Practice Questions

Define integers.

List all the integers between $-5$ and $2$ in increasing order.

What is the additive inverse of the integer $-21$?

Name the integer that is neither positive nor negative.

Explain how to compare the integers $-9$ and $-4$ using a number line. State which is greater.

A diver is at a depth of 25 meters below sea level. He swims 10 meters upwards. Calculate his new position relative to the sea level.

Calculate the value of the expression: $(+18) + (-25)$.

Formulate a real-world problem involving a submarine's depth that can be represented by the expression $(-200) + (+75)$.

The temperature in a high-altitude laboratory is kept at $-18^\circ\text{C}$. For an experiment, a substance is first warmed by $25^\circ\text{C}$, then cooled by $12^\circ\text{C}$, and finally warmed again by $5^\circ\text{C}$. Formulate a single mathematical expression using integers to find the final temperature of the substance and evaluate it.

List three examples of real-world contexts where negative numbers are used.

A student solved $(-5) - (-8)$ and got the answer $-13$. Critique this solution, explain the error in their reasoning, and propose the correct method to solve it.

Justify the statement: "Subtracting a larger positive integer from a smaller positive integer always results in a negative integer." Use a number line example to support your argument.

A student argues that since 0 is neither positive nor negative, it cannot have an additive inverse because inverses come in positive/negative pairs like $(+3, -3)$. Critique this argument and propose a correct explanation for the additive inverse of 0.

Solve the following expression: $(-32) - (+18) + (-50) - (-20)$.

From the sum of $33$ and $-47$, subtract $-84$.

In a quiz, a team scores $+10$ points for a correct answer and $-5$ points for an incorrect answer. The team answered 8 questions correctly and 5 questions incorrectly. They did not attempt 2 questions, for which they get 0 points. Calculate the team's final score.

A shopkeeper records a profit as a positive integer and a loss as a negative integer. Over five consecutive days, the shop's performance was: a profit of ₹450, a loss of ₹200, a loss of ₹150, a profit of ₹300, and a loss of ₹50. Calculate the net profit or loss for the shopkeeper over these five days.

Identify all the negative integers from the following list: $12, -5, 0, \frac{3}{4}, -1, 2.5, -100$.

Describe the concept of a 'zero pair' as used in the token model for integers. Explain why it is useful for addition.

Evaluate the two expressions: A) $(+9) - (+14)$ and B) $(+9) + (-14)$. Justify why they produce the same result by explaining the relationship between subtraction and the addition of an additive inverse.

A student claims, "The difference between two negative integers is always a negative integer." Justify whether this statement is always true, sometimes true, or never true. Provide one example where it is true (if possible) and one where it is false (if possible).

Summarize how to perform the subtraction $(-4) - (-6)$ using the token model.

Explain the relationship between subtraction and addition of integers. Use the expression $(+8) - (+3)$ as an example.

Describe, with the help of a diagram, how to represent the addition problem $(+3) + (-8)$ on a number line. Explain each step of the process.

Explain how subtraction of integers can be interpreted in two different ways using the "Bela's Building of Fun" analogy. Use the problem $(+2) - (-3)$ to illustrate both interpretations.

Create a sequence of exactly three operations (addition or subtraction) that starts at an initial value of $-5$ and arrives at a final value of $+10$. You must use three different non-zero integers of your choice. Write the complete expression.

Compare the integers $-43$ and $-34$ using the symbols $<$ or $>$. Justify your answer using the number line concept.

An elevator is on the 15th floor. It goes down 20 floors and then up 8 floors. Calculate the floor the elevator is on now.

Rohan starts with a balance of ₹2500 in his bank account. He deposits ₹1200, then withdraws ₹3000, and finally withdraws another ₹500. Calculate his final account balance.

A point is at $-5$ on the number line. It moves 11 units to the right and then 15 units to the left. Demonstrate this movement on a number line and calculate its final position.

Design a path on a number line that starts at $-4$, includes exactly one addition and one subtraction of two different integers, and ends at $+6$. The integers used for the operations must be between $-10$ and $+10$. Write down the mathematical expression representing your designed path.

Solve the equation to find the value of $k$: $(-9) + k = 5$.

The temperature in a city was $5^\circ\text{C}$ in the afternoon. It dropped by $8^\circ\text{C}$ at night. The next morning, it rose by $2^\circ\text{C}$. Calculate the temperature in the morning.

Propose an integer value for the box to make the statement $(-12) - (\Box) > 0$ true. Justify why your chosen value works.

A submarine is located at a depth of 150 meters below sea level. It performs the following maneuvers in order:

1. Ascends 60 meters.
2. Dives 200 meters.
3. Ascends 90 meters. Calculate the final depth of the submarine. Also, determine its change in position relative to its starting point.

A bank account has a starting balance of ₹150. Describe the final balance after the following transactions by explaining each step in terms of integer addition.

1. A debit of ₹80.
2. A credit of ₹120.
3. A debit of ₹250.

Analyze and determine which expression is greater: A = (-10) + (-5) or B = (-10) - (-5). Show your calculations.

Design a $2 \times 2$ grid and fill it with four different integers such that the sum of the integers in each of the two rows and each of the two columns is equal to $-4$. Justify your design by showing the calculations.

State Brahmagupta's rule for adding a positive number and a negative number. Provide one example for each of the three possible outcomes described in the rule.

The sum of two integers is $-16$. If one of the integers is $53$, calculate the other integer.

Summarize Brahmagupta's five rules for the addition of integers (positive, negative, and zero). For each rule, provide a unique numerical example.