Activity 9
Math 84
Rules for simplifying Integers
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TASK 1:Adding Integers (Positive and Negative Whole Numbers)
1. Simplify the following:
a) 1 + (-7)
b)
5 + (-3)
c) -9 + (-4)
d)
8 + (-15)
2. Explain in your own words how to add positive and negative numbers;
a) Case 1: When the two numbers have the same signs, what do you do to add
them?
b) Case 2:
When the two numbers have different signs, what do you do to add
them?
TASK 2: Subtracting Integers
1. Simplify the following:
a)
5–9
b)
(-2) – 4
c)
6 – (-1)
d)
-13 – (-3)
2. Explain in your own words, how to subtract positive and negative numbers
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TASK 3: Another Approach for Adding and Subtracting Integers
When you have double signs (two signs in terms of positive and/or negative signs, that occur
right next to each other), we can change this to a single (just one) sign.
If the double signs are the same, “+ +” or “- -“, then we can change this to a “+”. And if the
double signs are different, “+ -“ or “- +”, then we can change this into a “-“
1. Change the double signs into a single sign in the following:
a) 5 + (-7)
b) -3 – (-2) + 8 – (-9) + (-13)
After we change double signs into a single sign we may then, organize the numbers in columns,
depending on what sign is in front of them. We would then add the numbers that are in the
same columns together. Next, we can subtract the totals from each other and the answer
would include the sign of the largest total.
2. Now, let’s simplify: -3 – (-2) + 8 – (-9) + (- 13)
3. a) Simplify: -19 – (-2) – 52
(Change the double signs first)
b) 23 – (-15) – (-6)
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TASK 4: Multiplying Integers
1. Simplify the following:
a. 3(-7)
b) -2(-6)
b)
(-8)(9)
d)
-4(3)
2. Explain in your own words how to multiply positive and negative numbers.
a. Case 1: When the two numbers have the same sign, what do you do to multiply
them?
b. Case 2: When the two numbers have different signs what do you do to divide
them?
TASK 5: Dividing Integers
1. Simplify the following:
a) -8 ÷ 2
b)
36 ÷ (-6)
c) (-72) ÷ (-9)
d)
-6 ÷ (-2)
2. Explain in your own words how to divide positive and negative numbers.
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TASK 6: Absolute Value and Integers
Recall Absolute Value
Example:  9 = ____ ?
4 = _____ ?
Absolute value bars, are also grouping symbols, so we simplify inside the absolute value bars
first, and then take the absolute value of the resulting number inside, thus, dropping the bars
at the very end.
3. Simplify the following
a) 9  12
b)   4
Recall, if a number is in front of a grouping symbol and no operation (add, subtract, multiply or
divide) is between them, then the grouping symbol implies a multiplication with the number in
front of it
4. Simplify the following:
a) 2  7
b)  5 6  10
TASK 5: Exponents and Integers
Recall, an exponential expression is in the form: 2³
1. What is the base of this expression?
2. What is the exponent of the expression?
3. Simplify the expression:
2³ = ____________ ?
In an exponential expression, the exponent tells how many bases to multiply together
Consider the expression: ( - 4 )²
4. What is the base?
5. What is the exponent?
6. Simplify the expression:
( - 4 )² = ___________________ ?
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In an exponential expression, when a base is negative, it should always be enclosed in a
grouping symbol (such as a parentheses) with the exponent outside of the grouping symbol.
Consider the expressions:
( - 3 )²
versus
- 3²
7. What is the difference in how these two expressions look?
8. Simplify: ( - 3 )² = _______________ ?
9. Simplify: - 3²
= ________________?
TASK 7: Order of Operations
Now, let’s put it all together.
Simplify the following:
1. 2 – 5( 4 ) + ( - 25 )
 15  3
2.  4
2
 3
3.
8   3 4  5
4.
3(6)  11  1
4 2  32
ECC/Activity 9
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