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.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
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