September 1, 2015 ~ GSE Algebra 1
Name: ________________________________
 An irrational number is a real number that can NOT be expressed as a fraction. It is usually
expressed as a decimal that never ends and never repeats.
Examples: 1.398628502…, , e,
5
 A rational number is a real number that can be expressed as a fraction (and no number in this
fraction can be an irrational number). It can also be expressed as a decimal that is either
repeating or terminates.
Examples: 5, -3, 0.5,
1.
3
, 1.3̅, 2.424242…
2
Determine whether the following numbers are rational or irrational.
5
a. 5
b.
e. 5.75…
f. 0.343434…
7
c. 0.575
d. √5
g. 0.248502856…
h.
5

Mathematical Calculations with Rational and Irrational Numbers
 Rational + Rational = Rational
 Rational + Irrational = Irrational
 Rational - Rational = Rational
 Rational - Irrational = Irrational
 Rational x Rational = Rational
 Rational x Irrational = Irrational
 Rational  Rational = Rational
(as long as the divisor is not zero)
 Rational  Irrational = Irrational
 Irrational + Irrational = Irrational
 Irrational - Irrational = Irrational
 Irrational x Irrational = Either 
 Irrational  Irrational = Either 
 Irrational  Rational = Irrational
(as long as the divisor is not zero)
2.
Tell whether the following expressions are either rational or irrational.
a.
10  16
b. 2

c.
9 4
d.
30
e.
√10
2
g. (7 + √5)(5 - √5)
3.
Which statement is true about the value of 4
5 7

f. (5 + √5)(5 - √5)
h. (√18)( √50)


84 ?
A. It is rational, because the product of two rational numbers is rational.
B. It is rational, because the product of a rational and an irrational number is
rational.
C. It is irrational, because the product of two irrational numbers is irrational.
D. It is irrational, because the product of an irrational number and a rational
number is irrational.
4.
Tell whether the following expressions are either rational, irrational, or possibly either
given that R is a nonzero rational number and I is an irrational number. If your answer is
either, give an example of each.
a. I + 0
b. R + 0
c. R + I
d. I + I
e. R x 0
f. I x 0
g. R x R
h. I x I
i. R x I
j. R  I
k. R  R
l. I  I
5.
Explain what a rational number is. Then write three rational numbers not already listed
on this worksheet.
6.
Explain what a irrational number is. Then write three irrational numbers not already
listed on this worksheet.
7.
Determine if the following statements are always true, sometimes true, or never true.
a. Rational + Rational = Rational
b. Rational - Rational = Rational
c. Rational x Rational = Rational
d. Rational  Rational = Rational
e. Irrational + Irrational = Irrational
f. Irrational - Irrational = Irrational
g. Irrational x Irrational = Irrational
h. Irrational  Irrational = Irrational
i. Rational + Irrational = Rational
j. Rational - Irrational = Rational
k. Rational x Irrational = Rational
m. Rational  Irrational = Rational