Add & Subtract Integers Multiply & Divide Integers Add & Subtract Fractions Multiply & Divide Fractions One & Two Step Equations Combining Like Terms

1. -Step one: Clean out your file
in the back!
-Look for any notes handed in!
-Also, look for any vocabulary!
-Grab all your old tests!

2. • Integer: A positive or negative whole number
including zero.
• Whole Number: Any number over one.
• Number Line: A line where all negative numbers
are on the left, zero is in the middle, and
positive numbers are on the right.
• Positive Number: Any number on the right side
of the number line.
• Negative Number: Any number on the left side
of the number line.
• Increasing Order: Smallest to biggest.

3. • When Signs are the same, add the
numbers!
EX: -5 - 1 = 5 + 1
• Answer gets the sign of the larger
number.
5 is the largest number
it’s sign is a (-).
Answer is -6.

4. • When Signs are the different subtract the
numbers.
EX: -5 + 1 = 5 - 1
• Answer gets the sign of the larger
number.
5 is the largest number
it’s sign is a (-).
Answer is -4.

5. Let’s Practice
1) 5 - 6 =
2) -3 + 2 =
3) 6 + 5 =
4) -8 + 7 =
5) 9 - 9 =
Remember: If signs are the same add
the numbers, if signs are different
subtract the numbers. Then give the
answer the sign of the largest number!
-1
-1
+11
-1
0

6. Rules for Integers
• When Parenthesis ( ) are
involved we get to doodle!
• This is where you need to draw
some faces. (Bet you didn’t know
you’d be doing Art in Math!)

7. Rules for Adding & Subtracting Integers
Continued
• When you multiply a (+ x -) you get a (-).
• When you multiply a (- x -) you get a (+).
• When you multiply a (+ x +) you get a (+).
5 + (-1) = 4
5 – (-1) = 6
5 + (+5) = 10
-
+
+

8. Let’s Practice
1) 4 – (-5) =
2) 9 + (-7) =
3) 6 – (+2) =
4) 8 – (-7) =
5) 9 + (+3) =
Remember: DRAW the faces first! If signs are
the same add the numbers, if signs are
different subtract the numbers. Then give the
answer the sign of the largest number!
9
2
4
15
12
+
-
+
-
+

9. Let’s Practice Cont.
1) 5 + (-2) =
2) 3 – (-4) =
3) 1 – (+2) =
4) 5 – (-3) =
5) 7 – (-6) =
Remember: DRAW the faces first! If signs are
the same add the numbers, if signs are
different subtract the numbers. Then give the
answer the sign of the largest number!
-
+
+
-
+
3
7
-1
8
13

10. • Reciprocal: Flipping of a fraction.
• Rational Number: All real numbers… -
3, -2, -1, 0, 1, 2, 3…
• Absolute Value: Two lines on either
side of a number asking how far away
from zero.
• Product: To multiply
• Quotient: To divide

11. Rules for
Multiplying Integers (x)
• The product of two integers with
the same signs is POSITIVE.
• The product of two integers with
different signs is NEGATIVE.

12. Rules Summary for
Multiplication
• Positive x Positive = Positive
• Negative x Negative = Positive
• Positive x Negative= Negative
• Negative x Positive = Negative

13. Let’s Practice “Multiplication”
1) 6 x (-3) =
2) 3 x 3 =
3) -4 x 5 =
4) -6 x (-2) =
5) -7 x (-8) =
-18
9
-20
12
56
Remember:
Positive x Positive = Positive
Negative x Negative = Positive
Positive x Negative= Negative
Negative x Positive = Negative

14. Did you know that
the rules for
multiplication and
division are the
same?

15. Rules for
Dividing Integers (÷)
• The quotient of two integers
with the same signs is POSITIVE.
• The quotient of two integers
with different signs is NEGATIVE.

16. Rules Summary for
Division
• Positive ÷ Positive = Positive
• Negative ÷ Negative = Positive
• Positive ÷ Negative= Negative
• Negative ÷ Positive = Negative

17. Let’s Practice “Division”
1) 18 ÷ (-2) =
2) -48 ÷ (-6) =
3) -27 ÷ 9 =
4) 64 ÷ 8 =
5) 30 ÷ (-5) =
-9
+8
-3
+8
-6
Remember:
Positive ÷ Positive = Positive
Negative ÷ Negative = Positive
Positive ÷ Negative= Negative
Negative ÷ Positive = Negative

18. • Denominator: Bottom number of a
fractions.
• Numerator: Top number of a fraction.
• Whole Number: Any number over
one.
• Bar: The line between two numbers
creating a fraction.

