Q. 43.7( 3 Votes )

# Shown below is a method to the product 46× 28.i) Check this method for some other two-digit numbers.ii) Explain why this is correct, using algebra. (Recall that any two-digit number can be written 10m + n, as seen in the section, Two-digit numbers of the lesson, Numbers and Algebra, in the class 7 textbook).

Answer :

i)

ii) We know that we can express any 2-digit number as 10m+n , where m is the digit at tens place and n is the digit at ones place.

So, let (10m+n) and (10x+y) be the two numbers to be multiplied.

(10m+n)(10x+y) = 10m(10x+y)+n(10x+y) = 100 mx +10my +10nx + ny

= (100× mx) + ((m×y)+(n×x))× 10 +(n×y)

Now, carefully observe the above method, you will see that we were finding these terms only and then addition of these terms gives us the required product.

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