Long Multiplication Method for 8-Year-Olds: One-Digit Number on Top

Let's multiply 2,141,638,669 × 4 using long multiplication (start from the right):

2141638669 × 4

9 × 4 = 36 → write 6, carry 3 6 × 4 = 24 + 3 = 27 → write 7, carry 2 6 × 4 = 24 + 2 = 26 → write 6, carry 2 8 × 4 = 32 + 2 = 34 → write 4, carry 3 3 × 4 = 12 + 3 = 15 → write 5, carry 1 6 × 4 = 24 + 1 = 25 → write 5, carry 2 1 × 4 = 4 + 2 = 6 → write 6, carry 0 4 × 4 = 16 + 0 = 16 → write 6, carry 1 1 × 4 = 4 + 1 = 5 → write 5, carry 0 2 × 4 = 8 → write 8

Reading the result from left to right gives: 8,566,554,676.

Check: double the number twice (×2 then ×2 again) also gives 8,566,554,676. So the answer is 8,566,554,676.

7 × 8 = 56.

Here’s a simple way to see it:

• Count by 8 seven times: 8 + 8 + 8 + 8 + 8 + 8 + 8 = 56.
• Or imagine 7 groups with 8 things in each group. All together that’s 56 things.

So the answer is 56. Would you like another one to try?

Let's multiply 38 × 62 step by step:

1) Write the numbers: 38 × 62

2) Multiply by the ones digit (2): 8 × 2 = 16 → write 6, carry 1 3 × 2 = 6, plus carry 1 = 7 So first row: 76 (this is 38 × 2)

3) Multiply by the tens digit (6). Remember 6 stands for 60, so we put a 0 under the ones place: 8 × 6 = 48 → write 8, carry 4 3 × 6 = 18, plus carry 4 = 22 So second row: 228 → write it as 2280 because it's really 60 × 38 (shift one place)

4) Add the two rows: 76 +2280

2356

Answer: 38 × 62 = 2356.

Great — let’s do 29 × 56 step by step using long multiplication.

1) Write the numbers: 29 × 56

2) Multiply by the ones digit (6): 6 × 9 = 54 → write 4, carry 5 6 × 2 = 12, plus carry 5 → 17 First row: 174

3) Multiply by the tens digit (5). Remember this 5 is actually 50, so we put a 0 at the end: 5 × 9 = 45 → write 5, carry 4 5 × 2 = 10, plus carry 4 → 14 Second row (with the zero): 1450

4) Add the two rows: 1450

• 174

  1624

So, 29 × 56 = 1624.

Want to try another one together?

Let's do it step by step like in your example. We multiply 345051166720 by 4, digit by digit from right to left and carry when needed.

Start with the number and the 4: 345051166720 × 4

Work from the rightmost digit:

• 0 × 4 = 0 → write 0
• 2 × 4 = 8 → write 8
• 7 × 4 = 28 → write 8, carry 2
• 6 × 4 = 24, plus carry 2 = 26 → write 6, carry 2
• 6 × 4 = 24, plus carry 2 = 26 → write 6, carry 2
• 1 × 4 = 4, plus carry 2 = 6 → write 6
• 1 × 4 = 4 → write 4
• 5 × 4 = 20 → write 0, carry 2
• 0 × 4 = 0, plus carry 2 = 2 → write 2
• 5 × 4 = 20 → write 0, carry 2
• 4 × 4 = 16, plus carry 2 = 18 → write 8, carry 1
• 3 × 4 = 12, plus carry 1 = 13 → write 13 at the left (two digits)

Now put all those results together (from left to right): 1,380,204,666,880

So 345051166720 × 4 = 1,380,204,666,880.

Quick check: doubling twice gives the same result: 345051166720 × 2 = 690102333440, and × 2 again = 1,380,204,666,880.

Let's do 38 × 62 step by step.

Write the numbers one above the other: 38 × 62

1) Multiply by the ones digit (2):

• 2 × 8 = 16 → write 6, carry 1.
• 2 × 3 = 6; add the carry 1 → 7. So the first partial product is 76: 38 × 62

  ---

  76 (this is 38 × 2)

2) Multiply by the tens digit (6). Remember 6 means 60, so we will put a zero at the end of this partial product:

• 6 × 8 = 48 → write 8, carry 4.
• 6 × 3 = 18; add the carry 4 → 22. So 6 × 38 = 228. Because it's tens (60), write 2280: 38 × 62

  ---

  76 2280 (this is 38 × 60)

3) Add the partial products: 2280

• 76

  2356

So, 38 × 62 = 2356.

Quick check: 40 × 60 = 2400, and our answer 2356 is close, so it looks reasonable.

Let's do long multiplication with 9 (one-digit on top) using the same steps you know. Multiply each digit of 345051166720 by 9 starting from the right and keep the carry:

Write the problem: 9 ×345051166720 ——————

Step-by-step (right to left):

• 0 × 9 = 0 → write 0, carry 0
• 2 × 9 = 18 → write 8, carry 1
• 7 × 9 = 63, plus carry 1 = 64 → write 4, carry 6
• 6 × 9 = 54, plus carry 6 = 60 → write 0, carry 6
• 6 × 9 = 54, plus carry 6 = 60 → write 0, carry 6
• 1 × 9 = 9, plus carry 6 = 15 → write 5, carry 1
• 1 × 9 = 9, plus carry 1 = 10 → write 0, carry 1
• 5 × 9 = 45, plus carry 1 = 46 → write 6, carry 4
• 0 × 9 = 0, plus carry 4 = 4 → write 4, carry 0
• 5 × 9 = 45, plus carry 0 = 45 → write 5, carry 4
• 4 × 9 = 36, plus carry 4 = 40 → write 0, carry 4
• 3 × 9 = 27, plus carry 4 = 31 → write 31 (leftmost)

Now put the written digits together (left to right): 31 0 5 4 6 0 5 0 0 4 8 0

So the answer is: 3,105,460,500,480.

(Quick check: 345051166720 × 10 = 3,450,511,667,200; subtract the original number to get ×9 → 3,105,460,500,480.)