HOW TO IDENTIFY THE PROPERTY USED IN EACH STATEMENT

name the property illustrated by each statement.

Problem 1 :

x + y = y + x

Solution :

If two quantities are added, even we change the order we will get the same answer.

Property used :

Commutative property of addition.

Problem 2 :

6 ⋅ (m ⋅ n) = (6 ⋅ m) ⋅ n

Solution :

Here three quantities are multiplied. 6, m and n. Even we change the order of multiplication, the answer will never change.

Property used :

Associative property of multiplication.

Problem 3 :

k + 0 = k

Solution :

By adding a quantity by zero, we will get the same quantity. 

Property used :

Additive property of addition or zero property of addition.

Problem 4 :

6(u + 2v) = 6u + 12v

Solution :

6(u + 2v) = 6u + 12v

Considering 6(u + 2v),

by distributing 6 inside, we get

6 ⋅ u + 6 ⋅ 2v

= 6u + 12v

Property used :

Distributive property

Problem 5 :

0 ⋅ 100 = 0

Solution :

0 ⋅ 100 = 0

Multiplying a quantity by 0, we get 0.

Property used :

Zero property of multiplication.

Problem 6 :

2a + (3b + 4c) = (2a + 3b) + 4c

Solution :

Even we change the order of adding three quantities, we will never receive same answer.  

Property used :

Associative property of addition.

Problem 7 :

If x + y = 3, then 3 = x + y

Solution :

x + y = 3, then 3 = x + y

The sum of x and y is 3, then 3 can be represented as sum of x and y.

Property used :

Reflexive property

Problem 8 :

pq + n = qp + n

Solution :

Observing pq and qp, two quantities are multiplied. Even we switch the order, we will get the same product. 

Here commutative property of multiplication is used.

Sum of pq and n, qp and n, even we change the order, we get the same result.

Here commutative property of addition is used.

Property used :

Commutative property of multiplication and addition.

Problem 9 :

15c + 15d = 15(c + d)

Solution :

15c + 15d = 15(c + d)

Considering 15(c + d)

While distributing 15, we get

= 15 ⋅ c + 15 ⋅ d

= 15c + 15d

Property used :

Distributive property.

Problem 10 :

1 ⋅ y = y ⋅ 1

Solution :

1 ⋅ y = y ⋅ 1

Multiplying a quantity by 1, we get the same quantity.

Property used :

Multiplicative identity

Problem 11 :

0 = 0 ⋅ 12

Solution :

0 = 0 ⋅ 12

A quantity multiplied by 0, we get 0.

Property used :

Zero property of multiplication.

Problem 12 :

5 = 0 + 5

Solution :

5 = 0 + 5

A quantity added with zero, we get the same result. 

Property used :

Zero property of addition.