Tutorial 121 |
Multiplying two selected 3-digit numbers (middle digit 3)
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- Select a 3-digit number with a middle digit of 3 (last digit not zero).
- Choose a multiplier with the same first two digits, whose third digit sums to
10 with the third digit of the first 3-digit number.
- The last two digits will be the product of the third digits: _ _ _ _ X X.
- The third digit from the right will be 2: _ _ 2 _ _.
- The next digit to the left will be 7 times the first digit of the number plus
1 (keep carry): _ _ X _ _ _.
- The first digits will be the square of the first digit plus the carry: X X _
_ _ _.
As you determine the digits in the answer from right to left, repeat them to yourself
at each step until you have the whole answer.
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Example:
- If the first number is 631, choose 639 as the second number (same
first digits, third digits add to 10).
- 1 × 9 = 09 (multiply the third digits) - last two digits:
_ _ _ _ 0 9.
- The third digit from the right is 2: _ _ 2 _ _ _.
- 7 × 6 = 42, 42 + 1 = 43 (the next digit to the left is 7 times the first digit
plus 1 (keep carry 4): _ _ 3 _ _ _ .
- 6 × 6 = 36; 36 + 4 = 40 ( the first digits are the square of the first digit
plus the carry: 4 0 _ _ _ _.
- So 631 × 639 = 403209.
See the pattern?
- If the first number is 236, choose 234 as the second number (same
first digits, third digits add to 10).
- 6 × 4 = 24 (multiply the third digits) - last two digits: _ _ _ _ 2 4.
- The third digit from the right is 2: _ _ 2 _ _ _.
- 7 × 2 = 14, 14 + 1 = 15 (the next digit to the left is 7 times the first digit
plus 1 (keep carry 1): _ _ 5 _ _ _ .
- 2 × 2 = 4; 4 + 1 = 5 ( the first digits are the square of the first digit plus
the carry: 0 5 _ _ _ _.
- So 236 × 234 = 55224.
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