Regents Exam Questions
CC.N.RN.3: Classifying Numbers
Name: ________________________
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CC.N.RN.3: Classifying Numbers: Explain why the sum or product of two rational numbers is
rational; that the sum of a rational number and an irrational number is irrational; and
1 For which value of P and W is P  W a rational
number?
1
1
and W 
1) P 
3
6
1
1
2) P 
and W 
4
9
1
1
3) P 
and W 
6
10
1
1
4) P 
and W 
25
2
2 Given: L 
4 Which statement is not always true?
1) The product of two irrational numbers is
irrational.
2) The product of two rational numbers is rational.
3) The sum of two rational numbers is rational.
4) The sum of a rational number and an irrational
number is irrational.
5 Which statement is not always true?
1) The sum of two rational numbers is rational.
2) The product of two irrational numbers is
rational.
3) The sum of a rational number and an irrational
number is irrational.
4) The product of a nonzero rational number and
an irrational number is irrational.
2
M3 3
N
16
P 9
Which expression results in a rational number?
1) L  M
2) M  N
3) N  P
4) P  L
6 Ms. Fox asked her class "Is the sum of 4.2 and 2
rational or irrational?" Patrick answered that the
sum would be irrational. State whether Patrick is
correct or incorrect. Justify your reasoning.
3 Given the following expressions:
5 3
Ê
ˆ Ê
ˆ
I.  
III. ÁÁÁ 5 ˜˜˜  ÁÁÁ 5 ˜˜˜
8 5
Ë
¯ Ë
¯
1
ÊÁ
ˆ˜
II.  2
IV. 3  ÁÁ 49 ˜˜
2
Ë
¯
Which expression(s) result in an irrational number?
1) II, only
2) III, only
3) I, III, IV
4) II, III, IV
1
ID: A
CC.N.RN.3: Classifying Numbers: Explain why the sum or product of two rational numbers is
rational; that the sum of a rational number and an irrational number is irrational; and
Answer Section
1 ANS: 2
1
1 1 5
1

  
9 2 3 6
4
REF: 081522ai
2 ANS: 3
7
16  9  may be expressed as the ratio of two integers.
1
3
4
5
6
REF: 061413ai
ANS: 1
REF: 011604ai
ANS: 1
REF: 081401ai
ANS: 2
REF: 061508ai
ANS:
Correct. The sum of a rational and irrational is irrational.
REF: 011525ai
1