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# Adding 7 + 6

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?(28 votes)
- 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(40 votes)

- 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?(14 votes)- There are infinite possibilities because you can add negitive numbers to positive numbers. For example, 15+(-2) is 13.(8 votes)

- The number line is infinite. What does "infinite" mean? Is it complete?(10 votes)
- Here is an interesting piece of entomology, study of words. Finite means ending. In, as a prefix means not. So infinite means not ending.(11 votes)

- so when ever you add a even nuber and a odd number you will get a odd?(11 votes)
- Yes.

Even+Even=Even (6+8=14)

Odd+Even=Odd (6+5=11)

Odd+Odd=Even (3+7=10)(3 votes)

- Would it still work as "6 + 7"?(10 votes)
- 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!(5 votes)

- 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(5 votes)- 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)(6 votes)

- 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.(5 votes)

- Is it the same to add bigger numbers like hundreds or higher? Or does what you do change?(2 votes)
- Coleman Vaughn,

Yes. its all the same.(0 votes)

- 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?(0 votes)
- 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".

[1] https://www.smartick.com/blog/mathematics/addition-and-subtraction/review-vertical-adding/(2 votes)

- I still have trouble adding 7 + 6. Any more tips?(0 votes)
- Well, you can start with the basics of adding the numbers that are relative together (6+6) then add the remainders. Particularly, an easier equation will help in solving the your main problem.

(6+6) = ?

? + 1 = [The Solution](1 vote)

## Video transcript

Voiceover:Let's think about
what seven plus six is, and I encourage you to pause this video and think about it on your own. I'm assuming you've given a go at it. Let's think about it. We could do this as seven objects plus six more objects, and then think about how
many total objects we had. For example, we could view
it as seven, say, tomatoes, so one tomato, two tomatoes, three tomatoes, four tomatoes, five, six, and seven, and then to that, we're going to add six more objects. Let's say they're blueberries, and we care about the
total amount of fruit. So, one, two, three, four, five, and six - six blueberries. Now, how many total pieces of fruit do I have in all now? I started with seven, so that's seven. If I keep counting, this is seven so this is going to be eight, nine, 10, 11, 12 and 13. I now have a total of 13 pieces of fruit - 13 pieces of fruit. What are other ways that we could have thought about this? We could have also done
it on a number line. Let's draw ourselves a number line. Let me do this in a color that I haven't used yet, actually. Let's say I have a number line just like that. I can start the number line at seven. I could start at seven, and I'm going to add six more. I'm going to move six
more up the number line. This is one, two, three, four, five, six, and, of course, I could keep going. It's going to be eight,
nine, 10, 11, 12, 13. Of course, you could keep on going. Seven plus six - you could visualize this as starting at seven, and then making six jumps
up the number line - one, two, three, four, five, six. Either way, we get to 13. Another way to think about it is, look, we started with seven. We added three to get to 10, and so we have to add another three, which gets us to 13. That really goes to the heart of what the number 13 represents. The number 13 has a one as its left digit, This digit is in the tens place, so it literally represents one 10. So, it's one 10 plus
three, plus three ones. You see that right over here. When I added the pieces of fruit, this right over here is one group of 10. So, that's one group of 10. We had to add three to get to that one group of 10. We kind of filled that bucket, and then we had three more, so when you add seven plus six, you fill one whole group of 10 and then you have three ones left over. This is the three ones right over here. Another way you could think about it is seven plus six is the same thing as 10 plus three, which, of course, is 13. This is the same thing - one 10 is 10, plus three, plus three ones - 13 either way you look at it.