Tag: division of integers and its properties

Questions Related to division of integers and its properties

Observe the given multiplies of 37
$\displaystyle 37\times 3$ = 111
$\displaystyle 37\times 6$ = 222
$\displaystyle 37\times 9$ = 333
$\displaystyle 37\times 12$ = 444
-----------------------------------------------
-----------------------------------------------
Find the product of $\displaystyle 37\times 27$ ?

maths multiplication and division of integers division of integers and its properties multiplying and dividing integers multiplication of integers

  1. 999

  2. Greatest 3 digit number

  3. Either A or B

  4. Smallest 3-digit number

Show answer
Correct Option: C
Explanation:

$\displaystyle 37\times 3=37\times \left ( 3\times 1 \right )=111$
$\displaystyle 37\times 6=37\times \left ( 3\times 2\right )=222$
$\displaystyle 37\times 9=37\times \left ( 3\times 3\right )=333$
------------------------------------------
------------------------------------------
$\displaystyle 37\times 27=37\times \left ( 3\times 9 \right )=999$

The value of $555 \displaystyle \times   193 - 555 \displaystyle \times  93$ is

maths multiplication and division of integers division of integers and its properties multiplying and dividing integers multiplication of integers

  1. $555,931$

  2. $1,210,321$

  3. $53,912$

  4. $55,500$

Show answer
Correct Option: D
Explanation:

Solving the given expression,
$555$  $\displaystyle \times  $ $193 - 555$ $\displaystyle \times  $ $93$
$= 555 \displaystyle \times    (193 - 93)$
$= 555 \displaystyle \times   100 = 55500$

(-32) $\displaystyle \div  $ (-4)

maths multiplication and division of integers division of integers and its properties multiplying and dividing integers multiplication of integers

  1. +8

  2. -18

  3. +18

  4. -8

Show answer
Correct Option: A
Explanation:

$\dfrac{-32}{-4}$ = 8 

Solve $-132\div11$

maths multiplication and division of integers division of integers and its properties multiplying and dividing integers multiplication of integers

  1. $+101$

  2. $-101$

  3. $+11$

  4. $-12$

Show answer
Correct Option: D
Explanation:

We can write $-132÷11$ as $-132×\dfrac 1{11}$

Or, $\dfrac{-132}{11} =(-12)$

So option D is the correct answer.

Product of two integers with unlike signs is

maths multiplication and division of integers division of integers and its properties multiplying and dividing integers multiplication of integers

  1. negative

  2. 0

  3. positive

  4. none

Show answer
Correct Option: A
Explanation:

Negative

Solve ($-144\displaystyle \div  16$) 

maths multiplication and division of integers division of integers and its properties multiplying and dividing integers multiplication of integers

  1. $+9$

  2. $+11$

  3. $-9$

  4. $-11$

Show answer
Correct Option: C
Explanation:

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

-144/16 = -9
So option C is the correct answer.

If the dividend and divisor have unlike signs then the quotient will be _____

maths multiplication and division of integers division of integers and its properties multiplying and dividing integers multiplication of integers

  1. positive

  2. negative

  3. zero

  4. none

Show answer
Correct Option: B
Explanation:

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


Division of Integers is similar to the division of whole numbers (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 quotient will be positive.
(-16) ÷ (-4) = +4

If only one of the dividend or divisor is negative, the quotient will be negative.
(+16) ÷ (-4) = -4     or      (-16) ÷ (+4) = -4

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

-112 $\displaystyle \times $ _____ = +112

maths multiplication and division of integers division of integers and its properties multiplying and dividing integers multiplication of integers

  1. +1

  2. 0

  3. -1

  4. +112

Show answer
Correct Option: C
Explanation:

-112 $\displaystyle \times $ (-1) = +112

Evaluate $-12\displaystyle \times 21$ 

maths multiplication and division of integers division of integers and its properties multiplying and dividing integers multiplication of integers

  1. $-2412$

  2. $-242$

  3. $-252$

  4. $+252$

Show answer
Correct Option: C
Explanation:

The product of a negative and a positive number is always a negative number.


$-12×21= (-252)$


So option C is the correct answer.

Evaluate $(-6)$ $\displaystyle \times $ $(-2) $

maths multiplication and division of integers division of integers and its properties multiplying and dividing integers multiplication of integers

  1. $-8$

  2. $+8$

  3. $-12$

  4. $+12$

Show answer
Correct Option: D
Explanation:

The product of two negative numbers is always a positive number.


So, $-6×(-2)= +12$


So option D is the correct answer.