Generate Rational Numbers

A rational number is any value that can be written as a ratio of two integers: p/q with q never zero. That one simple idea quietly covers a lot of ground - every integer is a rational (5 = 5/1), every terminating decimal is a rational (0.5 = 1/2), and infinitely many numbers fall in between, some with decimal forms that repeat forever, like 1/3 = 0.333...

Generate Rational Numbers creates exact fractions from the ranges you choose. Pick numerator and denominator bounds, proper or improper or mixed, and reduced or not - then read each value with its terminating-or-repeating decimal. A rapid-fire fraction set for lessons, worksheets or data.

• Exact ratios: Every value is a precise p/q fraction, no rounding.
• Range control: Set separate bounds for numerators and denominators.
• Proper / improper / mixed: Shape the list for the lesson.
• Reduce or not: Simplest form, or keep the drawn pair for practice.
• Decimal companion: Each fraction shows its value plus terminating/repeating status.
• Copy or download: Export the whole list as text.

1. Set the numerator range - small values for simple fractions, larger for real spread.
2. Set the denominator range - avoiding zero automatically.
3. Choose type - proper, improper or mixed.
4. Choose reduction - yes for simplest form, no to keep raw pairs.
5. Generate and read - every fraction with its decimal companion.

1. Classic halves and thirds: numerators 1-3, denominators 2-4 - feeds like 1/2 = 0.5 and 1/3 = 0.333...

2. Proper only: numerators 1-5, denominators 6-10 - tidy lesson fractions.

3. Improper or mixed: numerators 3-9, denominators 2-5 - values like 8/3 = 2.666...

4. Reduced on: draw 6/8 and see it as 3/4 with decimal 0.75.

5. Mixed range: numerators 1-20, denominators 1-10 - a broad rational set for analysis.

• Exact forever: Fractions never round; 1/3 stays truly 1/3.
• Lesson-shaped: Proper/improper/reduced control matches classroom needs.
• Every value explained: The decimal companion shows terminate vs repeat at a glance.
• Range flexibility: Tiny lesson fractions or a broad data set - your call.
• Copy or download: The fraction list exports one per line.
• Private and free: All generation stays in the browser; nothing is uploaded or logged.