Demvry's Great Big Book Of Integers

Chapter 1 Grade 7 Integer Review

(+4) + (-2) = +2
Positive 4 and Negative 2 have 4 and owes 2 which is now 2+
Standard Form: 4 - 2 = 2
Making Zero Pairs:
-16 = +16
-5 = +5
+6 = -6
-2 = +2
-10 = +10
+3 = -3
+11 = -11
-9 = +9

Chapter 2 Multiplying Intergers

Sign Rule (Negative signs)
Even = When you have an even number of NEGATIVE factors, the product is POSITIVE
Odd = When you have an odd number of NEGATIVE factors the product is NEGATIVE

(+2) x (+3) = +6

Standard form
(2) x (3) = 6
2(3) = 6

o
o ooo ooo = 6
(+2) x (+3) = 6
or
2 groups of (+3) = 6

o
o ooo ooo = -6
(+2) x (-3) = -6 ← remove 2 groups of (+3) ← use zero pairs -remove all
or
2 groups of (-3) = -6

o ooo ooo
o
(-2) x (-3)
↑ remove 2 groups of (-3) = +6

o oooo oooo oooo
o
(-3) x (-4) = +12

o
o oooooooo
(+2) x (+4) = +8
(+5) x (-2) = -10 (-4) x (+2) = -8 ← 4 x 2 for zero pairs ← remove (+) left with (-)
(-6) x (-1) = 6

Chapter 3 Dividing Integers

Sign Rule
If you have no NEGATIVE or an even number of NEGATIVE signs in a division question, the quotient is POSITIVE. When you have an odd number of NEGATIVE signs in a division question the quotient is NEGATIVE.

2 Types of Division:
Partitive Division or making parts
Partitive Division is making parts.
6 ÷ 2 = 3, how many groups of 2 are in 6?
oo|oo|oo ← There are 3 groups of 2 in 6

6 ÷ 2 = 3 and -6 ÷ (-2) = 3
3 groups of 2 ←↓
***→2→ →2→ →2→
←2-----------------------6→

3 groups of 2←↓
*****←2← ←2← ←2←
←(-6)-----------------------(-2)→

Quotative Division or sharing your total with groups
Quotative Division is sharing your total with groups.
-6 ÷ 3 = -2, share 6 with 3 groups
oooooo ← 6 totals
( ) ( ) ( ) ← 3 groups
(oo) (oo) (oo) ← 2 out of 6 totals are in 1 group

Chapter 4 Order of Operations with Integers

BEDMAS

Brackets
Exponents
Division
Multiplication
Addition
Subtraction

Steps:

1) Brackets (if there's a square bracket, always do that first then the round bracket)

2) Multiply and divide in order, left to right.

3) Add and subtract in order, left to right.

(+5) x (-3) + (-6) ÷ (+3) = ?

(+5) x (-3) + (-2) = -17
(-15) + (-2) = -17

(+5) x (-3) = -15
(-6) ÷ (+3) = -2
(-15) + (-2) = -17
= -17