3. State the property represented by the following: a) (75 +32) + 29 = 75+ (32 +29) b) 21 + 52 = 52 +21 c) 5456 x 0 = 0 d) 7678 x 1 = 7678 e) 62 x (9 - 7) = 62 x 9 - 62 x 7 f) (64 +453) + 36 = 453 + (64 +36)
Answers
Answer:
a) (75 + 32) + 29 = 75 + (32 + 29)
A step to simplify the given equations so as to make out the property is to put variables in their place.
Here, we have (a + b) + c = a + (b + c).
This is the associative property of addition.
It says that the sum of three or more numbers remains the same, no matter how they are grouped.
b) 21 + 52 = 52 + 21
Here, we have a + b = b + a.
This is the commutative property of addition.
This property states that the order of adding numbers does not change the sum.
c) 5456 x 0 = 0
Here, we have a x 0 = 0.
This is the zero property of multiplication.
It states that any number multiplied with zero will give zero.
d) 7678 x 1 = 7678
Here, we have a x 1 = a (in this situation only 1 can be b).
This is the multiplicative identity.
The multiplicative identity of all numbers is 1, since when it is multiplied with a number, the result is the same.
e) 62 x (9 - 7) = 62 x 9 - 62 x 7
Here, we have a x (b - c) = a x b - a x c.
This is the distributive property of multiplication over subtraction.
This property states that a number multiplied with the difference of two numbers is the same as the difference of its products with each of the two numbers.
f) (64 + 453) + 36 = 453 + (64 + 36)
Here, we again have (a + b) + c = a + (b + c).
This is the associative property of addition.
Properties
There are some properties figured out by mathematicians to make calculations simpler and easier. But they can only be useful if they are used correctly. Below are some properties:
- Associative property holds true for only addition and multiplication.
- Additive identity for whole numbers is 0, since when 0 is added to a number, the number remains the same.
- Closure property of whole numbers holds true for only multiplication and addition. It states that a whole number multiplied or added to a whole number gives a whole number.