Expanding to Rational Numbers

Pre-Algebra · Axiom Academy

LESSON Expanding to Rational Numbers Fractions, decimals, and the integers are all one family — and that family packs the number line tighter than you'd think. A number is rational if it can be written as a fraction where a and b are integers and . That definition is a container: every integer already fits inside it, so the integers live inside the rationals . Watch the integer set drop into the larger set, and an integer get rewritten in fraction form to prove it belongs. A rational number = one integer over a nonzero integer 2. Every Integer Is Already a Fraction Why is an integer rational? Because dividing by 1 changes nothing: . Both the top and bottom are integers and the bottom isn't zero, so the definition is satisfied. The animation feeds integers through a " " step and lands each one back on its exact spot on the number line — the value never moves, only its form does. — zero on top is fine; only a zero bottom is banned. 3. Decimals Are Fractions in Disguise A terminating decimal is a fraction read off by place value. The digits of 0.75 sit in the tenths and hundredths places, so , which simplifies to . Watch each digit drop into its place-value column, build the fraction, then cancel down.

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