Operasi Bilangan Bulat

Integer Operations

• Addition:
  • The sum of two positive integers is always positive.
  • The sum of two negative integers is always negative.
  • The sum of a positive and a negative integer can be either positive, negative, or zero.
• Subtraction:
  • Subtracting a positive integer is equivalent to adding the opposite (negative) integer.
  • Subtracting a negative integer is equivalent to adding the positive integer.
• Multiplication:
  • The product of two positive integers is always positive.
  • The product of two negative integers is always positive.
  • The product of a positive and a negative integer is always negative.
• Division:
  • The quotient of two positive integers is always positive.
  • The quotient of two negative integers is always positive.
  • The quotient of a positive and a negative integer is always negative.

Ordering Integers

• Integers can be arranged in a number line from least to greatest (left to right).
• A positive integer is always greater than a negative integer.
• Zero is the middle point, separating positive and negative integers.

Comparing Integers

• Two integers can be compared using greater than (>), less than (<), equal to (=), greater than or equal to (≥), and less than or equal to (≤) symbols.
• Comparisons can be used to determine the relative size of integers.

Real-world Applications

• Temperature: Positive integers represent temperatures above 0°C, while negative integers represent temperatures below 0°C.
• Elevation: Positive integers represent elevations above sea level, while negative integers represent elevations below sea level.
• Finance: Positive integers represent gains, while negative integers represent losses or debts.

Integer Properties

• Commutative Property: The order of integers in an operation does not change the result. (e.g., a + b = b + a)
• Associative Property: The order in which integers are grouped in an operation does not change the result. (e.g., (a + b) + c = a + (b + c))
• Distributive Property: An integer operation can be distributed across multiple integers. (e.g., a × (b + c) = a × b + a × c)

Operasi Bilangan Bulat

• Penjumlahan:
  • Jumlah dua bilangan bulat positif selalu positif.
  • Jumlah dua bilangan bulat negatif selalu negatif.
  • Jumlah bilangan bulat positif dan negatif dapat positif, negatif, atau nol.
• Pengurangan:
  • Mengurangkan bilangan bulat positif sama dengan menambahkan bilangan bulat negatif yang berlawanan.
  • Mengurangkan bilangan bulat negatif sama dengan menambahkan bilangan bulat positif.

Perkalian Bilangan Bulat

• Perkalian:
  • Hasil kali dua bilangan bulat positif selalu positif.
  • Hasil kali dua bilangan bulat negatif selalu positif.
  • Hasil kali bilangan bulat positif dan negatif selalu negatif.

Pembagian Bilangan Bulat

• Pembagian:
  • Hasil bagi dua bilangan bulat positif selalu positif.
  • Hasil bagi dua bilangan bulat negatif selalu positif.
  • Hasil bagi bilangan bulat positif dan negatif selalu negatif.

Pengurutan Bilangan Bulat

• Bilangan bulat dapat diurutkan dari yang terkecil ke yang terbesar (dari kiri ke kanan) pada garis bilangan.
• Bilangan bulat positif selalu lebih besar dari bilangan bulat negatif.
• Nol adalah titik tengah, memisahkan bilangan bulat positif dan negatif.

Membandingkan Bilangan Bulat

• Dua bilangan bulat dapat dibandingkan menggunakan simbol lebih besar dari (>), lebih kecil dari (<), dan sama dengan (=).