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Multiplying 2 Numbers With The Same Ten's Digit:
A. From algebra we learn:
(10a+b)(10a+c) = 100(a2) + 10(a(b+c)) + bc
B. Using numbers instead of variables we get:
1.
Multiply the one's digits together. Write this down, carry if necessary.
2. Add the
one's digits together and multiply this value times the ten's digit. Write
this down, carry if necessary.
3. Square
the tens digit adding any carried numbers.
C.
Examples:
Ex [1] 37
x 32 = ______
a. 7 x 2 =
14. Write down 4, carry *1.
b. (7 + 2) x
3 = 9 x 3 = 27 + *1 = 28. Write 8, carry *2.
c. 32
= 9 + *2 = 11. Write 11.
d. The
answer is 1184.
Ex [2] 143
x 144 = ______
a. 3 x 4 =
12. Write 2, carry *1.
b. (3 + 4) x
14 = 7 x 14 = 98 + *1 = 99. Write 9, carry *9.
c. 142
= 196 + *9 = 205. Write 205.
d. The
answer is 20592.
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