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Years B.C. + A.D.

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Date: 10/01/97 at 22:13:57
From: John Masell
Subject: 7th Grade Level Math problem

Find the difference in the ages of two people if one was born in 27
B.C.and the other was born in 16 A.D. Please explain how you got the

Thank you.
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Date: 10/06/97 at 11:28:05
From: Doctor Chita
Subject: Re: 7th Grade Level Math problem

Hi John:

This person's life spanned the year when, in the Christian calendar,
Christ was said to have been born.

A way to solve the problem is to draw a number line. For example,
suppose that a person was born in 12 B.C. and died in 35 A.D.

<--------o==========|===================================o----->
12 B.C.    0                                   35 A.D.

Put the birth date on one side of 0, and the death date on the other
side of 0. The person's age is the length of the double-line segment
between 12 B.C. and 35 A.D.

Moving from left to right, it takes 12 years to get to 0, and
35 more years to get from 0 to 35. Therefore, the person must have
been 12 + 35 or 47 years old.

Make a number line like this for your problem and see if you can
calculate the answer. Just remember to count years from left to right,
moving from the year B.C., through 0, to year A.D.

You can also use signed numbers to solve this problem. Assume that
0 divides the line into positive numbers (on the right of 0) and
negative numbers (on the left of 0). The year the person was born
can then be written as -12, and the year he or she died can be written
as +35.

The distance between the two numbers can be found by subtraction. In
my example, the person's age would equal the difference between +35
and -12. This can be written as:

35 - (-12)

Simplifying the expression gives you 35 + 12 or 47, as before. Notice
that you should subtract the earlier date (when he/she was born) from
the later date (when he/she died).

I hope this helps you solve your problem.

-Doctor Chita,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
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Date: Sun, 15 Mar 1998 19:56:46 -0500 (EST)
From: Mark Lakata
Subject: A.D. and B.C

This is not a question, but a comment on the A.D./B.C. question in the
elementry school/addition section.  Besides the difficulty with
negative numbers, I believe that the year "0" did not exist, i.e. the
year after 1 BC is 1 AD.

Otherwise I'm having fun reading this web site.

cheers,
Mark
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Date: Tue, 17 Mar 1998
From: Dr. Ken

Thanks for pointing this out.  I think there's some level of disagreement
about whether the year "0" existed, but I think the prevailing thought
agrees with you.  This is the reason many people think the new millennium
should officially begin in 2001, not 2000.

In any case, if we choose to believe that there was no year "0", then we
should simply subtract 1 from our answer to the above problem.  So if a
person was born in 12 B.C. and died in 35 A.D., they would have lived to be
12-(-35)-1 = 12+35-1 = 46 years old.

-Dr. Ken, The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
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