Tutorial 120 |
Multiplying two selected 3-digit numbers (middle digit 2)
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- Select a 3-digit number with a middle digit of 2.
- 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 6: _ _ 6 _ _.
- The next digit to the left will be 5 times the first digit of the number (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 622, choose 628 as the second number (same
first digits, third digits add to 10).
- 2 × 8 = 16 (multiply the third digits) - last two digits:
_ _ _ _ 1 6.
- The third digit from the right is 6: _ _ 6 _ _ _.
- 5 × 6 = 30 (the next digit to the left is 5 times the first digit (keep carry
3): _ _ 0 _ _ _ .
- 6 × 6 = 36; 64 + 3 = 39 ( the first digits are the square of the first digit
plus the carry: 3 9 _ _ _ _.
- So 622 × 628 = 390616.
See the pattern?
- If the first number is 221, choose 229 as the second number (same
first digits, third digits add to 10).
- 1 × 9 = 9 (multiply the third digits) - last two digits:
_ _ _ 0 9.
- The third digit from the right is 6: _ _ 6 _ _.
- 5 × 2 = 10 (the next digit to the left is 5 times the first digit (keep carry
1): _ 0 _ _ _ .
- 2 × 2 = 4; 4 + 1 = 5 ( the first digits are the square of the first digit plus
the carry: 5 _ _ _ _.
- So 221 × 229 = 50609.
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