19. 1. Count by the bottom number.
2. Circle the match.
3. Count over to the match.
4. Multiply by the old top number.
5. Add/Subtract
• Play with the top-leave the bottom alone.
• Remember to borrow if you need to.
6. Divide if top number is bigger
7. Reduce if you need to.
New
Bottom
Number
New Top
Number

20. 𝟏
𝟔
𝟏
𝟒
+
12
18
24
8
12
16
20
24
=
𝟏𝟎
𝟐𝟒
÷ 2
÷ 2
=
𝟓
𝟏𝟐
𝟒
𝟐𝟒
+
𝟔
𝟐𝟒
=

21. 𝟐
𝟒
𝟏
𝟑
-
8
12
6
9
12
=
𝟐
𝟏𝟐
÷ 2
÷ 2
=
𝟏
𝟔
𝟔
𝟏𝟐
-
𝟒
𝟏𝟐
=

22. 𝟏
𝟒
𝟕
𝟖
+
8
=
𝟗
𝟖
𝟗8
= 𝟏
𝟏
𝟖
𝟐
𝟖
+
𝟕
𝟖
=
1
-8
1
𝟏
𝟖

23. 𝟓
𝟔
𝟓
𝟗
-
12
18
24
30
36
18
21
27
36
=
𝟏𝟎
𝟑𝟔
÷ 2
÷ 2
=
𝟓
𝟏𝟖
𝟑𝟎
𝟑𝟔
-
𝟐𝟎
𝟑𝟔
=

24. 𝟐
𝟕
𝟏
𝟐
+
14 4
6
8
10
12
14
=
𝟏𝟏
𝟏𝟒
𝟒
𝟏𝟒
+
𝟕
𝟏𝟒
=

25. • Improper Fraction: When the numerator is
larger than the denominator.
• Proper Fraction: When a fraction has been
simplified and reduced fully.
• Reduce: To divide the top and bottom
number of a fraction by the same number.
• Simplify: To make an improper fraction
proper.

26. Reduce if you can:
You can’t reduce side to side!
Multiply straight across.
Divide if top number is bigger.

27. 𝟐
𝟔
𝟑
𝟒
X =
𝟑
𝟗
𝟏
𝟔
𝟏
𝟒
X
𝟓
𝟏𝟎
=
1
2
1
2
1
2
3
1
𝟑
𝟔
𝟔
𝟏𝟎
X =
𝟑
𝟏𝟎
1
5
3
2
𝟑
𝟏𝟎
𝟓
𝟏𝟓
X =
𝟏
𝟏𝟎
1
5
1
2

28. Flip the SECOND fraction = Change the sign
Reduce if you can:
You can’t reduce side to side!
Multiply straight across.
Divide if top number is bigger.

29. 𝟐
𝟔
𝟑
𝟒
÷ =
𝟑
𝟗
𝟓
𝟏𝟎
𝟐
𝟔
÷
𝟓
𝟏𝟎
=
3
2
1
2
3
1
X
𝟒
𝟑
=
𝟒
𝟗
X
𝟗
𝟑
=
𝟑
𝟐
𝟑2
1
-2
1
𝟏
𝟐

30. • Inverse Operation: Addition & Subtraction
or Multiplication & Division.
• Fulcrum: Equal sign.
• Additive Inverse Strategy: Moves opposite
of the whole term to the other side.
• Multiplicative Inverse Strategy: Moves
part of the term to the other side.

31. Solve the following equation for x:
x – 4 = 9
+ 4 +4
x = 13
We are able to get the x by itself
by ADDING 4 to each side!

32. Solve the following equation for p:
p + 7 = 21
- 7 - 7
p = 14
We are able to get the p by itself
by SUBTRACTING 7 from each side!

33. Solve the following equation for m
3 m = 18
• Divide both sides by 3 and simplify --
your work should look like this :
3 m = 18
3 3
m = 6

34. Solve the following equation for n:
2n = 3
5 7
• Multiply each side by the inverse of 2
5 :
5 • 2n = 3 • 5
2 5 7 2
n = 15
14
= 1
1
14

35. • Variable: A letter or symbol that stands for an
unknown number.
• Terms: Parts of an algebraic expression of an
equation separated by operations.
• Coefficient: The number in front of a variable.
• Like Terms: Terms that have the same variable.
• Constant: A number not attached to a
variable.
• Combining Like Terms: Putting together terms
that have the same variable.

36. Rule 1: Each action should get the letter (variable) closer
to being alone.
Rule2: Additive inverse strategy moves the opposite of
the whole term to the other side.
>change signs - cancel – keep or put with a like
term
Rule 3: Multiplicative inverse strategy moves part of a
term to the other side.
>if a number is next to variable – divide
>if a number is below variable - multiply
Rule 4: Combining like terms put terms with same
ending together that are on the same side of the equal
sign.

37. 14m + 2 – 10m – 11
4m -9
22p + 6 – 32p +14
-10p + 20

38. 4n2 – 3n + 6n – 5n2
-1n2 +3n
4x(x-4) + 3(-x-5)
4x2 – 16x – 3x – 15
4x2 - 19x - 15