7TH NUMBERS TALENT PROPERTIES OF INTEGERS

Properties of Integers Quiz

1. Which property of integers is illustrated by: (-15) + 8 = 8 + (-15)?

A) Associative Property of Addition B) Commutative Property of Addition C) Distributive Property D) Additive Identity Property

Correct Answer: B) Commutative Property of Addition

Explanation: The Commutative Property states that changing the order of addends does not change the sum (a + b = b + a).

2. Evaluate using distributive property: (-25) × 98 + (-25) × 2

A) -2500 B) 2500 C) -2400 D) -250

Correct Answer: A) -2500

Explanation: Factor out (-25):
(-25) × (98 + 2) = (-25) × 100 = -2500.

3. Which operation does NOT satisfy the closure property for integers?

A) Addition B) Subtraction C) Multiplication D) Division

Correct Answer: D) Division

Explanation: Dividing two integers does not always yield an integer (e.g., 5 ÷ 2 = 2.5, which is not an integer).

4. What is the additive inverse of the integer -42?

A) 1/42 B) -1/42 C) 42 D) -42

Correct Answer: C) 42

Explanation: The additive inverse of a number a is -a such that a + (-a) = 0. Therefore, -(-42) = 42.

5. Simplify: (-18) × [(-5) + (-3)]

A) -144 B) 144 C) 36 D) -36

Correct Answer: B) 144

Explanation:
(-5) + (-3) = -8
(-18) × (-8) = 144 (product of two negative numbers is positive).

6. A submarine was at -250m. It descended 75m more, then ascended 120m. What is its current position relative to sea level?

A) -445 meters B) -205 meters C) -295 meters D) 205 meters

Correct Answer: B) -205 meters

Explanation:
Initial = -250
Descent = -75
Ascent = +120
Position = -250 + (-75) + 120 = -325 + 120 = -205 meters.

7. Which equation demonstrates the Associative Property of Multiplication?

A) a × (b + c) = (a × b) + (a × c) B) a × b = b × a C) [(-3) × 4] × (-5) = (-3) × [4 × (-5)] D) a × 1 = a

Correct Answer: C) [(-3) × 4] × (-5) = (-3) × [4 × (-5)]

Explanation: The Associative Property states that grouping does not affect the product: (a × b) × c = a × (b × c).

8. If x is any non-zero integer, what is the value of x × (-1)?

A) x B) -x C) 1 D) 0

Correct Answer: B) -x

Explanation: Multiplying any integer by -1 yields its additive inverse, -x.

9. Midnight temp was -4°C. Over 6 hours, it dropped 2°C per hour. Which expression calculates the 6 AM temperature?

A) -4 + 6 × (-2) = -16°C B) -4 - 6 × 2 = 8°C C) (-4 + 6) × (-2) = -4°C D) -4 × 6 + (-2) = -26°C

Correct Answer: A) -4 + 6 × (-2) = -16°C

Explanation: Initial temperature is -4. A drop of 2°C per hour for 6 hours is represented by 6 × (-2) = -12. Total = -4 + (-12) = -16°C.

10. Find k if: (-12) × [15 + (-7)] = [(-12) × 15] + [(-12) × k]

A) 7 B) -7 C) 15 D) -12

Correct Answer: B) -7

Explanation: By the Distributive Property, a × (b + c) = (a × b) + (a × c). Comparing terms shows k = -7.

11. A quiz gives +4 points per correct answer and -2 per wrong answer. Maya got 12 correct and 5 wrong. What is her score?

A) 48 B) 38 C) 28 D) 58

Correct Answer: B) 38

Explanation:
Correct points = 12 × 4 = 48
Incorrect points = 5 × (-2) = -10
Total = 48 + (-10) = 38.

12. Which statement correctly identifies the Multiplicative Identity for integers?

A) Multiplicative identity is 0, because a × 0 = 0 B) Multiplicative identity is 1, because a × 1 = a C) Multiplicative identity is -1, because a × (-1) = -a D) Integers do not have a multiplicative identity

Correct Answer: B) Multiplicative identity is 1, because a × 1 = a

Explanation: Multiplying any integer by 1 retains its identity value.

13. Simplify using integer properties: 47 × (-99)

A) -4653 B) -4753 C) -4603 D) -4703

Correct Answer: A) -4653

Explanation:
Rewrite -99 as (-100 + 1):
47 × (-100 + 1) = (47 × -100) + (47 × 1)
= -4700 + 47 = -4653.

14. Profit per pen = +$5, loss per eraser = -$2. If 20 pens and 30 erasers are sold, what is the net outcome?

A) Profit of $40 B) Loss of $40 C) Profit of $100 D) Profit of $160

Correct Answer: A) Profit of $40

Explanation:
Pens profit = 20 × 5 = +100
Erasers loss = 30 × (-2) = -60
Net = 100 + (-60) = +$40 (Profit).

15. Which of the following is true regarding subtraction of integers?

A) Subtraction is commutative and associative. B) Subtraction is commutative but not associative. C) Subtraction is neither commutative nor associative. D) Subtraction is closed, commutative, and associative.

Correct Answer: C) Subtraction is neither commutative nor associative.

Explanation: Order matters in subtraction (e.g., 5 - 3 ≠ 3 - 5) and grouping matters (e.g., (8 - 4) - 2 ≠ 8 - (4 - 2)).