Arithmethic Properties Flashcards
What are the natural numbers?
The natural numbers, also known as counting numbers, is the set of numbers found in nature, or in other words, the set of numbers we use to count the things in the real world. All positive numbers starting at one that have no decimal or fractional part.
N = {1,2,3,4,5,6,7,8,9,10,…}
What are whole numbers?
What are the Whole numbers?
It is the set of all the natural numbers and zero.
W = {0,1,2,3,4,5,6,7,8,9,10,…}
What are the Integer numbers?
The set of all whole numbers, including natural negative numbers.
Z = {…,-5,-4,-3,-2,-1,0,1,2,3,4,5,…}
What are the Rational numbers?
The set of all numbers that can be written dividing one integer by another.
Q = {1/2, 0,3, -8, …}
What are the Irrational numbers?
The set of all numbers that can not be written by dividing one integer by another. When a irrational number is written as decimal, it goes on forever, without repeat itself.
I = {
3.1415…,
2.2360…,
etc.
}
OBS: 0.34715715715715 … IS NOT IRRATIONAL BECAUSE IT REPEATS ITSELF
What are the real numbers?
The set of all numbers on a number line. Real numbers include all rational and irrational numbers.
R = {8, -19, 0, 3/2, etc}
For questions 1 through 10, classify each number in as many categories as possible.
1) 62
2) 8/10
3) 9.28519692714385…
4) 0
5) 3.7
6) -260
7) - 5/2
8) π
9) 3.25197197197197…
10) √49
1) Natural, Whole, Integer, Rational, Real.
2) Rational, Real.
3) Irrational, Real.
4) Whole, Integer, Rational, Real.
5) Rational, Real.
6) Integer, Rational, Real.
7) Rational, Real.
8) Irrational, Real.
9) Rational, Real.
10) Natural, Whole, Integer, Rational, Real.
Name all the basic arithmethic properties.
1° Commutative property of Addition;
2° Commutative property of multiplication;
3° Associative property of addition;
4° Associative property of multiplication;
5° Distributive property of multiplication over addition;
6° Distributive property of multiplication over subtraction;
Explain the commutative property of addition and the commutative property of multiplication.
First of all, it is important to notice the etymology of the word ‘commutative’: it comes from the French word commuter which means ‘to substitute’ and the suffix ative meaning tending to. So, the commutative property of adition and multiplication states that for any addition or multiplication does not matter the order of the numbers to get the correct result.
a + b = b + a
x * y = y * x
Explain the associative property of addition and multiplication.
When we are adding three numbers or multiplying three numbers the order in which we group the numbers does not matter.
(a + b) + c = a + (b + c)
(1 + 2) + 5 = 3 + 5 = 8 || 1 + (2 + 5) = 1 + 7 = 8
(a * b) * c = a * (b * c)
(2 * 3) * 5 = 6 * 5 = 30 || 2 * (3 * 5) = 2 * 15 = 30
What is the difference between the commutative and associative properties?
The commutative relates the order of the numbers, Associative relates to the grouping of numbers.
Explain the distributive property of multiplication over addition.
Given three numbers, a, b and c: a * (b + c) = (a * b) + (a * c)
EXAMPLE:
USE THE DISTRIBUTIVE TO EXPAND AND THEN SIMPLIFY THE EXPRESSION 3 * (6 + 8)
3 * (6 + 8) = (3 * 6) + (3 * 8) = 18 + 24 = 42
Explain the distributive property of multiplication over subtraction.
Given three numbers, a, b, and c: a * (b - c) = (a * b) - (a * b)
EXAMPLE:
USE THE DISTRIBUTIVE TO EXPAND AND THEN SIMPLIFY THE EXPRESSION 2 * (10 - 7)
2 * (10 - 7) = 2 * 10 - 2 * 7 = 20 - 14 = 6
Is possible to use the distributive property with multiple terms?
Yes, it is!
a * (b + c - d) = (a * b) + (a * c) - (a * d)
