Learning Objectives
- Multiply 2-digit and 3-digit numbers by 2-digit numbers
- Divide larger numbers by 1-digit and 2-digit numbers
- Learn different methods of multiplication and division
- Solve word problems using multiplication and division
Key Concepts
Multiplying Larger Numbers
To multiply 45 x 23, break it down: first multiply 45 x 3 = 135, then multiply 45 x 20 = 900, and add them: 135 + 900 = 1035. This is the standard column method. You write one number below the other, multiply by ones first, then by tens, and add the results. Always line up the digits properly!
Smart Multiplication Tricks
You can multiply faster using tricks. To multiply by 10, just add a zero at the end: 35 x 10 = 350. To multiply by 5, multiply by 10 and divide by 2: 24 x 5 = 24 x 10 ÷ 2 = 240 ÷ 2 = 120. To multiply by 25, multiply by 100 and divide by 4: 16 x 25 = 16 x 100 ÷ 4 = 1600 ÷ 4 = 400.
Long Division
Long division is a step-by-step method to divide larger numbers. To divide 756 ÷ 6: How many 6s in 7? One, with 1 left over. Bring down 5 to get 15. How many 6s in 15? Two, with 3 left over. Bring down 6 to get 36. How many 6s in 36? Six exactly. Answer: 126.
Checking Your Work
Always check your multiplication by estimation. If 43 x 28 gives you 1204, estimate: 40 x 30 = 1200. Since 1204 is close to 1200, your answer is probably correct. For division, check by multiplying: if 756 ÷ 6 = 126, then 126 x 6 should give 756. Checking prevents mistakes!
Important Terms
- Column Method: A method of multiplying by writing numbers in columns and multiplying step by step
- Long Division: A step-by-step method for dividing larger numbers
- Quotient: The answer when you divide
- Remainder: What is left over after dividing
- Product: The answer when you multiply
- Estimation: Rounding numbers to check if your answer is reasonable
Quick Revision
- Break multiplication into smaller steps: ones first, then tens
- Multiply by 10: add a zero; by 100: add two zeros
- Multiply by 5: multiply by 10, then halve
- Use long division for dividing larger numbers step by step
- Check: quotient x divisor + remainder = dividend
- Estimate to verify your answer makes sense