Homework Help

If 263+441 = 714 what is the base used. Please help me. A.5 B.6 C.7 D.8 E.9

user profile pic

christiano-cr7 | Salutatorian

Posted June 24, 2013 at 5:41 AM via web

dislike 1 like

If 263+441 = 714 what is the base used. Please help me.

A.5

B.6

C.7

D.8

E.9

1 Answer | Add Yours

user profile pic

jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted June 24, 2013 at 6:04 AM (Answer #1)

dislike 1 like

You need to be little tricky here.

The familiar base for us is base 10. As you know we use numbers 0 to 9 under base 10 to define any number. What important is we never use 10.

So if it is base 2 we never use 2. If it is base 4 we never use 4. The largest number we can use to define a number is 1 less than the base. If base is 10 the highest is 9. If 2 highest is 1 and for 4 it is 3.

`263+441 = 714`

Here we have number 7. So according to the above explanation you will never get base 5,6,7 as the answer.

Let us assume the answer is base 8.

`263_8 = (64xx2+8xx6+3)_10 = 179_10` (Because we are familiar with base 10)

`441_8 = 289_10`

 

`(263+441)_8 = 179+289 = 468_10`

`714_8 = 460_10`


So base 8 is not the answer. So definitely base 9 would be the answer.

`(263+441)_9 = 81xx2+9xx6+3+81xx4+9xx4+1 = 580`

`714_9 = 81xx7+9xx1+4 = 580`

 

So the answer is base 9. Answer is E.

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes