Multiplying by 101 and 1001 (Fast)

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Multiplying by 101 and 1001 (Fast)Let’s say we need to multiply 3874 × 101 Now, to do this, we make 101 = 100 + 1 3874 × 101 = 3874 × (100 + 1) = 387400 + 3874 Putting 387400 and 3874 below each other to add Since 101 = 100 + 1, we are adding the number to itself shifted by two places. The Rule: Instead of adding the immediate neighbor (like we did for 11), we add the digit that is two places to the right (skip one digit). So, for 3874 × 101, we do these steps Step 1: The Right End. Copy the last two digits down. The last two digits are 74. Write 74. (Current Answer: _ _ _ _ 74) Step 2: Add Neighbors two places to right (moving left). Add the last digit (4) to neighbor with a gap of 1 (8). 4 + 8 = 12. Write down 2 and carry over the 1. (Current Answer: _ _ _ 274) Step 3: Keep Moving Left. Add the next neighbors with a gap of 1: 7 + 3. 7 + 3 = 10. Add the carry (1) = 11. Write down 1 and carry over the 1. (Current Answer: _ _ 1274) Step 4: Keep Moving Left. Then, we get to 8, there is no neighbor with a gap of 1. Add the carry (1) = 8 + 1 = 9. Write down 9. (Current Answer: _ 91274) Step 5: Left end. We get to fist digit 3. There’s no carry. Write down 3. (Current Answer: 391274) Thus, final answer is 391274 Multiplying by 1001Let’s say we need to multiply 3874 × 1001 The Rule: Instead of adding the immediate neighbor (like we did for 11), we add the digit that is three places to the right (skip two digits) So, for 3874 × 1001, we do these steps Step 1: The Right End. Copy the last three digits down. The last three digits are 874. Write 874. (Current Answer: _ _ _ _ 874) Step 2: Add Neighbors three places to right (moving left). Add the last digit (4) to neighbor with a gap of 2 (3). 4 + 3 = 7. Write down 7. (Current Answer: _ _ _ 7874) Step 3: Keep Moving Left. Then, we get to 7, there is no neighbor with a gap of 2. Write down 7 (Current Answer: _ _ 77874) Step 4: Keep Moving Left. Then, we get to 8, there is no neighbor with a gap of 2. Write down 8. (Current Answer: _ 877874) Step 5: Left end. We get to fist digit 3. There’s no carry. Write down 3. (Current Answer: 3877874) Thus, final answer is 3877874