Properties of Integers

In a class test $+3$ marks are given for every correct answer and $-2$ marks are given for every incorrect answer and no marks for not attempting any question. Mohini scores $-5$ marks in this test, though she has got $7$ correct answers. How many questions has she attempted incorrectly?

In a class test $+3$ marks are given for every correct answer and $-2$ marks are given for every incorrect answer and no marks for not attempting any question. Radhika scored $20$ marks. If she has got $12$ correct answers, how many questions has she attempted incorrectly?

A cement company earns a profit of $₹9$ per bag of white cement sold and a loss of $₹5$ per bag of grey cement sold.

What is the number of white cement bags it must sell to have neither profit nor loss if the number of grey bags sold is $5400$.

A cement company earns a profit of $₹9$ per bag of white cement sold and a loss of $₹5$ per bag of grey cement sold.

The company sells $7000$ bags of white cement and $6000$ bags of grey cement in a month. What is its profit or loss?
 

In a class test containing 15 questions, 4 marks are given for every correct answer and (–2) marks are given for every incorrect answer.

Bharathi attempts all questions but only 9 answers are correct. What is her total score?

Take at least five pairs of integers and check whether they are closed under division?

Take at least 5 pairs of integers and observe whether the division of integers is associative or not?
 

An elevator descends into a mine shaft at the rate of $6$ meters per minute. If the descent starts from $10 \mathrm{m}$ above the ground level, how long will it take to reach $-350 \mathrm{m}$.

The temperature at $12$ noon was $10°\mathrm{C}$ above zero. If it decreases at the rate of $2°\mathrm{C}$ per hour until midnight, at what time would the temperature be $8°\mathrm{C}$ below zero? What would be the temperature at midnight?

$0 ÷ 1=$_____

$50 ÷ 0=$_____ $\left(0/\text{Not Defined}\right)$

If $k÷1=–49$ then $k=$_____.

If $\frac{-25}{k}=25$ then $k=$_____.

Take at least $5$ pairs of integers and observe whether the division of integers is commutative or not?

Take at least $5$ different pairs of integers and see if subtraction is commutative.

Find the product, using suitable properties.

$(–57)\times (–19)+57$

Find the product, using suitable properties.
$\left(-17\right)\times \left(-29\right)$

Find the product, using suitable properties.

$7\times (50–2)$

Find the product, using suitable properties.

$625\times (–35)+(–625)\times 65$

Find the product, using suitable properties.

$(–41)\times 102$