# 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

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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