Rational Numbers
Fractions, negatives, and the number line that unites them.
A rational number is any p/q with q ≠ 0. Adding is a slide on the number line; multiplying is a stretch. Between any two rationals there's always another — infinitely many, in fact.
A rational number is any number that can be written as p/q, where p and q are integers and q ≠ 0.
They connect fractions, integers, and decimals into one big family living on the number line.
You use them daily — splitting a pizza, calculating half-marks, or reading a temperature below zero.
What counts as rational
Every integer is rational (5 = 5/1), every fraction is rational, and terminating or repeating decimals are rational too. Only non-terminating, non-repeating decimals like √2 are not.
Closure property
Rational numbers stay rational under addition, subtraction, and multiplication. Division works too, except dividing by zero, which is never allowed.
Density on the number line
Between any two rational numbers, however close, there is always another rational number. So there is no 'next' rational number after any given one.
Additive and multiplicative identity
Adding 0 to a rational number leaves it unchanged; multiplying by 1 leaves it unchanged. These are called identity elements.
These are easy on purpose — they check understanding, not speed. Nothing here is scored.
1. Which of these is a rational number?
2. What is the additive inverse of 4/9?
3. Between 1/2 and 1/3, how many rational numbers exist?
Which is NOT rational?