In this lesson, we'll be
working on operations with real numbers, specifically
with integers. We've got examples
of integers listed here.They're positive and
negative whole numbers, like negative 3, negative 2, negative 1, 0, 1,2,3 and so on in
both directions. [NOISE] To add integers, if the integers
have the same sign, you'll add and keep the sign. If the integers have
different signs, you will subtract the
absolute value and keep the sign of the number with the larger absolute value. Remember that absolute value always gives you a
positive number. The absolute value of something
like negative 3 is three. The absolute value of
three is also three. Absolute value can
be thought of as the distance a
number is from zero. Let's look at Number 1. We get negative 3
plus negative 8. Those both have a negative
in front of them, so they have the same sign. We're going to add three
and eight together. That's the absolute value
of those two numbers. 3 plus 8 is 11. We're going to keep
the negative sign, so that'll be negative 11. Number 2, we have 18 plus 89. There's no negative
signs in there. Both those numbers are positive. I'm going to just
add 18 plus 89. Eight and nine is 17, 8 plus 1, plus 1 is 10. We get 107, added the numbers together
and we kept the sign. Number 3, negative 23 plus 85. The 23 is negative,
85 is positive. They have different signs, so we need to subtract
their absolute value. Right now we're not
going to really worry about the signs, which is know that that
tells us to subtract. The biggest absolute value
on top 5 minus 3 is 2, 8 minus 2 is 6. I got 62. I'm going to look
back at my numbers. Which is bigger 23, or 85? Eighty-five is the
larger number. My answer is going
to be positive 62 because 85 is
bigger than the 23, and 95 is positive. Number 4, 8 plus negative 3. The eight is positive, the three is negative. They have different signs. Subtract the absolute value. 8 minus 3 is 5. Now I have to
determine the sign. The sign is determined
by the number with the larger absolute value. Eight is bigger than three, eight has the larger
absolute value it is positive so my
answer is positive 5. Number 5, negative
26 plus negative 18. Both numbers are negative, so I'm going to add the
absolute value together, 26 and 18, 6 and 8 is 14, 2 and 1 and 1 is four. I get 44. The rule is if they have the same sign you
add and you keep the sign, they're both negative, so
my answer is negative. Number 6, 28 plus negative 32. Twenty-eight is positive,
32 is negative. I'm going to subtract
those two numbers 32 minus 28 is 4. Now I need to think
about what the sign is going to be on the four. Thirty-two has a larger
absolute value than 28, 32 is negative, so my
answer is negative 4. Let's do subtraction. Subtraction is like addition, except we're going to use the
rule, keep change, change. We're going to keep the
sign of the first number, change the subtraction
to an addition, and then change the sign
of the second number. An alternative
approach to this is, is just to pool that subtraction
sign into the number. For now I'm going to do
keep change, change. On Number 1 we have 7 minus 5. We know, that's
two, but let's use the rule and see how it works. We keep the sign on the seven. It's currently positive. There's no sign there,
so we know it's positive. We're
going to keep that. We're going to change
the subtraction sign to an addition sign, and then change the sign
on the five to negative. 7 plus negative 5 now
use your addition rules. We've got a positive
7 and a negative 5. Those signs are different, so we subtract 7
minus 5 and get 2. Then we determine the sign by whichever one has the
larger absolute value. Seven has the larger
absolute value. It's positive, so
my answer is two. Number 2, 5 minus 9. Keep the sign on the five, change the subtraction
to an addition, and then change the sign
of the nine to negative. Now they have different signs. The five is positive, the nine is negative. Subtract 9 minus 5 and get 4. Which one has the larger
absolute value five or nine? Well, nine is larger.
Nine is negative, so my answer is negative 4. Number 3, keep change, change, keep the sign on the negative 9, change the subtraction
to an addition problem, and then change the sign on the second number to a positive. I get a negative 9
and a positive 13. They have different signs, so we subtract the
absolute value. 13 minus 9 is 4,13 is
the larger number, 13, bigger than 9. It is positive so my
answer is positive 4. Number 4, I'm going to
keep change, change, keep the sign on the 17, change the subtraction
to an addition problem, and change the sign on
the following number. Now we have 17 plus 26. We just need to add
those together. They have the same signs. I'm going to add
and keep the sign. The answer is positive 43. Number 5, negative 18 minus 5. We're doing keep change, change, keep the sign on the first one. Negative 18 stays. Change the subtraction to an addition problem and change the sign on
the following number. We have negative 18
plus negative 5. They both have a minus sign. Add the absolute value of
those two numbers 18 and 5 is 23 and we keep the sign
that they both have. Then on Number 6 we have
negative 23 minus 37. Keep the sign on
the negative 23, change the subtraction
to an addition, and change the sign on
the 37 to negative. Now they're both negative,
negative 23 and negative 37. We'll add the absolute
value in 23 plus 37, 60. Both numbers are negative, so we're going to
keep that sign.