Random Fraction Generator: Proper, Improper or Mixed: how it works
This random fraction generator draws one fraction and shows the top number over the bottom number. It opens on proper fractions with bottom numbers up to 12: 66 fractions, from 1/2 to 11/12, each with the same chance. The line under the result gives the simplest form, the decimal, the percent and how it compares with one half. Tap Improper or Mixed number for fractions bigger than 1.
Top number, bottom number
The bottom number, the denominator, says how many equal parts the whole is cut into. The top number, the numerator, counts the parts you have: 3/8 means 3 of 8 equal parts. A top smaller than the bottom makes a proper fraction, always less than 1.
Worked example: 6/8
Say the draw is 6/8. The biggest number that divides both 6 and 8 is 2. Divide top and bottom by 2 to get 3/4. 6/8 and 3/4 are the same amount. For the decimal, divide the top by the bottom: 3 divided by 4 is 0.75, which is 75%. Work it out first, then check the line under the result.
Tips
- Improper fractions and mixed numbers here are always more than 1 and less than 4. 8/3 and 2 2/3 are the same amount, and the line under the result gives both.
- Tick Simplest form only and 6/8 never comes up: 45 of the 66 fractions are left.
- The Common Core standards, adopted by most US states, keep grade 3 to halves, thirds, fourths, sixths and eighths. Set Largest denominator to 4 and every result fits. Grade 4 adds fifths, tenths, twelfths and hundredths.
Questions and answers
Can you give me a random fraction that needs simplifying?
Yes. Keep pressing: 21 of the 66 fractions can be simplified, about one draw in three, and the line under each shows its simplest form. One half comes up most, because six fractions equal it: 1/2, 2/4, 3/6, 4/8, 5/10 and 6/12.
Why do some fractions make decimals that never end?
A decimal ends only when the bottom number of the simplest form is built from 2s and 5s, such as 4, 5, 8 or 10. Any other bottom gives digits that repeat forever, and the page marks them: 1/6 shows as 0.1666… (6 repeats), and in 1/7 the six digits 142857 repeat.
How do we play a fraction game with this?
Two players press once each. The bigger fraction scores a point, and the winner says how they know. A quick check is to compare each with a half: 5/12 is less, because 5 is under half of 12, and 4/7 is more, so 4/7 wins.