Rational Numbers

Drag the dot or tap anywhere on the number line to read off the rational number at that point. Learn the three elements of a number line — origin, positive direction and unit length — and how negative numbers, zero and positive numbers are positioned.

Place a number on the number line and tap "Take the opposite" to watch it flip across the origin to the equally distant other side. Random negatives and decimals show that a and −a stay the same distance from the origin, mirrored about it.

Guess what |a| equals first, then watch the distance-to-origin animation reveal the answer. Random positives, negatives and zero let you practice the three-branch rule: the absolute value of a positive is itself, of a negative is its opposite, and the absolute value of 0 is 0.

Join two journeys on the number line to add rational numbers: walk from 0 to a, then walk the second number. Convert subtraction to addition first, then apply the sign rules — same signs keep the sign and add absolute values, different signs take the sign of the larger absolute value. Random expressions with negatives, replayable again and again.

Multiplying and dividing rational numbers takes two steps: first decide the sign — same signs give positive, different signs give negative; second compute the value — multiply or divide the absolute values. Judge the sign of a random expression first, then watch the absolute-value animation verify it, with negative numbers throughout.

A power is repeated multiplication: (−2)³ = (−2)×(−2)×(−2). Adjust the base and exponent with buttons and watch the factors pop in and pair up, revealing the sign rule for negative bases — even exponents give positive, odd exponents give negative. Random bases and exponents for endless practice.

Write big numbers in standard form a×10ⁿ (1 ≤ a < 10): watch the decimal point glide from the end to just after the first digit while the exponent of 10 climbs place by place — the exponent equals the number of places moved. Random 5- to 9-digit numbers, then pick the correct notation from distractors (including exponents off by one).