Download integers - Nikmatul Husna

INTEGERS
By:
NIKMATUL HUSNA
oC
60
50
40
30
20
10
0
-10
-20
-30
Read the temperature on the
thermometer as it changes.
200C
oC
60
50
40
30
20
10
0
-10
-20
-30
Read the temperature on the
thermometer as it changes.
-100C
30m
30 m
25 m
Sea level
15m
20 m
Estimate the height above or below sea level of
the following points:
6m
5m
20m
10m
0m
-5 m
-10m
-10m
-15 m
-20m
-25 m
-30 m
-25 m
-30m
The Integers Consist of:
• Negative Numbers
• Zero
• Positive Numbers
NUMBER LINE
-5 -4 -3 -2 -1 0 1
2 3 4 5
1. Natural Numbers
2. Integers
3. Whole Numbers
4. Odd Numbers
5. Even Numbers
6. Prime Numbers
7. Ordinal Numbers
8. Addition
9. Subtraction
10.Multiplication
11.Division
12.Sum
13.Difference
14.Product
15.Quotient
1. Bilangan Asli
2. Bilangan Bulat
3. Bilangan Cacah
4. Bilangan Ganjil
5. Bilangan Genap
6. Bilangan Prima
7. Bilangan Tingkat
8. Penjumlahan
9. Pengurangan
10.Perkalian
11.Pembagian
12.Jumlah
13.Hasil pengurangan
14.Hasil Kali
15.Hasil bagi
Arithmetic operation
By:
NIKMATUL HUSNA
-5 -4 -3 -2 -1
0 1
2 3 4 5
Positive in the right and negative in the left
Plus = forward , minus = backward
Calculate 2 + 3
2
-5 -4 -3 -2 -1
0 1
2 3 4 5
3
So, 2 + 3 = 5
Calculate 2 + (–3)
2
-5 -4 -3 -2 -1
0 1
2 3 4 5
3
So, 2 + (– 3) = –1
Calculate –2 + 3
–2
0 1
-5 -4 -3 -2 -1
3
So, – 2 + 3 = 1
2 3 4 5
Calculate –2 +(–3)
–2
-5 -4 -3 -2 -1
0 1
2 3 4 5
3
So, – 2 + (– 3) = – 5
Calculate 2 – 3
2
-5 -4 -3 -2 -1
0 1
3
So, 2 – 3 = -1
2 3 4 5
Calculate 2 – (-3)
2
-5 -4 -3 -2 -1
0 1
2 3 4 5
3
So, 2 – (- 3) = 5
Calculate -2 – 3
–2
-5 -4 -3 -2 -1
0 1
3
So, -2 – 3 = -5
2 3 4 5
Calculate -2 – (-3)
–2
0 1
-5 -4 -3 -2 -1
2 3 4 5
3
So, -2 – (- 3) = - 1
ADDITION
1. Same Sign
125 + 234 = 359
- 58 + (-72) = -130
2. Different Sign
75 + (-90) = - 15
(-63) + 125 = 62
The Properties of Addition:
1. Commutative Law
a+b=b+a
7 + 4 = 11 and 4 +7 =11
2. Associative Law
(a+b)+c = a+(b+c)
(5+(-3))+8 = 10 and 5+((-3)+8) = 10
3. Identity Element
The identity of addition in integers
is 0
a+0=0+a=a
5+ 0 = 0 + 5 = 5
4. Closure Law
if a and b are the integers, then
a + b is also the integers.
3+5=8
3, 5, 8 are integers
5. Inverse of Addition
if a + b = 0, then b is called the
inverse of a
3 + (-3) = 0
SUBTRACTION
The Properties of Subtraction only:
Closure Law
If a and b are integers, a-b is also
integers.
8–3=5
8 + (-3) = 5
If a and b are the integers,
then a – b = a + (-b)
Change Into Addition
1.
2.
3.
4.
a–b
=
a – (-b) =
- a – (-b) =
-a–b
=
Multiplication
Calculate this example :
•
•
•
•
•
30 x 5 = …
-3 x 41 = …
21 x (-4) = …
(-50) x (-4) = …
15 x (-7) = …
The Properties of Multiplication
1. Closure Law
2. Commutative, Associative and
Distributive Law.
3. Identity Element
The identity of multiplication in
integers is 1
1 x a = a x 1= a
Distributive Law
3 x (-2 + 4) = 6
(3 x (-2)) + (3 x 4) = 6
a x (b + c) = (a x b) + (a x c)
Division
Calculate this example :
•
•
•
•
•
3:3=
28 : (-7) =
-35 : 5 =
40 : (-8) =
-72 : (-9) =
Division is inverse
of multiplication
24 : 3 = 8
And
3 x 8 = 24
a, b and c with b factor of c and b ≠ 0
a:b=ca=bxc
TASK :
1. 45 + 56 × 48 – 216 : 9 =
2. 15.762 : 37 – 512 + 96 × 72 =
3. 19 × 27 + 5.205 : 15 – 269 =
4. (–9) – 6 × (–72) : 16 – 20 =
5. (8.742 – 9.756) × 36 : (4.356 – 4.360) =
6. 168 : ((17 – 24) × (–19 + 15)) =
7. 24 × (240 : ((–36 + 40) × (–23 + 17)) =
8. 360 : (15 + ((27 – 32) × (–9 + 16))) =
9. 420 : (–7) + 70 – 30 × (–8) + 15 =
10. 13 × (140 : (–7)) + (–2) × 19 =