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Multiplication of the Algebraic Expressions

(i) Look at the following pattern of stars.
 

Pattern of Stars

Total No. of Stars

* * * * * * *

* * * * * * *

* * * * * * *

3 × 7

3 - rows, 7 columns

* * * * * *

* * * * * *

* * * * * *

* * * * * *

* * * * * *

5 × 6

5 - rows, 6 columns

m ×n

m rows, n - columns

 

(m + 2) × (n + 1)

(m + 2) rows

(n + 1) columns

 


To find the number of stars we have to multiply the expression for the number of rows by the expression for the number of columns.

 

The above pattern of stars shows the rectangle shape. We can think of area of a rectangle. The area of a rectangle is l × b, where l is the length and b is the breadth.

 

If the length of the rectangle is increased by 3 units.
 

Example :(l + 3) and breadth decreased by 8 units,

 

Example : (b - 8) then the area of the new rectangle will be (l + 3) (b - 8)

 


(iii) Consider an example of chalk box. What is the volume of chalk box?

Chalk box is rectangular in shape. Then the volume is given by

Length × breadth × height
 

(iv) When we buy or sell things of same type we have to carry multiplication.

For example, if cost of one dozen of apples is Rs. x and Sita buys z dozens of apples for a picnic. Find the cost which she has to pay.

Price of Apples per dozen = Rs.x

For picnic apples needed = z dozens

Cost sita has to pay = Rs. (xz)

Suppose, the price per dozen was less by Rs. 4 and the apples needed were less by 6 dozens.

Price of aples per dozen = Rs (x - 4)

Apples needed = (z- 6) dozens

Then Sita has to pay = Rs. (x - 4) × (z - 6)





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