help adding bases!!? please?

Question

435 base 7
+ 51 base 7
____________

I need details so i can really understand thank you so much!

Answer 1

Same rules, but 7 = 10. so 8 = 11, 9 = 12, etc.
So base 7:
435
+51
------
516

Alternatively,
435 + 51
= (4*7² + 3*7 + 5) + (5*7 + 1)
= 4*7² + 8*7 + 6
= 4*7² + (7+1)*7 + 6
= 4*7² + 7² + 1*7 + 6
= 5*7² + 1*7 + 6
= 516

Answer 2

Bases are kind of annoying to deal with but here's how I'd handle it.

In base 10 (the one we're used to) you have 10 digits to represent a number before you need to carry to the higher space (the 10's, 100's, 1000's etc). When you talk base, that is how many digits you have to play with.

SO break it down from the right hand side:

5 = 5 - in base 7 you have numbers 0 - 6 to deal with. If you add 1 above 6, then you have to carry and add a digit to the 7's slot. 5 < 7 therefore 5 = 5 (in base 10)

3 - this is the 2nd digit which is where you put carries when you have exceed 7. It is 3 which means you have done this 3 times, therefore this is equal to 21 (in base 10)

4 - this is the 3rd digit which is where you put carries when you have exceeded 7 * 7. This is because the second digit can also go up to 6 which it does when you have carried 7 , 6 times. Therefore when you get to the 3rd digit, you've carried 7, 7 times so it is equal to 7 * 7. It is 4 which means you have dones this 4 times. Therefore this is equal to 4 * 49 = 196 (in base 10).

So 435 base 7 = 196 + 21 + 5 = 222 (base 10)

Now the second number is:
1 from the right number
5 carries of 7 = 35
SO this is 36 (base 10)

Their sum is 258 base 10. To get back to base 7 you need to go the other way. 258 is > 5 * 49 and < 6 * 49 so the left most digit is 5. 5 * 49 = 245 so the remainder is 13. This is > 1 * 7 and < 2 * 7 so your 2nd digit is 1 and your remainder is 6. So your final value is 516 base 7

I think that's right.

Answer 3

from right to left, 1+5=6, 3+5=1carry 1, 1+4=5
516 base 7, think of it like the regular numbers we work with, which are base 10. Once you add 9+1, you have to start over, so technically 9+1=0, carry a 1, which 10.
Whenever you have a number in a certain base, know that you will never get a single digit that is greater than the base. So in base 7, all your numbers whenever you add or subtarct are always between 0-6. Take base 2 for example. Every numbers are always represented by 0 or 1, or a combination of the two. All you have to do is extend what you know about base 10 and apply it to other bases.

Let me show you the first few numbers of base 7
0, 0+1,1+1, 2+1, 3+1, 4+1, 5+1, 6+1, 10+1, 11+1, 12+1, 13+1, 14+1, 15+1, 16+1
In order they are written you have
0,1,2,3,4,5,6,10,11,12,13,14,15,16,20

Answer 4

Greetings,

base 7 has digits 0,1,2,3,4,5,6

just like normal addition but with different carrying rules

Lets start at the right and see

5 + 1 = 6 all ok nothing to carry

3 + 5 = 11 base 7 so write down a 1 and carry 1

4 + 1 = 5

giving 516 base 7 as the answer

Regards

Answer 5

= 486 base 7

Answer 6

49___7___1
4____3___5
0____5___1
¹__________
5____1___6