Tag: the integers

Questions Related to the integers

Fill in the blank : 
$[(-12) + (-15)] + (-5) = (-12) + [(-15) + .....]$

maths the integers properties of integer multiplication properties of addition and subtraction of integers propertie of integers

  1. $(-12)$

  2. $(-15)$

  3. $(-5)$

  4. $5$

Show answer
Correct Option: C
Explanation:

Addition is associative for integers
$i.e. (a + b) + c = a + (b + c)$
$\therefore [(-12) + (-15)] + (-5) = (-12) + [(-15) + (-5)]$

So, $C$ is correct.

Simplify using associative property:
$(-5) \times [(-8) \times 2] =$  $....$

maths the integers properties of integer multiplication properties of addition and subtraction of integers propertie of integers

  1. $40$

  2. $-80$

  3. $80$

  4. $-40$

Show answer
Correct Option: C
Explanation:

$(-5) \times [(-8)\times 2] = (-5)\times (2\times (-8))$ (commutative property)
$= [(-5)\times 2] \times (-8)$ (associative property)
$= (-10) \times (-8)$
$= 80$
(Here, we used various properties to skip $(-5)\times (-8)$ which could have been time consuming).

State whether true or false 
The sum of two negative integers is a positive integer. 

maths the integers properties of integer multiplication properties of addition and subtraction of integers propertie of integers

  1. True

  2. False

Show answer
Correct Option: B
Explanation:

The statements is false.

As, take $-2$ and $-3$, these are two negative integers.
Now their sum is $-2+(-3)=-5$, which is again a negative integer.

Suppose we represent the distance above the ground by a positive integer and that below the ground by a negative integer, then answer the following:
An elevator descends into a mine shaft at the rate of $5$meters per minute. What will be its position after one hour? 

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

  1. $250$

  2. $300$

  3. $100$

  4. $50$

Show answer
Correct Option: B
Explanation:

Since, the elevator going down, so the distance covered by it will be represented by a negative integer.
Change in position of elevator in one minute = $-5 m$.
Position of the elevator after $60$ minutes = $(-5)\times 60 =-300\ m$ 

i.e. $ 300\ m$ below ground level.

Integer used to represent $30$ km towards the right:

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

  1. $30$ km left

  2. $-30$ km

  3. $+30$ km

  4. $0$

Show answer
Correct Option: C
Explanation:

The integer used to represent $30$ km towards the west is $ +30 $ km

Hence, the answer is $+30$ km.