Subtracting Positive and Negative
Integers
Magic Bean Method
Magic Bean Model
• Green chips or tiles represent a positive 1
• Red chips or tiles represent a negative 1
• One of each tile represents a “zero pair”
-1
+1
Modeling -3 - (+4) = -7
Add three red “beans” to
represent -3
Now we have to subtract
4 positive “beans” from
the zero pairs to
represent the +4. The
negative beans that are
left now float up for an
answer of -7.
•
When subtracting using
the Magic Bean Model,
you have to keep some
“zero pairs” (which
equal zero, so have no
value) to borrow from
in the bottom of the
“jar”.
Modeling 2 – (-4)
Add two green beans to
represent the positive 2.
Now subtract 4
negative “beans” from
the zero pairs to
represent the -4. The
unmatched “beans”
will float to the top for
an answer of +6.
Start with the
zero pairs.
Rules for Subtracting Integers
• You can also use all of your rules for ADDING
integers by doing a simple change.
• When we divide fractions, we really just flip
and multiply. Similarly, when we subtract
integers, we change the sign and add.
The Rule to Remember:
KEEP, FLIP, FLIP
KEEP, FLIP, FLIP
Example:
− 3 − (− 4)
KEEP the – sign in front of the 3.
FLIP the next – sign to a +.
Flip the next – sign to a +.
You are left with an integer addition problem:
− 3 + (+4) = 1
KEEP, FLIP, FLIP
One more KEEP, FLIP, FLIP Example:
4 – (+2)
KEEP the implied + sign in front of the 4.
FLIP the negative sign.
FLIP the positive sign.
You are left with an integer addition problem:
4 + (-2) = 2