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Lesson 3: Associative property of multiplication

# 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?
• Parentheses
Exponents
Multiplication, Division (left to right)
• what is products
• The answer to an addition problem is a sum, subtraction, a difference. A product is the answer to a multiplication problem.
• 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!
• thank you but how is this gonna be used in my day to day life?
• [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.
• what property is 4(x+3)=(x+3)4
• That would be the commutative property of multiplication because 4 and (x+3) are switched.
• what is exponents
• Good question for 3rd grade!

The exponent (or power) is a raised number that tells us how many times to multiply the base (bottom number) by itself.

Example: if the base is 2 and the exponent is 3, we get 2 * 2 * 2 = 8.
So 2 to the 3rd power is 8.
This is also written as 2^3 = 8.

Note that 3^2 would give a different answer: 3 * 3 = 9.
So the order of the base and the exponent is important.

Later in math, you will learn how to do calculations with zero, negative, and fractional exponents.

Have a blessed, wonderful day!
• 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)