Q4 of 95 Page 68

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).

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.


More from this chapter

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3

Look at these:

1 × 4 = (2 × 3) – 2


2 × 5 = (3 × 4) – 2


3 × 6 = (4 × 5) – 2


4 × 7 = (5 × 6) – 2


i) Write the next two lines in this pattern.


ii) If we take four consecutive natural numbers, what is the relation between the products of the first and the last, and the product of the middle two?


iii) Write this as a general principle in algebra and explain it.

 3

Look at these:

1 × 4 = (2 × 3) – 2


2 × 5 = (3 × 4) – 2


3 × 6 = (4 × 5) – 2


4 × 7 = (5 × 6) – 2


i) Write the next two lines in this pattern.


ii) If we take four consecutive natural numbers, what is the relation between the products of the first and the last, and the product of the middle two?


iii) Write this as a general principle in algebra and explain it.

 4

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).

 1

Write number like this:


As in the calendar; mark four numbers in a square and find the difference of diagonal products. Is it the same for all squares of four numbers?