Tutorial 122 |
Multiplying two selected 3-digit numbers (middle digit 4)
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- Select a 3-digit number with a middle digit of 4 (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 three digits will be 0 and the product of the third digits: _ _ _ 0
X X.
- The third digit from the right will be 9 times the first digit + 2 (keep the
carry): _ _ X _ _.
- The first two 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 541, choose 549 as the second number (same
first digits, third digits add to 10).
- Last three digits: 0 and the product of the third digits: 1 × 9 = 9: _ _ 0 0
9
- Next digit: 9 times the first digit + 2: 9 × 5 = 45, 45 + 2 = 47 (keep carry
4): _ _ 7 _ _ _
- First two digits: square the first and carry: 5 × 5 = 25, 25 + 4 = 29: 2 9 _
_ _ _
- So 541 × 549 = 297009.
See the pattern?
- If the first number is 344, choose 346 as the second number (same
first digits, third digits add to 10).
- Last three digits: 0 and the product of the third digits: 4 × 6 = 24: _ _ 0 2
4
- Next digit: 9 times the first digit + 2: 9 × 3 = 27, 27 + 2 = 29 (keep carry
2): _ _ 9 _ _ _
- First two digits: square the first and carry: 3 × 3 = 9, 9 + 2 = 11: 1 1 _ _
_ _
- So 344 × 346 = 119024.
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