introduction about integers

1. This presentation will review different math skills that will help you
with every day math problems.
Each lesson takes approximately 15 minutes to do. Almost anyone
can find an extra 15 minutes out of his or her day, whether it be
during breakfast or right before bed. In just under 3 weeks, you
can review all the TABE Computation Math sections.
Look for the Professor. He has special hints to help make
working the math problems faster and easier.
15 Minute Math

2. 15 Minute Math
 Decimals
o Lesson 1 – What Are Decimals?
o Lesson 2 – Addition & Subtraction
o Lesson 3 – Multiplication
o Lesson 4 - Division
 Fractions
o Lesson 5 – What Are Fractions?
o Lesson 6 - Addition & Subtraction (no
whole #s)
o Lesson 7 – Addition & Subtraction
(with whole #s)
o Lesson 8 – Multiplication & Division
 Percentages
o Lesson 9 – Converting Decimals to
Fractions to Percents
o Lesson 10 – Calculating the Part
o Lesson 11 – Cross-Multiplication
Method
 Integers
o Lesson 12 – Addition & Subtraction
o Lesson 13 – Multiplication, Division, &
Absolute Value
 Algebra
o Lesson 14 – Adding & Subtracting
Variables
o Lesson 15 – Multiplying & Dividing
Variables
o Lesson 16 – Square Roots
 Order of Operations
o Lesson 17 – Please Excuse My Dear
Aunt Sally
o Lesson 18 – Order of Operations with
Variables
 Practice Tests
o Lesson 19 – Practice Test #1
o Lesson 20 – Practice Test #2

3. This lesson explains how to add and subtract
negative numbers.
Problem: You want to buy a house that costs $100,000. You only
have $5,000. If you buy the house, what will your debt be?
5,000
- 100,000
-95,000
If you spend more money than you have, you go into debt. Debt is a
good example of working with negative integers.
15 Minute Math – Integers
Lesson # 12 - Addition & Subtraction

4. Negative numbers are like a debt.
Positive numbers move to the right on the number line.
Negative numbers move to the left on the number line.
If you have 8 dollars, and then you get 2 dollars, you have 10 dollars.
 8 + 2 = 10
If you have 8 dollars, and then you lose 2 dollars, you have only 6 dollars.
 8 - 2 = 6
If you are 8 dollars in debt, and then you get 2 dollars, you are only 6 dollars in
debt.
 -8 + 2 = -6
If you are 8 dollars in debt, and then you lose another 2 dollars, you are 10
dollars in debt.
 -8 - 2 = -10
15 Minute Math – Integers
Lesson # 12 - Addition & Subtraction
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 2 3 4 5 6 7 8 9 10
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 2 3 4 5 6 7 8 9 10
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 2 3 4 5 6 7 8 9 10
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 2 3 4 5 6 7 8 9 10

5. Use these hints to help work problems.
If both numbers are negative, add the numbers, then make the answer
negative.
-8 – 2  -(8 + 2) = -10
When one sign is positive and one sign is negative, subtract the
numbers and take the sign of the larger.
8 – 2 = 6 (“8” is positive, so the answer is positive)
2 – 8 = -6 (think “8-2” and take the sign of the larger number, “8”)
Examples:
++  9 + 2 = 11
--  -9 – 2 = -11
+-  9 – 2 = 7
-+  -9 + 2 = -7
15 Minute Math – Integers
Lesson # 12 - Addition & Subtraction
Try using this chart:
Integer Addition/Subtraction
++  Add
--  Add
+-  Subtract
-+  Subtract
Always use the sign of the largest
number for the sign of the answer

