USE THE PROPERTIES OF REAL NUMBERS TO SIMPLIFY THE EXPRESSION

Use the properties of real numbers to help simplify each expression

Problem 1 :

(19 + 15)  + 5 = ______

Solution :

Property used :

Associative property

Problem 2 :

-3 + (23 + 48) = ______

Solution :

Property used :

Associative property of addition.

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

= -3 + (23 + 48)

From the given expression, using the property above.

= (-3 + 23) + 48

= 20 + 48

= 68

Problem 3 :

(2/3) + (-2/3)

Solution :

= (2/3) + (-2/3)

Property used :

Additive inverse

Additive inverse of 2/3 is -2/3. By simplifying, we get

= 0

Problem 4 :

-8 + 0

Solution :

= -8 + 0

Property used :

Additive identity

Adding 0 with any number, we will get the same number. So, answer is

= 0

Problem 5 :

0 (-5 . 4)

Solution :

Property used :

Multiplication property of zero.

Any numerical value multiplied by 0 is 0.So, answer is

= 0

Problem 6 :

10 (2y)

Solution :

Property used :

Commutative property of multiplication.

10(2y) = 2y(10)

= 20 y

Problem 7 :

($9.50 + $11.49) + $0.50

Solution :

= ($9.50 + $11.49) + $0.50

Property used :

Associative property of addition.

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

Using this property, we can simplify 9.50 and 0.50 first.

= $9.50 + $0.50 + $11.49

= $10 + $11.49

= $21.49

Problem 8 :

(9 ⋅ 25) ⋅ 4 = ______

Solution :

Property used :

Multiplicative property of multiplication.

a x (b x c) = (a x b) x c

Using this property, we can multiply 25 and 4. 

= (9 ⋅ 25) ⋅ 4

= 9 ⋅ (25 ⋅ 4)

= 9 ⋅ 100

= 900

Problem 9 :

(-0.50 + 9.89) + 0.50

Solution :

Property used :

Associative property of addition.

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

Inverse property of addition.

- a + a = 0

= -0.50 + 9.89 + 0.50

= - 0.50 + 0.50 + 9.89

= 9.89

Problem 10 :

6 × 8 × 5 = _______

Solution :

Property used :

Associative property of multiplication.

a x (b x c) = (a x b) x c

= 6 × (8 × 5)

= 6 x 40

= 240

Problem 11 :

4(x + 3)

Solution :

Property used :

Distributive property.

a(b + c) = ab + ac

= 4(x + 3)

= 4x + 12

Problem 12 :

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

Solution :

A pair of socks = $2.50

A pair of jeens = $14.95

A pair of shoes = $12.50

Total = $2.50 + $14.95 + $12.50

= $29.95

Hence, Sparky spend the money is $29.95.