Welcome to a lesson on subtracting integers
using the number line.
Every subtraction problem has an equivalent
addition problem.
Welcome to a lesson on subtracting integers
using the number line. Every subtraction problem
has an equivalent addition problem. When working
with integers, we say subtracting an integer
is equivalent to adding the opposite, which
means A - B equals A + (-B) and A - (-B) = A
+ B. And we showed why this is true in the
integer chip lesson. So for each subtraction
problem we will write the equivalent addition
problem and then show the model on the number
line. The model will be the same for the subtraction
problem as well as the addition problem. We
are first given 9 minus 3. Subtracting 3 is
equivalent to adding negative 3. 9 minus 3
equals 9 plus negative 3. To model the sum
as well as the difference, we begin by modeling
positive 9 on the number line. To do this,
we begin at 0 and move right 9 units to positive
9 on the number line. From here, because we
are subtracting positive 3, which is equivalent
to adding negative 3, we move left 3 units.
So whether we are subtracting 3 or adding
negative 3, we move left 3 units, which brings
up to positive 6 on the number line, which
is the difference as well as the sum. 9 minus
3 equals 6 and so does 9 plus negative 3.
Next we have 3 minus 9. Subtracting 9 is equivalent
to adding negative 9. 3 minus 9 equals 3 plus
negative 9. To model the difference as well
as the sum, we begin by modeling 3. To do
this we start at zero, move right 3 units
to positive 3. To subtract 9 or add negative
9, we move left 9 units from positive 3, which
brings us to negative 6, which is the difference
as well as the sum. 3 minus 9 equals negative
6 and 3 plus negative 9 equals negative 6.
Next we have negative 3 minus 7. Subtracting
7 is equivalent to adding negative. Negative
3 minus 7 equals negative 3 plus negative
7. To model the difference as well as the
sum, we first model negative 3. To do this
we start at 0 and move left 3 units to negative
3 on the number line. Then to subtract 7 or
add negative 7 we move left 7 units. From
here we move left 7 units to negative 10 on
the number line. Negative 3 minus 7 equals
negative 10 and so does negative 3 plus negative
7. Next we have negative 3 minus negative
7. Subtracting negative 7 is equivalent to
adding positive 7. Negative 3 minus negative
7 equals negative 3 plus positive 7. To model
the subtraction as well as the addition, we
first model negative 3 by starting at 0 and
moving left 3 units to negative 3. Let's first
model the addition. To add 7 we would move
right 7 units from negative 3. So if we move
right 7 units from negative 3 we would be
at positive 4 on the number line, which is
the sum as well as the difference. For the
subtraction, we know if we were subtracting
positive 7, we would move left 7 units. So
when subtracting a negative number or in this
case to subtract negative 7, we do move right
7 units to positive 4. Negative 3 minus negative
7 equals negative 3 plus 7, which equals positive
4. Let's look at one more example. For the
last example we have 4 minus negative 2. Subtracting
negative 2 is equivalent to adding positive
2. 4 minus negative 2 equals 4 plus 2. To
model the difference as well as the sum, we
first model positive 4 on the number line
by starting at 0 and moving right 4 units
to positive 4. Looking at the addition first,
we know to add positive 2, we move right 2
units from positive 4, which brings us to
positive 6. 4 plus 2 equals 6, which I'm sure
we already knew. But 4 minus negative 2 also
equals 6. From positive 4 we know if we were
subtracting positive 2, we would move left
2 units and therefore because we are subtracting
negative 2 we do move right 2 units to positive
6. I hope you found this helpful.