6. Try it yourself
3 + 6 = 9 -3 – 6 = -9 3 – 6 = -3 -3 + 6 = 3
4 + 7 = -4 – 7 = 4 – 7 = -4 + 7 =
7 + 4 = -7 – 4 = 7 – 4 = -7 + 4 =
5 + 1 = -5 – 1 = 5 – 1 = -5 + 1 =
10 + 20 = -10 – 20 = 10 – 20 = -10 + 20 =
4 + 7 = 11 -4 – 7 = -11 4 – 7 = -3 -4 + 7 = 3
7 + 4 = 11 -7 – 4 = -11 7 – 4 = 3 -7 + 4 = -3
5 + 1 = 6 -5 – 1 = -6 5 – 1 = 4 -5 + 1 = -4
10 + 20 = 30 -10 – 20 = -30 10 – 20 = -10 -10 + 20 = 10
15 Minute Math – Integers
Lesson # 12 - Addition & Subtraction
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7. If there are 2 signs next to each other, rewrite the
problem with just one sign.
To subtract a negative number, the 2 negatives make a positive.
8 – (-2)  8 - -2  8 + 2 = 10
Adding a negative number is the same as subtraction.
8 + (-2)  8 + -2  8 – 2 = 6
We don’t usually write the
positive sign, but you could if you
wanted to:
8 + 2  (+8) + (+2)
8 – 2  (+8) – (+2) or (+8) + (-2)
The parentheses are only
there to keep the signs
separate. You can remove
them if you want to.
15 Minute Math – Integers
Lesson # 12 - Addition & Subtraction

8. Try it yourself
3 – (+6)  3 – 6 = -3 -2 – (-4)  -2 + 4 = 2
4 – (-2) = -8 + (-3) =
-10 + (-3) = 10 – (+2) =
9 + (+2) = -7 – (-3) =
4 – (-2) = 6 -8 + (-3) = -11
-10 + (-3) = 7 10 – (+2) = 8
9 + (+2) = 11 -7 – (-3) = -4
15 Minute Math – Integers
Lesson # 12 - Addition & Subtraction
End of Lesson 12
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9. This lesson explains how to
multiply and divide negative numbers,
plus the absolute value sign,||.
Problem: You are $30 in debt. If your debt is increased 2 times, how
much is your debt?
-30 x 2 = -60
Multiplying by a negative number is multiplying your debt.
15 Minute Math – Integers
Lesson # 13 – Multiplication, Division, &
Absolute Value

10. Some simple rules will help you when multiplying negative numbers. The
rules are the same for division.
 If there is one negative number, then the answer is negative.
 If two numbers are negative, then the answer is positive.
8 x 5 = 40 40 ÷ 8 = 5
-8 x 5 = -40 -40 ÷ -8 = 5
8 x -5 = -40 -40 ÷ 8 = -5
-8 x -5 = 40 40 ÷ -8 = -5
 If you have more than 2 numbers, the rule is:
 An odd number of negative #s = negative answer
 An even number of negative #s = positive answer
(-1 )x (-2) x (-3) x (4) = -24 (3 negative #s)
(-1) x (-2) x (-3) x (-4) = 24 (4 negative #s)
15 Minute Math – Integers
Lesson # 13 – Multiplication, Division, &
Absolute Value
If the signs are the same = positive answer.
If the signs are different = negative answer.
Integer Mult./Division
++  Answer is +
--  Answer is +
+-  Answer is -
-+  Answer is -

11. The absolute value symbols “| |” make everything positive.
To work an absolute value problem, first work everything inside
the absolute value symbols.
Then, make it positive.
| -10 | = 10
| 10 | = 10
| 6 x -3 | = 18
Work inside the symbols | 3 – 7 |= | -4 |
Now, make it positive  | -4 | = +4
| 3 – 7 | = | -4 | = 4
15 Minute Math – Integers
Lesson # 13 – Multiplication, Division, &
Absolute Value

12. Try it yourself
2 x 3 = 6 -2 x 3 = -6 2 x -3 = -6 -2 x -3 = 6
6 x 8 = - 6 x 8 = 6 x -8 = -6 x -8 =
7 x 4 = -7 x 4 = 7 x -4 = -7 x -4 =
54  6 = -54  6 = 54  -6 = -54  -6 =
|-8 x 3| = |5 x (-2) – 1| = 2 x |3 – 9| = |-12  -4| =
6 x 8 = 48 - 6 x 8 = -48 6 x -8 = -48 -6 x -8 = 48
7 x 4 = 28 -7 x 4 = -28 7 x -4 = -28 -7 x -4 = 28
54  6 = 9 -54  6 = -9 54  -6 = -9 -54  -6 = 9
|-8 x 3| = 24 |5 x (-2) – 1| = 11 2 x |3 – 9| = 12 |-12  -4| = 3
15 Minute Math – Integers
Lesson # 13 – Multiplication, Division, &
Absolute Value
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