PROPERTIES OF NUMBERS WORKSHEET

Identifying Properties : Identify and apply the properties of real numbers (closure, commutative, associative, distributive, identity, inverse)

Problem 1 :

Which property is illustrated by the equation ax + ay = a(x + y) ?

1) associative           2) commutative

3) distributive           4) identity

Solution :

Given, ax + ay = a(x + y)

ax + ay = ax + ay

The property is illustrated by the equation is distributive property.  

So, option 3) is correct.

Problem 2 :

The statement 2 + 0 = 2 is an example of the use of which property of real numbers ?

1) associative                2) additive identity 

3) additive inverse         4) distributive

Solution :

2 + 0 = 0 + 2 = 2

Zero is the additive identity for rational numbes.

So, option 2) is correct.

Problem 3 :

The equation 3(4x) = (4x)3 illustrates which property ?

1) commutative       2) associative     3) distributive

4) multiplicative inverse

Solution :

3(4x) = 12x

(4x)3 = 12x

So, 

3(4x) = (4x)3

Therefore, Commutative property is true for multiplication.

So, option 1) is correct.

Problem 4 :

Tori computes the value of 8 ⋅ 95 in her head by thinking

8(100 - 5) = 8 × 100 - 8 × 5

Which number property is she using ?

1) associative          2) distributive      3) commutative

4) closure

Solution :

8(100 - 5) = 8 × 100 - 8 × 5.

The property is illustrated by the equation is distributive property.  

So, option 2) is correct.

Problem 5 :

Which property of real numbers is illustrated by the equation - √3 + √3 = 0 ?

1) additive identity       2) commutative property of addition

3) associative property of addition        4) additive inverse

Solution :

Additive inverse of -√3 is √3.

Additive inverse of √3 is -√3.

So, option 4) is correct.

Problem 6 :

The equation ∗(Δ + ♥) = ∗Δ + ∗♥ is an example of the 

1) associative law        2) commutative law

3) distributive law          4) transitive law

Solution :

∗(Δ + ♥) = ∗Δ + ∗♥

The property is illustrated by the equation is distributive law.  

So, option 3) is correct.

Problem 7 :

While solving the equation 4(x + 2) = 28, Becca wrote 4x + 8 = 28. Which property did she use ?

1) distributive       2) associative       3) commutative

4) identity

Solution :

4(x + 2) = 28 

4x + 8 = 28

The property is illustrated by the equation is distributive .  

So, option 1) is correct.

Problem 8 :

If M and A represent integers, M + A = A + M is an example of which property ?

1) commutative         2) associative         3) distributive

4) closure

Solution :

Addition of two numbers is commutative.

If 'M' and 'N' are any two numbers, then 

M + A = A + M

So, option 1) is correct.

Problem 9 :

Which property is illustrated by the equation 3/2 x + 0 = 3/2 x ?

1) commutative property of addition      2) distributive property

3) additive inverse property       4) additive identity property

Solution :

3/2 x + 0 = 3/2 x

Zero is the additive identity for rational numbers.

So, option 4) is correct.

Problem 10 :

Which property is represented by the statement 1/2 (6a + 4b) = 3a + 2b ?

1) commutative     2) distributive          3) associative

4) identity

Solution :

1/2 (6a + 4b)

6a/2 + 4b/2 

3a  +2b

It is represented by the statement is distributive.

So, option 2) is correct.

Problem 11 :

Which property is illustrated by the equation 6 + (4 + x) = 6 + (x + 4) ?

1) associative property of addition

2) associative property of multiplication

3) distributive property

4) commutative property of addition

Solution :

6 + (4 + x) = 6 + (x + 4)

Addition of two numbers is commutative.

6 + (4 + x) = 10 + x

6 + (x + 4) = 10 + x

So, 6 + (4 + x) = 6 + (x + 4)

So, option 4) is correct.

Problem 12 :

Which property is illustrated by the equation 4x(2x - 1) = 8x² - 4x ?

1) associative      2) commutative      3) distributive

4) identity

Solution :

4x(2x - 1) = 8x² - 4

The property is illustrated by the equation is distributive property.  

So, option 3) is correct.

Problem 13 :

Which property of real numbers is illustrated by the equation 52 + (27 + 36) = (52 + 27) + 36 ?

1) commutative property               2) associative property

3) distributive property            4) identity property of addition

Solution :

52 + (27 + 36) = 52 + 63 = 115

(52 + 27) + 36 = 79 + 36 = 115

Addition  of numbers is associative.

So, option 1) is correct.

Problem 14 :

A teacher asked the class to solve the equation  3(x + 2) = 21. Robert wrote 3x + 6 = 21 as his first step. Which property did he use ? 

1) associative property         2) commutative property

3) distributive property        4) zero property of addition

Solution :

3(x + 2) = 21

3x + 6 = 21

The property is illustrated by the equation is associative .  

So, option 1) is correct.

Problem 15 :

When solving for the value of x in the equation

4(x - 1) + 3 = 18

Aaron wrote the following lines on the board.

Which property was used incorrectly when going from line 2 to line 3 ?

1) distributive          2) commutative     3) associative

4) multiplicative inverse

Solution :

Distributive property :

4(x - 1) = 4x - 4

Here it is, 4(x - 1) = 4x - 1

Therefore, distributive property was used incorrectly.

So, option 1) is correct.

Problem 16 :

A method for solving 5(x - 2) – 2(x - 5) = 9 is shown below. Identify the property used to obtain each of the two indicated steps.

5(x - 2) – 2(x - 5) = 9 

5x – 10 – 2x + 10 = 9 ____________

5x – 2x – 10 + 10 = 9 ____________

3x + 0 = 9

3x = 9

x = 3

Solution :

5(x - 2) – 2(x - 5) = 9 

5x – 10 – 2x + 10 = 9 (distributive property)

5x – 2x – 10 + 10 = 9 (commutative property)

3x + 0 = 9

3x = 9

x = 3