Real Number System
What is the Real Number System?
A set of all numbers that can be found on the number line including rational and irrational numbers. It also contains natural and whole numbers and integers.
What are Natural Numbers and how are they used in the real life?!
Positive counting numbers.
Any example is correct.
What does it mean when we say Natural Numbers are a subset of Whole Numbers?
It means all natural numbers are also whole numbers, but whole numbers include zero as well.
What is the Associative Property?
The associative property states that when adding or multiplying, the grouping of numbers does not change the result.
Which set of numbers is the foundation of the Real Number System?
Natural Numbers
What makes Whole Numbers different from Natural Numbers?
Whole Numbers include zero (0) along with all Natural Numbers.
How are Integers related to Whole Numbers?
Whole numbers are part of the integers. Integers include negative numbers, zero, and positive numbers.
Does the associative property apply to subtraction or division?
No. It only applies to addition and multiplication, not subtraction or division.
How are Whole Numbers different from Natural Numbers?
Whole Numbers include 0, while Natural Numbers start from 1.
What are Integers and give one real world use.
Numbers including positive and negative whole numbers and zero.
Any example is correct.
Explain the relationship between Rational Numbers and Integers.
Every integer is a rational number because it can be written as a fraction with denominator 1.
Give a real-life example of the associative property in addition.
When adding money:
If you add $5 + ($10 + $15) = ($5 + $10) + $15 → both equal $30.
So the order in which you group the amounts doesn’t change the total.
Give a real life example of an Integer and explain it.
Any Integer given is correct.
Give an example of a Rational number.
Explain.
Any answer given is correct.
Why are Irrational Numbers not a subset of Rational Numbers?
Because irrational numbers cannot be written as fractions — their decimals never end or repeat, unlike rational numbers.
How does the associative property work in multiplication?
Changing the grouping of factors doesn’t change the product.
Example: (2 × 3) × 4 = 2 × (3 × 4) → both equal 24.
Why is pi (π) considered an irrational number?
Because it is a never ending decimal.
Find the 3 Irrational Number?
17 , -36, π, 1000, √3, √2.
π
√3
√2
Describe how all number sets fit inside the Real Number System.
The Real Number System includes all rational and irrational numbers.
It can be shown as:
Natural ⊂ Whole ⊂ Integers ⊂ Rational ⊂ Real, and Irrational ⊂ Real.
Why is the associative property important in mathematics?
It helps simplify complex calculations by allowing you to group numbers in any order to make computation easier.