Addition and Subtraction (2) Chapter Notes | Year 6 Mathematics IGCSE (Cambridge) - Class 6 PDF Download

Adding and subtracting decimal numbers

• The objective is to compose, decompose, and regroup decimals with up to 3 decimal places.
• Estimate, add, and subtract numbers with the same or different numbers of decimal places.
• Decimals are used in precise measurements, e.g., Usain Bolt’s 100 m record time of 9.58 seconds compared to the Olympic qualifying time of 10.05 seconds.
• Composing decimals:
  • Combine place values, e.g., 3 + 1/10 + 3/100 = 3.13.
  • Example: 6.075 = 6 + 0.07 + 0.005.
• Decomposing decimals:
  • Break into place value components, e.g., 37.844 = 30 + 7 + 0.8 + 0.04 + 0.004.
• Regrouping decimals:
  • Rearrange place values, e.g., 4.49 = 4 + 0.4 + 0.09, 3.09 = 3 + 0.09.
• Adding decimals:
  • Align decimal points and add, using trailing zeros if needed for consistent decimal places.
  • Example (Method 1, regrouping): For 4.49 + 3.09, decompose as 4 + 0.4 + 0.09 + 3 + 0.09 = 7 + 0.4 + 0.18 = 7.58.
  • Example (Method 2, column method): 4.49 + 3.09 = 7.58.
    • 4.49
    • + 3.09
    • ------
    • 7.58
  • Real-world: 65.98 + 32.75 = 98.73 (sum of two amounts).
• Subtracting decimals:
  • Align decimal points, subtract, and use trailing zeros if needed.
  • Example: For 10.00 - 7.58 (change from $10 after spending $7.58):
    • Method 1 (regrouping): 10 = 9 + 0.9 + 0.10, subtract 7 + 0.5 + 0.08, result = 2 + 0.4 + 0.02 = 2.42.
    • Method 2 (column): 10.00 - 7.58 = 2.42.
  • Real-world: 54.31 - 46.76 = 7.55 (difference between two values).
  • Example: Difference in heights, 1.4 m - 1.2 m = 0.2 m.
  • Example: Time difference, 10.05 - 9.58 = 0.47 seconds.
• Estimation:
  • Round numbers to estimate results, e.g., for 4.49 + 3.09, estimate 4 + 3 = 7, then 10 - 7 = 3, so change is about $3 (actual: $2.42).
• Trailing zeros:
  • Added to ensure consistent decimal places, e.g., write 10 as 10.00 when subtracting 7.58.
• Applications include calculating change, comparing times, summing weights (e.g., 8.45 kg + 10.5 kg = 18.95 kg), or finding remaining amounts toward a target (e.g., $350 - $158.73 = $191.27).

Adding and subtracting fractions

• The objective is to add and subtract two fractions with different denominators.
• Fractions represent parts of a whole, e.g., dividing a pizza into 8 or 5 pieces.
• Common denominator:
  • A shared multiple of the denominators to enable addition or subtraction.
  • Find by listing multiples, e.g., for 5 and 4: multiples of 5: 5, 10, 15, 20, …; multiples of 4: 4, 8, 12, 16, 20, …; common denominator is 20.
• Adding fractions:
  • Convert fractions to equivalent fractions with a common denominator, add numerators, and simplify if possible.
  • Example: 9/5 + 3/4:
    • Common denominator: 20.
    • Convert: 9/5 = 36/20, 3/4 = 15/20.
    • Add: 36/20 + 15/20 = 51/20.
    • Convert to mixed number: 51/20 = 2 11/20.
  • Real-world: Eating 3/8 of a pizza and 1/5 of another, total = 3/8 + 1/5, with common denominator 40: 3/8 = 15/40, 1/5 = 8/40, 15/40 + 8/40 = 23/40.
  • Examples:
    • 3/4 + 2/5 (common denominator 20: 15/20 + 8/20 = 23/20 = 1 3/20).
    • 7/8 + 3/5 (common denominator 40: 35/40 + 24/40 = 59/40 = 1 19/40).
• Subtracting fractions:
  • Convert to a common denominator, subtract numerators, and simplify.
  • Example: 5/6 - 1/2:
    • Common denominator: 6.
    • Convert: 1/2 = 3/6.
    • Subtract: 5/6 - 3/6 = 2/6 = 1/3.
  • Examples:
    • 3/2 - 4/5 (common denominator 10: 15/10 - 8/10 = 7/10).
    • 9/8 - 2/3 (common denominator 24: 27/24 - 16/24 = 11/24).
• Applications:
  • Calculate remaining fractions, e.g., if 3/4 vote for a theme park and 2/9 for a zoo, fraction for a river trip is 1 - (3/4 + 2/9), with common denominator 36: 3/4 = 27/36, 2/9 = 8/36, 27/36 + 8/36 = 35/36, 1 - 35/36 = 1/36.
  • Gardening: 1/3 potatoes, 1/4 carrots, onions = 1 - (1/3 + 1/4), common denominator 12: 1/3 = 4/12, 1/4 = 3/12, 4/12 + 3/12 = 7/12, 1 - 7/12 = 5/12.
  • Spending: 1/6 on a dress, 1/3 on a coat, total = 1/6 + 1/3 = 1/6 + 2/6 = 3/6 = 1/2.