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Lesson 2: Multiply 2-digit numbers with area models

# Multiplying with area model: 78 x 65

Sal uses an area model to multiply 78x65. Created by Sal Khan.

## Want to join the conversation?

• if you do 78 times 65 and then 65 times 78 will you get the same answer?
• 78*65=5070
65*78=5070
78*65=65*78
You will get the same answer because of the commutative property of multiplication.
• at he says "i just made it a little more explicit" what does that mean in math?(i know it does not mean what it normally means)
• According to the Merriam-Webster dictionary, explicit means "fully revealed or expressed without vagueness, implication, or ambiguity : leaving no question as to meaning or intent".
Basically, he's saying that he made it easier to see; in this use, it's just a general phrase, not a math one.
• all you have to do is multiply the numbers then you add then all up and you get your answer its that easy
• my mom said please make this easily pls
• yes make it more easy
(1 vote)
• sal how do this stuff are you really good at it
• because hes the best
• me just wondering what he just did
• Say you have 3 × 25 on a rectangle. Add 3× 2 which would be 6 and then add 3× 5 which would be 15 add 6+ 15 which would be 21. That is your answer. I hope this helps!💖
• What are factors
• Factor, in mathematics, a number or algebraic expression that divides another number or expression evenly—i.e., with no remainder. For example, 3 and 6 are factors of 12 because 12 ÷ 3 = 4 exactly and 12 ÷ 6 = 2 exactly. The other factors of 12 are 1, 2, 4, and 12.
• Isn't the shape a square? If not I'm confused.
• No it isn't. It's a rectangle.

So basically we represent this multiplication with 4 major squares.

70 * 60
1. Tens Digit * Tens Digit (The largest one)

70 * 5
2. Tens Digit * Ones Digit (The light green)

8 * 60
3. Ones Digit * Tens Digit (The purple)

8 * 5
4. Ones Digit * Ones Digit (The blue)

Then the sum of all areas are equal to 78 * 65.

Let's observe 70 * 60 and 70 * 5.

When we add those areas together, we are basically saying
70 * 60 + 70 * 5
Factor the 70 out
70 * (60 + 5)
= 70 * 65

Now, let's observe 8 * 60 and 8 * 5.
8 * 60 + 8 * 5
= 8 * (60 + 5)
= 8 * 65

Last, we add these 2 areas together.
70 * 65 + 8 * 65
= (70 + 8) * 65
= 78 * 65