Integers Mastery: Number Lines, Order, and Operations (Grade 6)

1. True / False (1 pts)

Zero is its own additive inverse.

✓ Answer

True

2. True / False (1 pts)

The absolute value of any integer is always positive.

✓ Answer

False

3. True / False (1 pts)

Moving left on a number line decreases the value of an integer.

✓ Answer

True

4. True / False (1 pts)

The sum of two odd negative integers is a negative even integer.

✓ Answer

True

5. True / False (1 pts)

The difference of two equal integers is zero.

✓ Answer

True

6. True / False (1 pts)

-3 is greater than -1.

✓ Answer

False

7. True / False (1 pts)

The product of a positive and a negative integer is positive.

✓ Answer

False

8. True / False (1 pts)

The opposite of the predecessor of 2 is -1.

✓ Answer

True

9. True / False (1 pts)

Any integer added to zero remains unchanged.

✓ Answer

True

10. True / False (1 pts)

There are infinitely many integers between 0 and 1.

✓ Answer

False

11. Multiple Choice (2 pts)

Which integer has the greatest value?

✓ Answer

B. -3

12. Multiple Choice (2 pts)

Which integer is 7 units to the left of 0 on the number line?

✓ Answer

B. -7

13. Multiple Choice (2 pts)

The successor of -9 is

✓ Answer

B. -8

14. Multiple Choice (2 pts)

How many integers are strictly between -3 and 2?

✓ Answer

B. 4

15. Multiple Choice (2 pts)

Which integer best represents a deposit of ₹350?

✓ Answer

C. 350

16. Multiple Choice (2 pts)

Start at -2 and move 6 steps to the right. Where do you land?

✓ Answer

B. 4

17. Multiple Choice (2 pts)

Evaluate (-5) + (-7).

✓ Answer

A. -12

18. Multiple Choice (2 pts)

Evaluate 18 - (-9).

✓ Answer

B. 27

19. Multiple Choice (2 pts)

The opposite of -14 is

✓ Answer

C. 14

20. Multiple Choice (2 pts)

Which list is ordered from least to greatest?

✓ Answer

A. -5, -2, 0, 3

21. Fill in the Blank (2 pts)

The integer located 10 units to the right of 0 is _____.

✓ Answer

10

22. Fill in the Blank (2 pts)

The additive inverse of 23 is _____.

✓ Answer

-23

23. Fill in the Blank (2 pts)

The absolute value | -12 | equals _____.

✓ Answer

12

24. Fill in the Blank (2 pts)

A withdrawal of $45 can be represented by the integer _____.

✓ Answer

-45

25. Fill in the Blank (2 pts)

To subtract an integer, you add its _____.

✓ Answer

additive inverse

26. Fill in the Blank (2 pts)

The predecessor of 0 is _____.

✓ Answer

-1

27. Fill in the Blank (2 pts)

The sum -8 + 3 + -4 equals _____.

✓ Answer

-9

28. Fill in the Blank (2 pts)

The integer between -1 and 1 is _____.

✓ Answer

0

29. Fill in the Blank (2 pts)

If the temperature rises from -6°C to 5°C, the change is _____ degrees.

✓ Answer

11

30. Fill in the Blank (2 pts)

The opposite of the opposite of -3 is _____.

✓ Answer

-3

31. Word Problem (5 pts)

A bank account has a balance of $120. The owner makes a purchase of $75 and later deposits $40. What is the new balance? Show your working.

✎ Worked Solution

Step 1: Model the changes: 120 - 75 + 40

Step 2: 120 - 75 = 45

Step 3: 45 + 40 = 85

Answer: $85

32. Word Problem (5 pts)

An elevator is at floor -2. It goes up 9 floors, then down 4 floors. Which floor is it on now? Show your working.

✎ Worked Solution

Step 1: Start at -2 and add the moves: -2 + 9 - 4

Step 2: -2 + 9 = 7

Step 3: 7 - 4 = 3

Answer: Floor 3

33. Word Problem (5 pts)

In a city, the morning temperature is -3°C. It drops by 7°C by noon, then rises by 5°C in the afternoon. What is the final temperature? Show your working.

✎ Worked Solution

Step 1: Combine changes: -3 - 7 + 5

Step 2: -3 - 7 = -10

Step 3: -10 + 5 = -5

Answer: -5°C

34. Word Problem (5 pts)

A hiker stands at 250 m above sea level and descends 420 m into a canyon. What is the elevation relative to sea level after the descent? Show your working.

✎ Worked Solution

Step 1: Compute final elevation: 250 - 420

Step 2: 250 - 420 = -170

Answer: -170 m (170 m below sea level)

35. Word Problem (5 pts)

What is the distance on the number line between -11 and 6? Show your working.

✎ Worked Solution

Step 1: Use distance formula: |6 - (-11)|

Step 2: 6 - (-11) = 6 + 11 = 17

Answer: 17 units

36. Word Problem (5 pts)

In a game, a player starts with 0 points, then gains 8, loses 15, and gains 12. What is the final score? Show your working.

✎ Worked Solution

Step 1: Sum the changes: 0 + 8 - 15 + 12

Step 2: 0 + 8 = 8; 8 - 15 = -7; -7 + 12 = 5

Answer: 5 points

37. Word Problem (5 pts)

A submarine is at -150 m. It descends 60 m and then ascends 95 m. What is its depth now? Show your working.

✎ Worked Solution

Step 1: Combine movements: -150 - 60 + 95

Step 2: -150 - 60 = -210

Step 3: -210 + 95 = -115

Answer: -115 m

38. Word Problem (5 pts)

City A has a low of -9°C and City B has a low of -4°C. How many degrees colder is City A than City B? Show your working.

✎ Worked Solution

Step 1: Find the difference: |-9 - (-4)|

Step 2: -9 - (-4) = -9 + 4 = -5; absolute value = 5

Answer: 5°C colder

39. Word Problem (5 pts)

The sum of three consecutive integers is -6. What are the integers? Show your working.

✎ Worked Solution

Step 1: Let the integers be n, n+1, n+2; sum = n + (n+1) + (n+2) = -6

Step 2: 3n + 3 = -6 → 3n = -9 → n = -3

Step 3: Integers are -3, -2, -1

Answer: -3, -2, -1

40. Word Problem (5 pts)

A robot starts at position 5 on a number line, moves left 12 units, then right 7 units. Where does it stop? Show your working.

✎ Worked Solution

Step 1: Compute final position: 5 - 12 + 7

Step 2: 5 - 12 = -7

Step 3: -7 + 7 = 0

Answer: 0