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### Course: 3rd grade (Eureka Math/EngageNY)>Unit 1

Lesson 6: Topic F: Distributive property and problem solving using units of 2–5 and 10

# Properties of multiplication

Sal uses pictures and practice problems to see commutativity and associativity in multiplication.   Created by Sal Khan.

## Want to join the conversation?

• What is PEMDAS?
• This is called the order of operations, which we call PEMDAS because there is a reason behind it.

P (Parentheses)
E (Exponents)
M (Multiplication)
D (Division)
S (Subtraction)
Or as my teacher calls it- Please Excuse My Dear Aunt Sally, which also contains the same abbreviation- I don't get it.
But there is an example for this.
Let's say you have this problem on your test ( or whatever )
(64*3)+ ( 54 divided by 4 )- 13=x

• what property is 4(x+3)=(x+3)4
• That would be the commutative property of multiplication because 4 and (x+3) are switched.
• Hi in multiplication how would you calculate three digit numbers? Example 124 multiplied by 675= what?
• An interesting method is the Vedic (Indian) multiplication method called vertical and crosswise, which is not usually taught in U.S. schools.

Step 1: Multiply first digits: 1x6 = 6. This represents 6 ten-thousands so far.

Step 2: Cross multiply the first two digits by the first two digits, and add the products: (1x7)+(2x6) = 7+12 = 19. This represents 19 thousands. Adding this to 6 ten-thousands (or 60 thousands) gives a total of 79 thousands so far.

Step 3: Cross multiply the three digits by the three digits, and add the products: (1x5)+(2x7)+(4x6) = 5+14+24 = 43. This represents 43 hundreds. Adding this to 79 thousands (or 790 hundreds) gives a total of 833 hundreds so far.

Step 4: Cross multiply the last two digits by the last two digits, and add the products: (2x5)+(4x7) = 10+28 = 38. This represents 38 tens. Adding this to 833 hundreds (or 8,330 tens) gives a total of 8,368 tens so far.

Step 5: Multiply last digits: 4x5 = 20. This represents 20 units. Adding this to 8,368 tens (or 83,680 units) gives a final answer of 83,700.

Have a blessed, wonderful day!
• [Solved]At do you have to put the second numbers in brackets?
• No, the brackets just tell you what order to operations in. With multiplication, you can do it in any order
(2x3) x4 and (3x4)x2 are going to mean the same thing.
• If I had an equation like this (6+3)x9 could I switch the 9 to the front of the equation like this 9x(6+3)
• Yes, you will get the same answer either way.
• Do you need the parenthesis to solve the problems?
• ( )- these are parentheses
parentheses are used in math to define which part of a problem should be done first in order to get the desired answer.
for example: 5+(3*6)=?
Since the parentheses are around 3*6, then that means that you have to multiply 3*6 first and then add 5 to the product of 3*6, or 18.
So basically, you would solve it like this-
5+(3*6)=?
5+18=?
5+18=23
And so the answer is 23.
• How did he know 8 divided by 3 was a fraction of 8 over 3?
• 8 over 3 is a different way to divide
• Why is it called the commutative property?
• The word "commutative" comes from "commute" which means to move around. In multiplication, the commutative property says you can move the numbers around and it is still the same answer. So, it's called commutative property because you can move the numbers around, hence "commutative."
• who came up with PEMDAS and why?
`8x9=?` can be pronounced 'eight times 9 equals what?', or one can say 'what is the product of 8 and 9?'