following the order of operations? paranthesis first right?
•   I assume you are referring to about in the video where Sal changes 4*(5+2) into 4(5)+4(2).
Sal is using the distributive property. It distributes multiplication across addition or subtraction. It is an acceptable way of eliminating parentheses.
Hope this helps.
• how would you solve (6x4)x5
can you solve that or no because the 5 should be in the front
•    You would solve that still as normal, but follow the order of operations(Parentheses, Exponents, Multiplication & Division, Addition & Subtraction) and do (6x4) first, then multiply that by 5. You could rearrange the equation as 5x(6x4) and the answer would still be the same, because of the Communicative Property. You would always do the expression within the parentheses first because that's how the order of operations goes. With these numbers though, you can rearrange the numbers however you want(whichever one makes it look the simplest to you) and the answer would always be the same, just make sure the operators stay the same(i.e don't turn the multiplication into division or subtraction).
• is this boring for you guys cus this is boring for me • why is it that when a number is out alone ( with no operation) next to parenthesis that you have to multiply
• I don't understand what he says about distributing the number, in this case 6, to 30 and 6.
• Think of 6x36 as 36 groups of 6, and note that 36 = 30+6.
30 groups of 6 are 30x6 = 180.
6 groups of 6 are 6x6 = 36.
So 6x36 = (6x30)+(6x6) = 180+36 = 216.

The distributive property is very important in arithmetic, algebra, and higher levels of math. Make sure to take the time to understand it well and get more help if you need it. This property says that when we multiply a number by a sum (or difference) of two or more numbers, we can multiply this number by each number in the sum (or difference), then add (or subtract) the products.

Have a blessed, wonderful day!
• how many properties of multiplication are there?
• There are four properties involving multiplication that will help make problems easier to solve. They are the commutative, associative, multiplicative identity and distributive properties.

Commutative property: When two numbers are multiplied together, the product is the same regardless of the order of the multiplicands. For example 4 * 2 = 2 * 4

Associative Property: When three or more numbers are multiplied, the product is the same regardless of the grouping of the factors. For example (2 * 3) * 4 = 2 * (3 * 4)

Multiplicative Identity Property: The product of any number and one is that number. For example 5 * 1 = 5.

Distributive property: The sum of two numbers times a third number is equal to the sum of each addend times the third number. For example 4 * (6 + 3) = 4*6 + 4*3
• I get the concept but does anyone have helpful hints for remembering 7's so I do not have to skip count / break it down every time like @ ?
• How can I remember the Order of Operations
•  I learned order of operations with the phrase "Please Excuse My Dear Aunt Sally". The "P" means to solve the parentheses first, if there are any. "E" is the second step: solve exponents. "M" and "D" means to solve multiplication and or division. Be sure to solve from left to right! Lastly, "A" and "S" means to solve addition and subtraction, moving from left to right.
For example, (4+3) + 5^2 x 7 - 8 would be solved by PEMDAS:
Step 1. Solve parentheses. 7 + 5^2 x 7 - 8
Step 2. Solve exponents. 7 + 25 x 7 - 8
Step 3. Solve multiplication/division. 7 + 175 - 8
Step 4. Solve addition/subtraction. 182 - 8
= 174
•  