Multiplication of integer worksheet with answer

Q.1 State the sign of the products without actually multiplying the integers 

(i) (-8)×(-3)×(-4)×(-6) 

(ii) (-5)×(-10)×(-9) 

(iii) 1×(-6)×4×(-2) 

Q.2 Find the product of following 

(i) -18×19 

(ii) 100000×1 

(iii) (-1)×537 

(iv) -11×(-11)×(-11) 

Q.3 Find the following products using suitable properties 

(i) 725×(-35)+(-725)×65 

(ii) 8×67×(-125)×(-1) 

(iii) 8225×999+8225 

Answer key 

To solve these problems, you must know the multiplication properties of integer

Q.1 State the sign of the products without actually multiplying the integers 

(i) (-8)×(-3)×(-4)×(-6) 

(ii) (-5)×(-10)×(-9) 

(iii) 1×(-6)×4×(-2) 

Solution: (i) 

(-8)×(-3)×(-4)×(-6) 

Consider only signs of given numbers 

(-1)×(-1)×(-1)×(-1) 

If even numbers of the negative integer are multiplied together ,then the product obtained is a positive integer 

{(-1)^4}=1 

Sign of its product is positive 

(ii) (-5)×(-10)×(-9) 

Consider only signs of given numbers 

(-1)×(-1)×(-1) 

If odd numbers of the negative integer are multiplied together, then the product obtained is a negative integer 

{(-1)³}=-1 

Sign of its product is positive 

(iii) 1×(-6)×4×(-2) 

Consider only signs of given numbers 

(+)×(-)×(-)×(+) 

Two given numbers are already positive, and the number of negative numbers is even. So ,their final product will positive 

(+) ×(-)²=+ × (+) = + 

Sign of its product is positive 

Q.2 Find the product of following 

(i) -18×19 

(ii) 100000×1 

(iii) (-1)×537 

(iv) -11×(-11)×(-11) 

Solution: 

(i) -18×19 

We can it as (-1) ×18×19 

=(-1) × 342 

Here an odd number of a negative integer is being multiplied, then the obtained product will negative integer 

= -342 

(ii) 100000×1 

We know, a property of multiplication of integer 

so, 100000×1 =100000

(iii) (-1)×537 

Here an odd number of a negative integer is being multiplied, then the obtained product will negative integer 

(-1)×537 =-537 

(iv) -11×(-11)×(-11) 

We can write it as (-1) ×(-1) ×(-1) ×11×11×11

Here odd numbers of the negative integer are being multiplied, then the obtained product will negative integer 

(-1)×1331

=-1331 

Q.3 Find the following products using suitable properties 

(i) 725×(-35)+(-725)×65 

(ii) 8×67×(-125)×(-1) 

(iii) 8225×999+8225 

Solution: 

(i) 725×(-35)+(-725)×65 

We know ,distributive law of multiplication over addition 

= 725{(-35)+(-65) }

= 725{-35-65}

=725{-100}

= -72500 

(ii) 8×67×(-125)×(-1) 

= 8×67×125                     [(-125)×(-1)=125 ]

= 8×8375 

= 67000 

(iii) 8225×999+8225 

=8225{(999+1)}

=8225{1000}

= 8225000

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