INTEGERS By: NIKMATUL HUSNA

200C oC 60 Read the temperature on the thermometer as it changes. 50 40 30 20 200C 10 -10 -20 -30

-100C oC 60 Read the temperature on the thermometer as it changes. 50 40 30 20 -100C 10 -10 -20 -30

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

The Integers Consist of: Negative Numbers Zero Positive Numbers

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

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

Arithmetic operation By: NIKMATUL HUSNA

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

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

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

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

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

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

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

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

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

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

The Properties of Addition: Commutative Law a + b = b + a 7 + 4 = 11 and 4 +7 =11 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.

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)

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

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

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

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)

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 = b x c

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 =