9th grade · Math · Unit 6 of 22
Number Sets
Whole, rational and irrational
What your child practices
Natural numbers, whole numbers, integers, rational and irrational numbers, how they fit inside each other, and why there are always more numbers between any two rational numbers.
New York State Learning Standards learning standard: AI-N.RN.3 · rational and irrational numbers and their different forms
How we explain it
Children can open this short lesson before they practice.
- Natural numbers count: 1, 2, 3. Integers add 0 and negatives.
- Rational numbers can be written as fractions. Irrational numbers cannot.
- Between any two rational numbers there is always another one.
Example: Is 0.25 rational or irrational? 0.25 = 25/100 = 1/4. It is a fraction of whole numbers. Answer: Rational
Number Sets in New York
In the New York State Learning Standards, this is unit 6 of 22 in 9th grade Math, after Statistics in Society and before Expressions.
Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.
Sample questions
A taste of this unit. In the app, questions change every time and get easier or harder to match your child.
Question 1
Which number is rational but not an integer?
- 12
- 0
- −6
- 3/4
3/4
Hint: An integer has no fraction part. 3/4 is a ratio of integers that falls between 0 and 1.
Question 2
Which number is irrational?
- −2/9
- √10
- 0.125
- √25
√10
Hint: √25 = 5, 0.125 = 1/8 and −2/9 are all ratios of integers. √10 is not a perfect square, so its decimal never ends or repeats.
Question 3
Which statement is true?
- Every irrational number is a rational number
- Every integer is a rational number
- Every rational number is an integer
- No integer is a rational number
Every integer is a rational number
Hint: Any integer n can be written as the fraction n/1.
Question 4
Which number belongs to the whole numbers but is not a natural number?
- 0
- 1
- 5
- −1
0
Hint: Natural numbers start at 1. Whole numbers add 0.
Question 5
Which number is rational?
- π
- √7
- √11
- −3/8
−3/8
Hint: A rational number can be written as a ratio of two integers. −3/8 is exactly that.
Question 6
What does it mean to say the rational numbers are dense?
- Every rational number is a whole number
- Between any two rational numbers there is always another one
- Rational numbers cannot be written as fractions
- There is a largest rational number
Between any two rational numbers there is always another one
Hint: Dense means there are no gaps: the average of two rational numbers is another rational number between them.