Question

Needing help please 322base of seven divided by 3 base of seven??? The numbers base 7 are supposed to be small right next to 322 and 3 sorry cant type it like that...thanks!

Answer 1

Yes, but the site is giving major problems and that is why you see less than the usual number of people.

I will explain how to solve this shortly.

Answer 2

First convert the base 7 number to base 10 (decimal system)

If you take a decimal number such as 348 it means:
\[348_{10} = 8 + (4 \times 10^{1}) + 3 \times 10^{2})\]

So 322 to the base 7 means:

\[322_{7} = 2 + (2 \times 7^{1}) + (3 \times 7^{2})\]

So can you calculate the right hand side and tell me what it is?

Answer 3

sorry im here now

Answer 4

ok so how did you get 2? sorry I am very confused

Answer 5

oh so its right to left?

Answer 6

2 is the last or the third digit in 322. The next 2 is the second digit. 3 is the third digit from the right.

Answer 7

Ok I understand that...so I got the answer 163 is that right?

Answer 8

Correct 322 to the base 7 is equal to 163 to the base 10 or the decimal system.

Answer 9

ok so the second part of the equation is 5base7 so its just 5 right?

Answer 10

Can you check the problem again to see if you typed all the numbers correctly?
Does it look like this:
\[322 _{7} \div 3_{7}\]

Answer 11

I have a option of answers 1) 1610seven 2) 2243seven 3)525seven 4)5523seven 5) 520seven .............just so you know........... yes it does!

Answer 12

so but I dont understand the 5 base of 7 it stays a 5 right?

Answer 13

but when I multiply 163 x 5 I dont get any of those options so confused!

Answer 14

Correct, 5 base 7 is 5.
But we are not done with the first problem yet. Are you sure the original problem says 322 base 7 divided by 3 base 7?

Answer 15

OH ok geez sorry I am horrible with math

Answer 16

See now you are saying multiplication but in the original problem you say division. Which is it?

Answer 17

It says Multiply 322seven X 5seven in the given base.

Answer 18

Sorry I wrote that wrong I see where you were getting the 3 from is where I put that wrong

Answer 19

its 5 base of seven (second part) sorry

Answer 20

Also in the original post you say "divided by" but here you say "Multiiply". Which is it?

Answer 21

Multiply

Answer 22

Sorry I have 10 of these problems I looked at the one below

Answer 23

OK. So the problem is: Multiply 322seven X 5seven
First convert each number to base 10 or the decimal system
322 base 7 = 163 base 10
5 base 7 = 5 base 10.
Once you have both in decimal you can just multiply: 163 x 5 = 815.
But the 815 is in decimal system or it is 815 base 10.
You now need to convert 815 base 10 to the base 7 system.
Do you know how to do that?

Answer 24

no thats where I dont understand

Answer 25

To convert a decimal number to base 7, keep dividing by 7 and in each step note down the remainders. 815/7 What is the quotient and what is the remainder?

Answer 26

116.4 ?

Answer 27

116 is the quotient. But don't put it in decimal form. Just divide 815 by 7 by hand (not calculator) and tell me what the quotient is and what the remainder is?

Answer 28

116R428....it just keeps going?

Answer 29

No. If I divide 5 by 2, the quotient is 2 and the remainder is 1.
If I divide 14 by 3, the quotient is 4 and the remainder is 2.

Answer 30

Sorry you probably think Im dumb but I dont see where you got the 5 by 2 and 14 by 3 sorry I appreciate your patience

Answer 31

116 R 4?

Answer 32

No "5/2" and "14/3" are my own examples I am giving you to make it clear what I am looking for when I ask what is the quotient and what is the remainder for 815/7

Answer 33

R 4 is wrong but try again.

Answer 34

Ok I see what you are doing.... did I do that right though?

Answer 35

ok let me try again

Answer 36

Ok so Im doing all by hand and I still get 116 with R 428 so forth ughhhh so confused I know division why am I not getting this

Answer 37

So quotient = 116 ; Remainder = 3

Answer 38

Do you follow the division?

Answer 39

OH YES!!!!!!!! I was going with the 3 then bringing down a zero whoops

Answer 40

Yes I understand that

Answer 41

Take the quotient 116 and divide it again by 7 and tell me the quotient and the remainder.

Answer 42

16 R 4

Answer 43

Good.
Now take the quotient 16 and divide it again by 7 and tell me the quotient and the remainder.

Answer 44

2 R 2

Answer 45

Good. Now for the last time divide the quotient 2 again by 7 and tell me the quotient and remainder.

Answer 46

you mean 7 into 2? doesnt go?

Answer 47

It goes zero times. And so the quotient is 0 and the remainder is 2. Follow that?

Answer 48

Yes I do

Answer 49

Okay, now gather up all the remainders and that will be your answer. The very first remainder we found earlier will be the last digit in the answer. The next remainder will be the next digit to the left, etc. until you have all the remainders. Can you gather up all the remainders?

Answer 50

ok let me see

Answer 51

2243 right?

Answer 52

cause we are going left to right right?

Answer 53

I mean right to left duh

Answer 54

Correct! But you should say 2243 base 7.
So when we convert 815 base 10 to base 7 system we get 2243 base 7.

Answer 55

YES that makes sense!!!!!!!!!!!!!!!!! Thank you!!!!!!! gosh now I have 9 more of these and some are division and addition great!