Form 1 Chapter 1: Rational Numbers

Topics Covered

• 1.1 Integers
• 1.2 Basic Arithmetic Operations Involving Integers
• 1.3 Positive and Negative Fractions
• 1.4 Positive and Negative Decimals
• 1.5 Rational Numbers

1.1 Integers

Positive and Negative Integers

• Whole numbers: 0, 1, 2, 3, 4, 5, etc. (No fractions or negatives)
• Integers: Positive, negative whole numbers and zero.

Exercise: Determine if Integer or Not

• Integers: 15, 23, -76, 0, 6, 301, -239
• Non-Integers: -3.4, 0.5, 0.88, -4/5

Number Line

• Positive numbers > 0
• Negative numbers < 0
• Right direction = Larger values, Left direction = Smaller values

Exercise: Complete the Number Line

• Numbers provided: -30, 6, -6, -36
• Arrangement: -36, -30, -12, -6, 6

Compare and Arrange Integers

• Ascending Order: -5, -3, -1, 0, 2, 4, 6
• Descending Order: 5, 3, 2, -1, -2, -4, -5

1.2 Basic Arithmetic Operations Involving Integers

Addition and Subtraction

• Same signs give positive
• Different signs give negative
• Examples:
  • 8 + 3 = 11
  • 5 + (-2) = 3
  • 2 - 4 = -2
  • -1 - (-4) = 3

Multiplication and Division

• Same signs give positive
• Different signs give negative
• Examples:
  • -5 x -4 = 20
  • -6 x 4 = -24
  • 6 ÷ -2 = -3
  • -12 ÷ 2 = -6

Combined Operations

• Priority: Brackets > Multiply/Divide (L to R) > Add/Subtract (L to R)
• Examples:
  • -8 x (-2 + 2) = -8
  • 7 + 2 x (-3) = 1
  • 4 - 12 ÷ -2 + (-1) = 9
  • -12 + -16 ÷ -22 + 24 = -14

Arithmetic Laws

• Commutative Law:
  • a + b = b + a
  • a x b = b x a
• Associative Law:
  • (a + b) + c = a + (b + c)
  • (a x b) x c = a x (b x c)
• Distributive Law:
  • a x (b + c) = (a x b) + (a x c)
  • a x (b - c) = (a x b) - (a x c)
• Identity Law:
  • a + 0 = a
  • a x 0 = 0
  • a x 1 = a
  • a + -a = 0
  • a x 1/a = 1

1.3 Positive and Negative Fractions

Concepts

• Fraction: Numerator/Denominator
• Positive Fractions: > 0
• Negative Fractions: < 0

Operations

Example: Arrange fractions

• Convert to common denominators for comparison
• Represent on number line: -5/8, -1/4, -3/4, -3/8, 1/8, 1/2

Example: Calculations

• (5/3) x 12 - 25/30 = -13/18
• (5/8) + (4/3) x (-6/5) = -39/40

1.4 Positive and Negative Decimals

Concepts

• Positive Decimals: > 0
• Negative Decimals: < 0

Example: Compare and Arrange Decimals

• -1.6, 0.5, -0.3, 1.4, -0.7
• Descending Order: 1.4, 0.5, -0.3, -0.7, -1.6

Example: Calculations

• 3.5 - (-6.5 x 0.2) = 4.8
• 7.23 + 2.77 ÷ -0.8 = -12.5
• -3.7 + (2.85 x 0.3) = -1.57

1.5 Rational Numbers

Concepts

• Rational Numbers: Fraction form p/q, q ≠ 0
• Example: 1 & 4/5, 3/4, -9, 3.5 are rational (can be written as fractions)

Examples: Calculations

• -0.4 + (3/2) x -1/8 = -47/80
• 18 x (-7/12) + 3/2 ÷ 3/10 = -30

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