Hi! I'm Vidi. Let's learn Multi-Digit Multiplication together — read with me, then play the games to win a ⭐!
🔵Multiply 4-Digit by 1-Digit
Multiplying a 4-digit number by a 1-digit number means repeated addition. We use the column method (standard algorithm) with carrying.
Steps:
- Align numbers by the rightmost digit
- Multiply each digit from right to left
- If the product has two digits, write the units digit and carry the tens digit
- Add the carry to the next multiplication
Example: 4,523 x 4 = 18,092
👀 See a worked example
Multiply 4,523 x 4.
Step 1: 4x3=12, write 2 carry 1. Step 2: 4x2=8+1=9, write 9. Step 3: 4x5=20, write 0 carry 2. Step 4: 4x4=16+2=18, write 18. Answer: 18,092.
Multiply 7,068 x 8.
Step 1: 8x8=64, write 4 carry 6. Step 2: 8x6=48+6=54, write 4 carry 5. Step 3: 8x0=0+5=5, write 5. Step 4: 8x7=56, write 56. Answer: 56,544.
A stadium has 2,456 seats. Each ticket costs Rs.9. What is the total collection for a full house?
Multiply 2,456 x 9. 9x6=54 (write 4, carry 5). 9x5=45+5=50 (write 0, carry 5). 9x4=36+5=41 (write 1, carry 4). 9x2=18+4=22. Answer: Rs.22,104.
🤖 Vidi's Key Points
- Align numbers so the rightmost digits line up
- Multiply from right to left — ones, tens, hundreds, thousands
- When product has two digits, write units and carry tens to next column
- Always add the carry before writing the final digit
🟢Multiply 2-Digit by 2-Digit (Area Model)
When multiplying by a 2-digit number, we split it into two parts and multiply separately, then add the partial products.
Area Model: Break both numbers into tens and ones, then multiply each part.
Example: 23 x 45 = (20+3) x (40+5) = 800 + 100 + 120 + 15 = 1,035
Column Method:
- Multiply by the ones digit first
- Then multiply by the tens digit (add a placeholder zero)
- Add both partial products
👀 See a worked example
Multiply 34 x 26.
Step 1 (ones): 34 x 6 = 204. Step 2 (tens): 34 x 20 = 680. Add: 204 + 680 = 884. Answer: 884.
Multiply 67 x 58.
Step 1: 67 x 8 = 536. Step 2: 67 x 50 = 3,350. Add: 536 + 3,350 = 3,886. Answer: 3,886.
A box has 24 packets. Each packet has 75 pencils. How many pencils are there in total?
Multiply 24 x 75. 24 x 5 = 120. 24 x 70 = 1,680. Total = 120 + 1,680 = 1,800. Answer: 1,800 pencils.
🤖 Vidi's Key Points
- Split the multiplier into tens and ones for easier calculation
- Multiply by ones digit first, then by tens digit (add a zero placeholder)
- Add both partial products to get the final answer
- The Area Model shows visually why the multiplication works
🟣Estimate Products Before Calculating
Estimation helps us check if our answer is reasonable. We round numbers to a convenient value before multiplying.
How to Estimate:
- Round each number to the nearest 10, 100, or 1,000
- Multiply the rounded numbers
- Compare with the actual answer — they should be close
Estimation is especially useful to detect calculation errors!
👀 See a worked example
Estimate and then find the actual product of 487 x 32.
Estimate: 487 rounds to 500; 32 rounds to 30. Estimate = 500 x 30 = 15,000. Actual: 487 x 32 = 15,584. The estimate (15,000) is close to the actual (15,584).
Estimate 2,345 x 7.
Round 2,345 to 2,000. Estimate = 2,000 x 7 = 14,000. Or round to 2,300: 2,300 x 7 = 16,100. Actual: 2,345 x 7 = 16,415. Both estimates are in the right range.
A farmer harvests 1,236 kg of wheat per day. Estimate how much he harvests in a week (7 days).
Round 1,236 to 1,200. Estimate = 1,200 x 7 = 8,400 kg. Actual: 1,236 x 7 = 8,652 kg. The estimate (8,400) is a good approximation.
🤖 Vidi's Key Points
- Round numbers to the nearest 10, 100 or 1,000 before estimating
- Estimation catches big errors in your calculations
- The actual answer should be close to the estimated answer
- Useful in real life when exact calculations are not needed
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