In this lesson, we will subtract integers
using the number line
and the comparison model.
The directions are to
first plot the numbers
in a subtraction problem
on the same number line,
draw a directed arrow
from the second number to
the first number.
Where the first number
is called the menu end,
and the second scepter end.
Determine their distance from each other
by counting, then determine
the sign of the answer
by determining whether the
arrow points left or right.
If the arrow points to the left, or in the
negative direction,
the answer is negative.
If the arrow points to the
right or the positive direction,
the answer is positive.
Let's first consider positive
seven minus positive two.
We begin by plotting positive
seven and positive two
on the number line,
and now because the two is second and the
seven is first, or because
the scepter hand is two,
and the menu end is
seven, we draw an arrow
from two to seven on the number line.
Notice how the arrow points to the right,
indicating the difference is positive.
But the next question
is, what is the distance
between the two numbers?
The distance between two and seven is
five units or five.
The next question is, what
is the sign of the answer,
is it positive or negative?
Again, because the arrow
points to the right,
the answer is positive.
Which means, positive
seven minus positive two
equals positive five.
This is difference is
positive five because
seven is five more than two.
Now lets change the
order of the subtraction,
and consider two minus seven.
The first step is to plot two and seven
on the number line.
But now because the
menu end is two and the
scepter hand is seven, or
because the first number is two
and the second number is seven,
we draw an arrow from positive
seven to positive two.
Notice now, the arrow points to the left,
or in the negative direction.
The distance between the
two numbers is still five,
but now because the
arrow points to the left,
the answer is negative.
Which means, two minus
seven equals negative five.
This difference is negative
five because positive two
is five less than positive seven.
Let's look at some more examples.
Here we have negative
two minus positive five.
We begin by plotting negative
two and positive five
on the number line.
And now we draw an arrow from
the five to the negative two,
notice how the arrow points
to the left, which means the
difference is negative.
But the next question
is, what is the distance
between the two numbers,
the distance between
negative two and positive
five is seven units, or seven.
Next, because the arrow
points to the left,
the answer is negative.
Which means, negative two minus
five equals negative seven.
The reason this difference
is negative seven
is because negative two is
seven less than positive five.
Next we have positive
two minus negative five,
we begin by plotting positive
two and negative five
on the number line.
Because the second number is negative five
and the first number is positive two,
we draw an arrow from
negative five to positive two,
notice the arrow points to the right,
indicating the difference is positive.
The distance between the two numbers is
seven units or seven.
Because the arrow points to the right,
the answer is positive.
Which means two minus negative
five equals positive seven.
The difference is positive
seven because positive two
is seven more than negative five.
Let's look at two more examples.
Here we have negative
nine minus negative four.
We first plot negative
nine and negative four
on the number line.
Because negative four
is the second number and
negative nine is the first,
we draw an arrow from
negative four to negative nine.
The arrow points to the left,
indicating the difference is negative.
The distance between the two
numbers is five units or five.
The sign is negative,
because the arrow points
to the left.
Which means, negative
nine minus negative four
equals negative five.
The difference is negative
five because negative nine
is five units less than negative four.
And for the last example, notice how the
first number and the second
number, or the menu end
and scepter hand are the
same, so we plot negative six
on the number line.
In this case though,
we cannot draw an arrow
from the second number
to the first number,
because it's the same number.
And therefore, the distance
between the two numbers
is zero, and zero is
not considered positive
or negative, but now we
do know the final answer
is negative six minus
negative six equals zero.
I hope you found this helpful.
