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### Course: Early math review>Unit 4

Sal adds 7 + 6 using the number line. Created by Sal Khan.

## Want to join the conversation?

• Why are number lines used? Isn't the adding or taking objects away thing easier than a number line?
• You will need to know numbers lines later on, when you start geometry with points, lines, curves and vectors.
Also, numbers lines can be more useful than objects when it comes to:
* Negative numbers
* Large numbers (think thousands)
* Decimal numbers (1.623, 76.8).
* Skip counting
• Hey, I'm curious to know if someone wants to answer my question.
Can someone tell me all the possibilities (of additions) to make 13?
• There are infinite possibilities because you can add negitive numbers to positive numbers. For example, 15+(-2) is 13.
• The number line is infinite. What does "infinite" mean? Is it complete?
• Here is an interesting piece of entomology, study of words. Finite means ending. In, as a prefix means not. So infinite means not ending.
• so when ever you add a even nuber and a odd number you will get a odd?
• Yes.

Even+Even=Even (6+8=14)
Odd+Even=Odd (6+5=11)
Odd+Odd=Even (3+7=10)
• Would it still work as "6 + 7"?
• Yes! There is this one law for adding numbers, which is called the Commutative Law.

This Commutative Law states that
When we add or multiply two numbers then the resultant value remains the same, even if we change the position of the two numbers. Or we can say, the order in which we add or multiply any two real numbers does not change the result.

In short, a + b = b + a.

If we have more terms, let's say
a + b + c, does it equal to b + a + c?

We can consider a + b first
Since a + b = b + a, we get
b + a + c, which is what we wanted!
• Is there an easier and quicker way to work it out? If there is then you should edit the video. I know the other ways are quick but what if you have to answer it instantly?

Kindly Regards
Emma Winstanley
• If you know what 7+7 is, than all you need to do is subtract one. Since 7+7 = 14, 7+6 = 13. (That is the easiest way to answer it fast besides memorizing it)
• how do you do expanded form on one-digit numbers?
(1 vote)
• Whatever one-digit number you choose, will already be in its expanded form.
• Is it the same to add bigger numbers like hundreds or higher? Or does what you do change?
• Coleman Vaughn,
Yes. its all the same.
• Is there a certain rule mathematicians use for deciding whether to write out an equation vertically or horizontally, or is it a matter of personal preference?
• It should only be written horizontally.

The expression you seen that is written vertically is called the vertical addition. Vertical addition is a method of adding where the numbers are lined up in columns according to their place values. [1]

We use vertical addition because it is clearer to compute as place values are lined up.

In short, when representing equations formally, we only write the equation horizontally, and never write it vertically, which is used for "self notes".