 # Subtracting Positive and Negative Integers

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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