HOW TO IDENTIFY THE PROPERTY USED IN EACH STATEMENT

Using the properties of real numbers to help and simplify each expression.

Problem 1 :

(19 + 15) + 5

Solution :

Here three quantities are involved 19, 15 and 5. Using associative property of addition,

(a + b) + c = a + (b + c)

Here a = 19, b = 15 and c = 5

(19 + 15) + 5 = 19 + (15 + 5)

Grouping 15 and 5, we get 20

= 19 + 20

= 39

Problem 2 :

-3 + (23 + 48)

Solution :

a = -3, b = 23 and c = 48

Here three quantities are involved. Using associative property of addition,

a + (b + c) = (a + b) + c

-3 + (23 + 48) = (-3 + 23) + 48

= 20 + 48

= 68

Problem 3 :

$9.50 + $11.49 + $0.50

Solution :

a = $9.50, b = $11.49 and c = $0.50

a + (b + c) = (a + b) + c

= ($9.50 + $0.50) + $11.49

= $10 + $11.49

= $21.49

Problem 4 :

(9 ⋅ 25) ⋅ 4

Solution :

Here three quantities are involved and the operations multiplication is used. So, using associative property of multiplication, we can simplify.

= (9 ⋅ 25) ⋅ 4

= 9 ⋅ (25 ⋅ 4)

= 9 ⋅100

= 900

Problem 5 :

(-0.50 + 9.89) + 0.50

Solution :

Here three quantities are involved and the operation multiplication is used. Using associative property of addition, we get

= (-0.50 + 9.89) + 0.50

= -0.50 + 9.89 + 0.50

= 9.89

Problem 6 :

6 x 8 x 5

Solution :

Here a = 6, b = 8 and c = 5

Using associative property of multiplication, we get

= 6 x 8 x 5

= 6 x (8 x 5)

= 6 x 40

= 240

Problem 7 :

Sparky went shopping at Wally World and bought a pair of socks for $2.50, a pair of jeans for $14.95, and some shoes for $12.50. How much did Sparky spend during his shopping spree?

Solution :

Cost of pair of socks = $2.50

Cost of pair of jeans = $14.95

Cost of pair of shoes = $12.50

Amount that she spent = 2.50 + 14.95 + 12.50

= 2.50 + 12.50 + 14.95

= 15 + 14.95

= 29.95

Amount she spent is $29.95

Using mental math to simplify each expression.

Problem 8 :

(98 + 3) + 2

Solution :

(98 + 3) + 2

Here by grouping 98 and 2, we will get a rounded figure.

= 98 + 2 + 3

= 100 + 3

= 103

Problem 9 :

(20 ⋅ 16) ⋅ 5

Solution :

(20 ⋅ 16) ⋅ 5

Multiplying 20 and 5, we will get the rounded figure.

= (20 ⋅ 5) ⋅ 16

= 100 ⋅ 16

= 1600

Problem 10 :

Suppose you buy snacks costing $0.45, $0.65 and $1.55. Using mental math to find cost of these snacks.

Solution :

Cost of snacks are 0.45, 0.65 and 1.55

= 0.45 + 0.65 + 1.55

= 0.45 + 1.55 + 0.65

= 2 + 0.65

= 2.65