Integers you use in everyday life?

Answer 1

I presume you're talking in particular about places where we use

numbers that may be either positive or negative, and it's really

helpful to be able to treat them as the same kind of number, instead of

needing a separate rule for each combination of negative and positive

numbers. Some examples aren't really integers but positive or negative

real numbers.

How about temperatures? Conversion between Fahrenheit and Celsius on a

sub-freezing day is a good exercise in using negative numbers.

Elevations go negative in places like Death Valley and the Dead Sea.

Comparing the base-to-peak heights of Mount Everest and Mauna Loa is

an exercise in subtracting negative numbers.

Latitude and longitude are easier to work with if you take east/north

as positive and west/south as negative. The most obviously useful

calculation here is in working with time zones - you'll find charts

with time zones labeled EST = -5, Eastern Europe = +2, etc.

Years are a peculiar case. AD and BC were invented around AD 525,

before negative numbers (or zero) were really understood, so there was

no year zero. The year after 1 BC was AD 1. If it had been done right,

we would have been able to compute the years between 43 BC and 33 AD

as 33 - (-43) = 76. But because dates aren't integers, you have to say

33 + 43 - 1 = 75. In other words, when the calendar was devised, people

just accepted the need for special cases, but with the invention of

integers, we found a better way.

By the way, the federal government does not assume that taxpayers

understand integers, so the 104 form uses the special-case approach:

"If line 64 is LESS than line 59, subtract line 64 from line 59 and

write it in line 65. If line 64 is GREATER than line 59, subtract line

59 from line 64 and write it in line 66." (That's the idea anyway, I

got my form yesterday but I don't have it in front of me.)

I can't think of any everyday cases where we multiply negatives by

negatives. But when your students learn about quadratic equations,

they will be benefiting again from the no-special-cases property of

integers. Early developers of algebra had to present solutions for 6

kinds of quadratic equations:

Money can also be used as an integer because when you think about it as its in piggy bank going in and out of it, it makes you think about it.