1. INTEGERS
By: NIKMATUL HUSNA

2. 200C oC 60 Read the temperature on the thermometer as it changes. 5040 30 20
200C 10
-10
-20
-30

3. -100C oC 60 Read the temperature on the thermometer as it changes. 5040 30 20
-100C 10
-10
-20
-30

4. Sea level 30m 20m 10m 0m -10m -20m -30m 30 m 25 m 20 m 15m 6 m 5 m
Estimate the height above or below sea level of the following points:
6 m
5 m
-10m
-20m
-30m
-5 m
-10m
-15 m
-25 m
-25 m
-30 m

5. The Integers Consist of:
Negative Numbers
Zero
Positive Numbers

6. NUMBER LINE -5 -4 -3 -2 -1 1 2 3 4 5

7. Natural Numbers
Integers
Whole Numbers
Odd Numbers
Even Numbers
Prime Numbers
Ordinal Numbers
Addition
Subtraction
Multiplication
Division
Sum
Difference
Product
Quotient
Bilangan Asli
Bilangan Bulat
Bilangan Cacah
Bilangan Ganjil
Bilangan Genap
Bilangan Prima
Bilangan Tingkat
Penjumlahan
Pengurangan
Perkalian
Pembagian
Jumlah
Hasil pengurangan
Hasil Kali
Hasil bagi

8. Arithmetic operation
By: NIKMATUL HUSNA

9. -5 -4 -3 -2 -1 1 2 3 4 5
Positive in the right and negative in the left
Plus = forward , minus = backward

10. Calculate 2 + 3 2 1 -1 2 -2 3 -3 4 -4 5 -5 3
So, = 5

11. Calculate 2 + (–3) 2 1 -1 2 -2 3 -3 4 -4 5 -5 3
So, 2 + (– 3) = –1

12. Calculate –2 + 3 –2 1 -1 2 -2 3 -3 4 -4 5 -5 3
So, – = 1

13. Calculate –2 +(–3) –2 1 -1 2 -2 3 -3 4 -4 5 -5 3
So, – 2 + (– 3) = – 5

14. Calculate 2 – 3 2 1 -1 2 -2 3 -3 4 -4 5 -5 3
So, 2 – 3 = -1

15. Calculate 2 – (-3) 2 1 -1 2 -2 3 -3 4 -4 5 -5 3
So, 2 – (- 3) = 5

16. Calculate -2 – 3 –2 1 -1 2 -2 3 -3 4 -4 5 -5 3
So, -2 – 3 = -5

17. Calculate -2 – (-3) –2 1 -1 2 -2 3 -3 4 -4 5 -5 3
So, -2 – (- 3) = - 1

18. ADDITION Same Sign 125 + 234 = 359 - 58 + (-72) = -130 Different Sign
= 359
(-72) = -130
Different Sign
75 + (-90) = - 15
(-63) = 62

19. The Properties of Addition:
Commutative Law
a + b = b + a
7 + 4 = 11 and =11
Associative Law
(a+b)+c = a+(b+c)
(5+(-3))+8 = 10 and 5+((-3)+8) = 10

20. 3. Identity Element The identity of addition in integers is 0 a + 0 = 0 + a = a 5+ 0 = = 5 4. Closure Law if a and b are the integers, then a + b is also the integers = 8 3, 5, 8 are integers

21. 5. Inverse of Addition if a + b = 0, then b is called the inverse of a 3 + (-3) = 0

22. SUBTRACTION
The Properties of Subtraction only: Closure Law If a and b are integers, a-b is also integers.

23. If a and b are the integers, then a – b = a + (-b)
8 – 3 = 5
8 + (-3) = 5
If a and b are the integers, then a – b = a + (-b)

24. Change Into Addition
a – b =
a – (-b) =
- a – (-b) =
- a – b =

25. Calculate this example :
Multiplication
Calculate this example :
30 x 5 = …
-3 x 41 = …
21 x (-4) = …
(-50) x (-4) = …
15 x (-7) = …

26. The Properties of Multiplication
Closure Law
Commutative, Associative and Distributive Law.
Identity Element
The identity of multiplication in integers is 1
1 x a = a x 1= a

27. Distributive Law a x (b + c) = (a x b) + (a x c)
3 x (-2 + 4) = 6 (3 x (-2)) + (3 x 4) = 6
a x (b + c) = (a x b) + (a x c)

28. Division Calculate this example : 3 : 3 = 28 : (-7) = -35 : 5 =
40 : (-8) =
-72 : (-9) =

29. Division is inverse of multiplication
24 : 3 = 8 And x 8 = 24
a, b and c with b factor of c and b ≠ 0
a : b = c  a = b x c

30. TASK :
× 48 – 216 : 9 =
: 37 – × 72 =
3. 19 × : 15 – 269 =
4. (–9) – 6 × (–72) : 16 – 20 =
5. (8.742 – 9.756) × 36 : (4.356 – 4.360) =

31. : ((17 – 24) × (– )) =
7. 24 × (240 : ((– ) × (– )) =
: (15 + ((27 – 32) × (–9 + 16))) =
: (–7) + 70 – 30 × (–8) + 15 =
× (140 : (–7)) + (–2) × 19 =