Multiplication and Division Chapter Notes | Year 4 Mathematics IGCSE (Cambridge) - Class 4 PDF Download

Using an efficient column method for multiplication

• The objective is to estimate the answer to multiplying a whole number up to 1000 by a 1-digit number.
• Multiply a whole number by a 1-digit number using an efficient column method.
• Multiplication is a critical skill used in various professions, such as calculating fuel needs for a plane by multiplying fuel burned per hour by journey time.
• Estimation:
  • Round numbers to simplify calculations, e.g., for 346 × 9, estimate 350 × 10 = 3500.
  • Helps verify if the final answer is reasonable.
• Column method for multiplication (e.g., 346 × 9 = 3114):
  • Write the numbers vertically, with the 1-digit number below the multi-digit number.
  • Step 1: Multiply the ones place: 6 × 9 = 54, write 4 in the ones column, carry 5 tens.
  • Step 2: Multiply the tens place: 4 × 9 = 36, add carried 5 tens = 50 to get 36 + 50 = 41 tens, write 1 in the tens column, carry 4 hundreds.
  • Step 3: Multiply the hundreds place: 3 × 9 = 27, add carried 4 hundreds = 400 to get 27 + 400 = 31 hundreds, write 1 in the hundreds column and 3 in the thousands column.
  • Result: 3 thousands + 1 hundred + 1 ten + 4 ones = 3114.
  • Check: Answer 3114 is close to estimate 3500.
• Key terms:
  • Product: The result of multiplication.
  • Estimate: An approximate calculation to check reasonableness.

17.2 Using an efficient method for division

• The objective is to estimate the answer to a division of a 2-digit number by a 1-digit number.
• Divide a number up to 100 by a 1-digit number.
• Decide whether to round up or down after division to provide a sensible answer to a problem.
• Division is useful for solving real-world problems, such as determining the number of teams in a competition, e.g., 224 ÷ 7 to find the number of 7-a-side football teams.
• Key terms:
  • Dividend: The number being divided.
  • Divisor: The number dividing the dividend.
  • Quotient: The result of the division.
  • Remainder: The amount left over after division.
• Estimation:
  • Round numbers to estimate the quotient, e.g., for 75 ÷ 4, calculate 40 ÷ 4 = 10 and 80 ÷ 4 = 20, so the answer is between 10 and 20, closer to 20.
• Division method (e.g., 75 ÷ 4 = 18 r3):
  • Split the dividend into parts divisible by the divisor: 75 = 40 + 35.
  • Divide each part: 40 ÷ 4 = 10, 35 ÷ 4 = 8 r3 (since 8 × 4 = 32, and 35 - 32 = 3).
  • Combine quotients: 10 + 8 = 18, with remainder 3.
  • Result: 75 ÷ 4 = 18 r3.
• Rounding in context:
  • For practical problems, decide whether to round up or down based on the situation, e.g., if 27 ÷ 8 = 3 r3 for paper plates, round up to 4 packs to ensure enough plates.
• Remainder properties:
  • The highest possible remainder is one less than the divisor, e.g., when dividing by 3, the highest remainder is 2; for 4, it is 3.