Step by step
The question
Question: is −2/3 rational or irrational?
−23
Rational means: it can be written as a fraction, with whole numbers on top and at the bottom.
Then its decimal stops, or repeats for ever.
Irrational means: no fraction works.
Its decimal never stops and never repeats.
rational = a fraction of whole numbers
decimal stops or repeats
1 Look at the fraction
It is already a fraction.
The top, 2, and the bottom, 3, are whole numbers.
top 2, bottom 3: whole numbers
Careful!
The decimal may go on for ever.
That is fine, if it repeats.
Rational only asks for a fraction.
Careful: its decimal may go on, but it repeats
So −2/3 is rational.
A fraction of whole numbers is rational.
= −23 is rational
2 Check
Let's check with the decimal: 2 divided by 3 is 0.666666, and so on.
It repeats.
So the answer is right!
2 ÷ 3 = 0.666666…
Let's look back.
First: look at the fraction.
Last: check.
Answer
= −23 is rational