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Addition : Addition is the mathematical operation that describes increasing a number by an amount equal to a second number. The mathematical symbol for addition is the plus sign $+.$ The term addition is also used for a generalization of this basic operation on numbers to functions, vectors and matrices.
Partial products method : A method for calculating a product of two multi-digit numbers by writing both numbers as a sum of ones, tens, hundreds and so on, then multiplying each pair of terms and finally summing up all the terms. For example $12\cdot 34=(10+2)\cdot(30+4)$ $=10\cdot 30+10\cdot 4+2\cdot 30+2\cdot 4$ $=300+40+60+8=408.$
Sum : A sum is the result of an addition.
Zero : The number 0.
We want to calculate 89×38 using the partial products method. That means we have to calculate the sum on the right side of $89\cdot38=80\cdot 30+80\cdot 8+9\cdot 30+9\cdot 8.$ What is $80\cdot 30?$