EVALUATE EACH EXPREESION USING PROPERTIES OF NUMBERS

Commutative property :

If two quantities are added or multiplied, we will get the same result even we switch the order.

This is called commutative property.

a + b = b + a 

a x b = b x a

Associative property :

In this property, three quantities will be involved. Even we switch the numbers, we will get the same answer.

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

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

Distributive property :

The quantity which is outside should be distributed inside, that is

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

(b + c) x a = ab + ac

Identity property of addition :

The sum of number and zero, we will get the result as the number. 

a + 0 = a

0 + a = a

Identity property of multiplication :

The product of the number and zero is zero.

a x 0 = 0

0 x a = 0

The above two properties are known as zero property of addition and multiplication.

Additive inverse :

Consider the number as a, then its additive inverse will be -a.

Then,

a + (-a) = 0

Multiplicative inverse :

Consider the number as a, then its multiplicative inverse will be 1/a.

a x (1/a) = 1

Evaluate each expression using properties of numbers. Name the property used in each step.

Problem 1 :

25 + 14 + 15 + 36

Solution :

= 25 + 14 + 15 + 36

Using commutative property of addition, we can group numbers

= (25 + 15) + (36 + 14)

= 40 + 50

= 90

Problem 2 :

11 + 7 + 5 + 13

Solution :

11 + 7 + 5 + 13

Using commutative property of addition, we can group numbers

= 11 + 5 + 13 + 7

= 16 + 20

= 36

Problem 3 :

Solution :

Find the value of x. Then name the property used.

Problem 4 :

8 = 8 + x

Solution :

Given that,

8 = 8 + x

The value of x is 0, then 8 = 8 + 0 will become true.

Property used :

Zero property of addition

Problem 5 :

10 x = 10

Solution :

Given that,

10 x = 10

The value of x is 1, then 10 (1) = 10 will become true.

Property used :

Multiplicative identity.

Problem 6 :

Solution :

Property used :

Multiplicative identity.

Problem 7 :

1 ⋅ x = 3

Solution :

1 ⋅ x = 3

When x = 3, then 1 ⋅ 3 = 3 will become true.

Property used :

Multiplicative identity.

Problem 8 :

5 ⋅ (1/5) = x

Solution :

5 ⋅ (1/5) = x

Multiplying a number and its reciprocal, we will get 1.

Property used :

Multiplicative inverse

Problem 9 :

2 + 8 = 8 + x

Solution :

2 + 8 = 8 + x

When x = 2, the given expression will be come true.

Property used :

Commutative property of addition

Problem 10 :

A Jaguar can run 40 miles per hour while a giraffe can run 32 miles per hour. If they both run for 4 hours, how much farther will Jaguar run ?

Solution :

Speed of Jaguar = 40 miles per hour

Speed of Giraffe = 32 miles per hour.

Each runs 4 hours.

The difference between these two 

= 4(40) - 4(32)

= 4(40 - 32)

Using distributive property, we create the expression. By evaluating this,

= 4 (8)

= 32 miles

Jaguar will be 32 miles farther than Giraffe.

Problem 11 :

Bobby baked 2 dozen chocolate chip cookies, 3 dozen sugar cookies, and a dozen oatmeal raisin cookies. How many total cookies did he bake?

Solution :

1 dozen = 12

Number of dozens of chocolate chip cookies = 2

Number of dozens of sugar cookies = 3

Number of dozen of raisin cookies = 1

Total number of cookies 

= 2(12) + 3(12) + 1(12)

Using distributive property,

= 12(2 + 3 + 1)

= 12 (6)

= 72 cookies

Problem 12 :

A football team is on the 35-yard line. The quarterback is sacked at the line of scrimmage. The team gains 0 yards, so they are still at the 35-yard line. Which identity or property does this represent? Explain.

Solution :

If a football team starts on the 35-yard line and gains zero yards, it can be represented by the equation

35 + 0 = 35

This represents the Additive Identity, which states that the sum of any number and zero is equal to the number.

Recent Articles

  1. Finding Range of Values Inequality Problems

    May 21, 24 08:51 PM

    Finding Range of Values Inequality Problems

    Read More

  2. Solving Two Step Inequality Word Problems

    May 21, 24 08:51 AM

    Solving Two Step Inequality Word Problems

    Read More

  3. Exponential Function Context and Data Modeling

    May 20, 24 10:45 PM

    Exponential Function Context and Data Modeling

    Read More