Addition and Subtraction Chapter Notes | Year 4 Mathematics IGCSE (Cambridge) - Class 4 PDF Download

Adding and subtracting efficiently

• The objective is to use a column method to add or subtract whole numbers.
• Addition and subtraction are essential skills for everyday calculations, such as determining the cost of lunch in a café or managing resources in various settings.
• The column method involves aligning numbers by place value (hundreds, tens, ones) for accurate computation.
• Addition:
  • Numbers are written vertically, aligning digits by place value.
  • Add digits in each column from right to left, carrying over to the next column if the sum exceeds 9.
  • Example: Adding items from a menu (e.g., sandwich $4.00 + orange juice $1.50 = $5.50).
• Subtraction:
  • Two methods for subtraction, as shown in the example 367 - 185 = 182:
    • Method 1 (Decomposition):
      • Break numbers into place values: 367 = 300 + 60 + 7, 185 = 100 + 80 + 5.
      • Regroup if necessary, e.g., 60 tens becomes 50 tens + 10 ones, so 367 = 300 + 50 + 17.
      • Subtract corresponding parts: (300 - 100) + (50 - 80) + (17 - 5), adjusting for negative results by regrouping further.
      • Final result: 100 + 80 + 2 = 182.
    • Method 2 (Column Method):
      • Write numbers vertically: 367 above 185.
      • Subtract ones: 7 - 5 = 2.
      • Regroup tens if needed: 3 hundreds + 6 tens = 2 hundreds + 16 tens.
      • Subtract tens: 16 - 8 = 8 tens.
      • Subtract hundreds: 2 - 1 = 1 hundred.
      • Result: 1 hundred + 8 tens + 2 ones = 182.
• Estimation before calculation helps verify the reasonableness of answers.
• Carrying (in addition) and regrouping (in subtraction) are key techniques to handle multi-digit numbers efficiently.

Adding and subtracting fractions with the same denominator

• The objective is to add and subtract fractions with the same denominator, including cases where the total is greater than 1.
• Fractions with the same denominator can be added or subtracted by operating on the numerators while keeping the denominator unchanged.
• Proper fraction: A fraction where the numerator is less than the denominator, e.g., 3/5.
• Improper fraction: A fraction where the numerator is greater than or equal to the denominator, e.g., 7/5, which may result from adding fractions.
• Example: For a cake divided into 5 equal pieces, if 2 pieces are taken, the fraction left is calculated as 1 - 2/5 = 3/5.
• Addition:
  • Add numerators and keep the denominator: 7/10 + 3/10 = (7 + 3)/10 = 10/10 = 1.
  • If the result is improper, it indicates a total greater than 1, e.g., 4/5 + 3/5 = 7/5.
• Subtraction:
  • Subtract numerators and keep the denominator: 6/7 - 3/7 = (6 - 3)/7 = 3/7.
  • Example: 5/12 - 1/12 = 4/12.
• Common errors to avoid:
  • Adding or subtracting denominators, e.g., incorrectly computing 3/9 + 2/9 as 5/18 instead of 5/9.
• This unit extends Stage 3 learning, where fractions were within a whole, to include totals greater than 1.