Tutorial 123 |
Multiplying two selected 3-digit numbers (middle digit 5)
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- Select a 3-digit number with a middle digit of 5 (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 the first digit + 3 (keep the carry):
_ _ X _ _.
- The first digit will be the first digit times the next number plus the carry:
X X _ _ _ _.
Repeat those digits from left to right as you get them.
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Example:
- If the first number is 752, choose 758 as the second number (same
first digits, third digits add to 10).
- Last three digits: 0 and the product of the third digits:
2 × 8 = 16: _ _ 0 1 6
- Next digit: first digit + 3: 7 + 3 = 10 (keep carry 1):
_ _ 0 _ _ _
- First two digits: first digit times next number plus carry: 7 × 8 = 56, 56 +
1 = 57: 5 7 _ _ _ _
- So 752 × 758 = 570016.
See the pattern?
- If the first number is 654, choose 656 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: first digit + 3: 6 + 3 = 9: _ _ 9 _ _ _
- First two digits: first digit times next number:
6 × 7 = 42: 4 2 _ _ _ _
- So 654 × 656 = 429024.
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