IXL - Properties of operations on rational and irrational numbers (Algebra 1 practice)

The number

is irrational. Which statement about

is true?

is rational.

is irrational.

can be rational or irrational, depending on the value of

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Learn with an example

question

The number

is irrational. Which statement about

–

is true?

–

is rational.

–

is irrational.

–

can be rational or irrational, depending on the value of

key idea

A rational number is a real number that can be expressed as a quotient of two integers. For example, the following are rational numbers:

1
2
0.75
=
3
4
–
1
=
–
1
1
0
=
0
1
0.6
=
2
3

An irrational number is a real number that is not rational. For example,

and e are irrational numbers.

and

are both irrational, then

–

and

could be either rational or irrational, depending on the specific values of

and

solution

First, note that the number is irrational.

The number

–

can be rational for some irrational values of

For example, if

then

is irrational and

–

is rational.

The number

–

can be irrational for some irrational values of

For example, if

then

is irrational and

–

is irrational.

So, whether

–

is rational or irrational depends on the value of

Looking for more? Try these:

Lesson: Rational numbers

Lesson: Irrational numbers

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Teacher tools

Work it out

Not feeling ready yet? These can help:

A.11Classify rational and irrational numbers

Lesson: Rational numbers

Lesson: Irrational numbers

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