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

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.

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 :

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 :

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

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

Using distributive property,

= 12(2 + 3 + 1)

= 12 (6)

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.

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