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## Integers Division Rules

Rule 1: The quotient value of a positive integer number and a negative integer number is negative.

Rule 2: The quotient value of two positive integer numbers is a positive number.

Rule 3: The quotient value of two negative integer numbers is a positive number.

### Division of Integers Rules and Examples

**Question 1: Find the value of ||-17|+17| / ||-25|-42|**

**Solution:**

||-17|+17| / ||-25|-42|

= |17+17| / |25â€“42|

= |34| / |-17|

= 34 / 17

= 2

**Question 2:** Simplify: {36 / (-9)} / {(-24) / 6}

**Solution:**

{36 / (-9)} / {(-24) / 6}

= {36/-9} / {-24/6}

= – (36/9) / – (24/6)

= -4/-4

= 4/4

=1

**Question 3:** Find the value of [32 + 2 x 17 + (-6)] Ã· 15

**Solution:**

[32+2 x 17+(-6)] / 15

= [32+34+(-6)] / 15

= (66-6) / 15

= 60 / 15

= 4

**Question 4:** Divide the absolute values of the two given integers?

**Solution: **

The quotient of the absolute value of integer +24 and the absolute value of integer -8

From the rules given above, dividing the integers with different signs gives the final result as negative.

When positive(+) 24 is divided by negative(-) 8 results negative(-) 3, which can be defined as +24/(-8) = -3

**Question 5:** Prove that [((-8) / (-4)] â‰ =-8 / [(-4) / (-2)]

**Solution:**

From the given question

[((-8)/(-4)]/(-2)] â‰ -8/[(-4)/(-2)]

First of all, we will consider the LHS part i.e., [((-8) / (-4)] / (-2)]

To solve the equation, first, we divide 8 by 4, we get the result as 2

As both numbers have a negative sign, it will be positive.

Then we divide the result (2) by -2, then the final result will be -1.

Therefore, the result of the LHS part is -1.

Now, we consider the RHS part i.e., -8 / [(-4) / (-2)]

First of all, we divide -4 by -2, the result will be 2.

As both the numbers have a negative sign, the result will be positive.

Now, divide -8 by the above result 2.

Hence, the result will be -4.

Therefore, the result of RHS is -4.

Hence, LHS â‰ RHS

The above given equation [((-8) / (-4)] / (-2)] â‰ -8 / [(-4) / (-2)] is thus satisfied.

**Question 6:** In a maths test containing 10 questions, 2 marks are given for every correct answer and (-1) marks are given for every wrong answer. Rohith attempts all the questions and 8 questions answers are correct. What is Rohith’s total score?

**Solution:**

From the given question,

The marks given for every correct answer = 2 marks

Marks given for 8 correct answers = 2 * 8= 16 marks

Marks given for 1 incorrect answer = -1 marks

Marks given for 2 incorrect answers = -1 * 2 = -2 marks

Rohit’s total score = 16-2 = 14 marks

Therefore, the answer is 14 marks.

**Question 7:** Priya sells 20 pens and some pencils losing 2 Rs in all. If Priya gains 2 Rs on each pen and loses 1 Rs on each pencil. How many pencils does Priya sell?

**Solution:**

Suppose that Priya sells x pencils.

Total gain on pens = 2*20 = 40 Rs

Total loss on pencils = 1x = x

Total loss on selling pens and pencils = (-2)

40-x = (-2)

40+2 = x

x = 42

Therefore, Priya sells 42 pencils.

Thus, the answer is 42 pencils.

**Question 8:** To make ice cream, the room temperature must be decreased from 45degree C at the rate of 5 degrees C per hour. What will be the room temperature 12 hours after the freezing point of the icecream?

**Solution:**

As given in the question,

Temperature after 12 hours = 12*5 = 60degree C

Room temperature = 45degree C

Hence, the room temperature after freezing process of 12 hours = (45-60)degree C

= -15degree C

**Question 9:**

A car runs at a rate of 50km/hr. If the car starts at 5 km above the starting point, how long will it take to reach 2505km?

**Solution:**

As per the question,

Total distance covered by car = (2505-5) km = 2500 km

Rate of car = 50km/hr

From the above values, Distance = 2500 km, speed = 50 km/hr

Therefore, the time required by the car = distance/speed

=2500/50 = 50 hours

Therefore, the car will take 50 hours to travel 2505 km.

Hence, The final solution is 50 hours.

**Question 10:** Jason borrowed $5 a day to buy launch. She now owes $65 dollars. How many days did Jane borrow $5?

**Solution:**

As per the question,

Jason borrowed a launch at =Â $5

Now she owes = $65

No of days = (-65) / (-5)

= 13 days

Therefore, Jane borrows $5 for 13 days.

Hence, The final solution is 13 days.

### Division of Integers Word Problems

**Question 11: **Allen’s score in a video game was changed by -120 points because he missed some target points. He got -15 points for each of the missed targets. How many targets did he miss?

**Solution:Â **

As per the given question,

Allen scored points in a video game = -120

He got points for missed targets = -15

No of targets he missed = -120/-15 = 8 targets.

Therefore, he missed 8 targets.

**Question 12:** Karthik made five of his truck payments late and was fined five late fees. The total change in his savings of late fees was -$30. What integer represents the one late fee?

**Solution:**

As given in the question, Karthik has made five of his truck payments. Therefore, it is positive.

He was fined -$30 as the late fees.

To find one late fee, we have to divide the fine by no of payments he did.

Therefore, One Late fee = -$30/5

=-$6

Thus, He paid $6 for each payment as late fees.

Hence, the final answer is -$6.