Tutorial 39 |
Squaring a 2-digit number ending in 9
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- Choose a 2-digit number ending in 9.
- The last digit of the answer is always 1: _ _ _ 1
- Multiply the first digit by 8 and add 8 (keep the carry): _ _ X _
- Multiply the first digit by the next consecutive number and
add the carry: the product is the first two
digits: XX _ _.
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Example:
- If the number is 39:
- The last digit of the answer is 1: _ _ _ 1
- Multiply the first digit (3) by 8 and add 8 (keep the
carry): 8 × 3 = 24, 24 + 8 = 32; the next digit of
the answer is 2 (keep carry 3): _ _ 2 1
- Multiply the first digit (3) by the next number (4)
and add the carry (3): 3 × 4 = 12, 12 + 3 = 15
(the first two digits): 1 5 _ _
- So 39 × 39 = 1521.
See the pattern?
- For 79 × 79
- The last digit of the answer is 1: _ _ _ 1
- Multiply the first digit (7) by 8 and add 8 (keep the
carry): 8 × 7 = 56, 56 + 8 = 64; the next digit of
the answer is 4 (keep carry 6): _ _ 4 1
- Multiply the first digit (7) by the next number (8)
and add the carry (6): 7 × 8 = 56, 56 + 6 = 62
(the first two digits): 6 2 _ _
- So 79 × 79 = 6241.
Practice other examples using this pattern, and in no time you'll be able
to give these squares faster than someone using a calculator.
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