Integers Test - 5

The multiplication property states that theproduct of any number and zero is zero. It doesn't matter whatthe number is, when you multiply it to zero, you get zero as theanswer. So: 2 x 0 = 0.

We observe that the product of any whole numberand zero is zero. Multiplicative Identity: If a is anywhole number, then a × 1 = a = 1 × a. In other words, theproduct of any whole number and 1 is the number itself.

$\frac{(-8)\times 8\times (-8)\times (-8)}{(-4)\times (-4)\times (-4)\times (-4)}$

As there are 3 negative numbers in the numerator and 4 inthe denominator, the answer will be negative.

Canceling out the common factors and simplifyingwe get

$\frac{(-8) \times 8 \times (-8) \times (-8)}{(-4) \times (-4) \times (-4)\times (-4)}$=2×−2×2×2=−16

Whenwe multiply negative integer with −1 because we get a positive quantity when wemultiply two negative quantities we get a positive quantity.

Let the number is A.

So, the negative integer = -A

And, square of the integer number = (-A)²

= -A x –A = A² which is a positivenumber.

5.$\overline{63}$

= 5.636363...

Let x = 5.6363         (i)

∴ 100x= 563.6363 (ii)

Subtracting (i) from (ii) we get,

=> 99x = 558 
=> x = $\frac{558}{99}$

Now,

$5.\overline{63}\times 11$

=> $\frac{558}{99}\times 11$

=> 62

Let’ssimplify
$=\frac{39\times (-42)}{-13}$as

= 3 × (−42) – 1 = 3 × (−42)−1

= 126

285 x 10 ÷ ? = 75

⇒ ? =$\frac{285x10}{75}$=38.

Let the other integer is x.

Then according to the problem,

x × (−9) = 72

Or, 

Given,(−32) ÷ (−4)

$\therefore (-32) ÷ (-4) = -32 \times (-1/4)$

= 8

2 negative signs will give resultant division positive.

As there are 2 negative numbers in the numerator and 2 inthe denominator, the answer will be positive.

Canceling out the common factors and simplifying we get

$\frac{5\times (-144)\times (-27)}{-\left(15\right)\times 18\times (-16)}=\frac{9\times 27}{3\times 18}=\frac{9}{2}$

Given, $\frac{(-60) \times (-72)}{36\times (-15)}$

As there are 2 negative numbers in the numerator and 1 inthe Denominator, the answer will be negative.
Cancelling out the common factors and simplifying we get $\frac{(-60)\times (-72)}{36\times (-15)}=-4\times 2 =-8$

Weneed to find x in −319÷x=−11

$\frac{-319}{x}=-11$

(−12)×(−3)×4×(−6)=(36)×4×(−6)

=144×(−6)

=−864

Positive of a negative integer is negative.

Example: + (−40) = −40