Rational numbers: ordering and the four operations
Put negative fractions and decimals on one number line, compare them, then add and multiply them as moves and as scalings.
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Guide
A rational number is any number you can write as a fraction of two integers: 23, −34, −0.6 (which is −35) and −1 are all rational.
−34 is the opposite of 34: three quarters of the way from 0 towards −1. The minus sign belongs to the whole fraction, so −34 is the same as −34 and 3−4.
On the number line, numbers get bigger from left to right, for fractions too. −12 is further from zero than −13, so it is further left and smaller: −12 < −13.
Adding a fraction is a move along the line: right for a positive one, left for a negative one. Multiplying by a fraction scales the distance from zero: × 34 keeps three quarters of it, on the same side.