Integers Test - 8

The positive integer 144 can be divided by a negativeinteger −12 as follows:

144 ÷ −12 = $\frac{144}{12}$=-12

Hence, 144 ÷ −12 = −12

As there is 1 negative number in the numerator and 1 in thedenominator, the answer will be positive.

Cancelling out the common factors and simplifying we get
$\frac{-18\times 5}{3\times \left(-10\right)}=3$

Let the two integers be x and y. One of the integers isgiven, that is −16. So let y = −16

Also, it is given that one integer is greater than the otherby +4. Therefore, we have:

x – y = +4

⇒ x− (−16) = 4

⇒ x + 16 = 4

⇒ x = 4 – 16

⇒ x = −12

Hence, the other integer is −12.

If the dividend and divisor have unlike signs then thequotient will be Negative.

Division of Integers is similar to the division of wholenumbers (both positive) except the sign of the quotient needs to be determined.

If both the dividend and divisor are positive,the quotient will be positive.

(+16) ÷ (+4) = +4

If both the dividend and divisor are negative, the quotientwill be positive.

(-16) ÷ (-4) = +4

If only one of the dividend or divisor is negative, thequotient will be negative.

(+16) ÷ (-4) = -4    or      (-16) ÷ (+4) = -4

In other words, if the signs are the same the quotient willbe positive, if they are different, the quotient will be negative

Hence Option B

3 ×1 = -3

The product of any number and zero is zero.

Theorem: 0 × a = 0 for any integer a.

So option B is the correct answer.

(148)÷(−4)=−148÷4=−37

96 × (−25) ÷ (−75) × (−16)

= − 2400 ÷ 1200

= −2

7290+ 290 = 7580

Let the other integer be x. One of the integers is giventhat is −6.

Also, it is given that the product of the twointegers is −48. Therefore, we have:

$x\times (-6)=-48$
$\Rightarrow -6x=-48$
$\Rightarrow 6x=48$
$\Rightarrow x=\frac{48}{6}$
x = 08

Hence, the other integer is +8.

When you divide a negative number by a positive number thenthe quotient is negative. When you divide a positive number by a negativenumber then the quotient is also negative. So, in this case,

-9855/27 = -365

So option C is the correct answer.

Ifthe dividend and divisor have same signs then the quotient will be positive.

Fore.g.- $\frac{132}{12}=11 and \frac{-132}{-12}=11$

Let 2 and -3 be the two factors.

Clearly, 2 × -3 = −6, which is negative.

Hence, Option B is correct.

Multiplication of 2 negative integers results into positiveinteger.

If we multiply 3 negative integers, then the result will benegative integer

Now if we multiply 4 positive numbers with 3 negativeintegers we will get a negative integer because multiplication of negative andpositive integer will always result in negative integer.

Hence option A is correct.