Numbers
Rational numbers
Place, compare, add and subtract numbers that can be written as one whole number over another.
A rational number is any number you can write as one whole number over another, like 3/4, -5/2 or 7/1. The bottom number is never allowed to be zero, because nothing can be shared into zero parts.
You already know hundreds of them
Every whole number is rational: 7 is 7/1, and -3 is -3/1. Every fraction you have met is rational. So is every decimal that stops, because 0.25 is 25/100. Rational numbers are not a new kind of number so much as a name for nearly all the ones you already use.
Worked example
Which is greater, -3/4 or -2/3?
Write both with the same denominator: -3/4 is -9/12 and -2/3 is -8/12.
Twelfths are the smallest pieces that both fractions divide into evenly, so now only the top numbers have to be compared.
Try it together
Now let us work out -5/6 + 1/3 together.
Adding rational numbers is adding fractions with the sign rules for integers on top. Same denominator first, then add the top numbers as integers.
1.The denominators are 6 and 3. What is the smallest number both of them divide into?
Have a go
Have a go on your own: which is greater, -1/2 or -1/3? Type the greater one.
Hint: Halves are bigger pieces than thirds, so a whole one of them takes you further from zero.
Ready to practise?
Eight questions on what you have just read. Nothing is timed, and you can play as many times as you like.