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### Course: Arithmetic (all content)>Unit 3

Lesson 1: Multiplication intro

# Multiplication as equal groups

Sal uses arrays and repeated addition to visualize multiplication.  Created by Sal Khan.

## Want to join the conversation?

• can you multiply fractions?
• Yes you can! Just multiply the tops of both of the fractions then the bottoms, then simplify. Hope that helps!
• who first used multiplication and in which country?
• The oldest known multiplication tables were used by the Babylonians about Iraq 4000 years ago . But he early Egyptians were the first to discover multiplication and to use it effectively as well as teach it to one another.
The modern method of multiplication based on the Hindu–Arabic numeral system was first described by Brahmagupta (598 - died after 665) was an Indian mathematician and astronomer.
Brahmagupta gave rules for addition, subtraction, multiplication and division.
• Is it possible to multiply with powers?
• can you multiply a decimal?
• Sure!
As we know when you multiply, you would line up the numbers like this:
134
* 5
-------
670

Now if you wanted to multiply a decimal, it would look like this:

10.42
* 3
--------
31.26

See? You pretty much do the same thing! However, you may stumble across the the problem where you do not know where to put the decimal. You would move the decimal to where the place value of the numbers multiplied. For example, if you did 10.001 * 3 it would be 30.003. The decimal is in the thousandths place on the first number so the answer would have it go to the thousandths place.

But remember, there is an exception to this rule. If you did 10. 05 * 2 it would be 20.1. This may be confusing, because that is in the tenths place instead of the hundredths.
This is because 10.05 * 2 really is 20.10 but you would round off the zero because it is not needed.

ΩΩΩΩΩΩΩΩΩΩΩΩΩΩΩΩΩ

This all may be confusing to grasp at first, but as you get better at math, this will make more and more sense. If you need more help, either reply or ask an adult.
• Can we multiply negative variables??
• Yes.
A negative times a negative is positive.
A positive times a negative is negative.
Ex.: (-5) x (-5) = 25
(-4) x 2 = -8
• But how do we multiply a four digit number by a four digit number?
example: 1234 times 5678
• why is the place holder zero?
• Because zero is nothing to it just takes up a place.
• At why do they do addition in multiplication?
• At , they show you that multiplication is basically just a short form for repetitive addition. It's not that they are adding and multiplying, but that they show you that multiplying is a way to add on a larger scale.

Once you know how to multiply, you will no longer have to add the same number over and over again, like 3 + 3 + 3 + 3, you can just multiply 3 * 4 and get the same answer, 12.