Quiz - Properties of Real Numbers worksheet - Free Printable

Let’s go through each problem one by one and match it with the correct property.

We are given these properties:

(a) Additive Identity → Adding 0 doesn’t change a number: a + 0 = a
(b) Additive Inverse → Adding a number and its opposite gives 0: a + (-a) = 0
(c) Associative Property of Addition → Grouping doesn’t matter in addition: (a + b) + c = a + (b + c)
(d) Associative Property of Multiplication → Grouping doesn’t matter in multiplication: (a·b)·c = a·(b·c)
(e) Commutative Property of Addition → Order doesn’t matter in addition: a + b = b + a
(f) Commutative Property of Multiplication → Order doesn’t matter in multiplication: a·b = b·a
(g) Distributive Property of Mult over Addn → Multiply across parentheses: a(b + c) = ab + ac
(h) Multiplicative Identity → Multiplying by 1 doesn’t change a number: a·1 = a
(i) Multiplicative Inverse → Multiplying a number by its reciprocal gives 1: a·(1/a) = 1

Now let’s solve each:

1. m + 3 = 3 + m → Order changed in addition → (e) Commutative Property of Addition

2. w · 1 = w → Multiplying by 1 → (h) Multiplicative Identity

3. a + (b + c) = (a + b) + c → Grouping changed in addition → (c) Associative Property of Addition

4. (2·x)·y = (x·2)·y → Inside the parentheses, 2 and x swapped → That’s commutative multiplication inside → But note: the outer grouping is same. Actually, this shows that 2·x = x·2, so it’s using commutative property of multiplication within the expression → (f) Commutative Property of Multiplication

Wait — let’s look again: (2·x)·y = (x·2)·y → The only change is 2·x became x·2 → So yes, commutative property of multiplication → (f)

5. 2x(x + 3) = 2x² + 6x → Distributing 2x over (x+3) → (g) Distributive Property of Mult over Addn

6. k + (-k) = 0 → Number plus its opposite → (b) Additive Inverse

7. (a + b) + c = a + (b + c) → Same as #3 → (c) Associative Property of Addition

8. u + 0 = u → Adding zero → (a) Additive Identity

9. r · (1/r) = 1 → Number times its reciprocal → (i) Multiplicative Inverse

10. m·a·t·h = h·a·m·t → All factors reordered → Commutative property of multiplication → (f)

11. (-y) + y = 0 → Opposites add to zero → (b) Additive Inverse

12. ab + xy = ba + yx → Each product has order swapped → ab=ba and xy=yx → Commutative multiplication → (f)

13. (1/n)·n = 1 → Reciprocal times number → (i) Multiplicative Inverse

14. (2 + m) + 3 = 3 + (2 + m) → Left side: group (2+m)+3; right side: 3 + (2+m) → This is actually showing that you can swap the entire grouped part with 3 → But more precisely, it’s using commutative property on the whole expression: A + B = B + A where A=(2+m), B=3 → So still commutative addition → (e)

Wait — let’s check: (2 + m) + 3 = 3 + (2 + m) → Yes, it’s swapping two terms: the group (2+m) and the number 3 → So commutative property of addition → (e)

15. a·(j·e) = (a·j)·e → Grouping changed in multiplication → (d) Associative Property of Multiplication

16. (2·a)·b = 2·(a·b) → Grouping changed in multiplication → (d) Associative Property of Multiplication

17. 2x + 6 = 2(x + 3) → Factoring out 2 → which is reverse of distributing → still distributive property → (g)

18. 0 + h = h → Adding zero → (a) Additive Identity

Now let’s list all answers clearly:

1. e
2. h
3. c
4. f
5. g
6. b
7. c
8. a
9. i
10. f
11. b
12. f
13. i
14. e
15. d
16. d
17. g
18. a

Double-checking a few tricky ones:

#4: (2·x)·y = (x·2)·y → Only difference is 2·x vs x·2 → definitely commutative multiplication → f ✔️

#14: (2 + m) + 3 = 3 + (2 + m) → It’s like saying A + B = B + A where A = (2+m), B = 3 → commutative addition → e ✔️

#17: 2x + 6 = 2(x + 3) → This is factoring, but it’s based on distributive property → g ✔️

All look good.

Final Answer:
1. e
2. h
3. c
4. f
5. g
6. b
7. c
8. a
9. i
10. f
11. b
12. f
13. i
14. e
15. d
16. d
17. g
18. a