Examples

Sum of two random irreducible fractions

Consider creating an exercise where students must calculate the sum of two randomly generated irreducible fractions.

# Generate the first fraction
# Choose a random numerator "a" from 1 to 9
a = random(1,9)    
# Define set "B" of denominators that are coprime with "a"                 
B = { b with b in 2..9 where gcd(a,b)=1 }  
# Choose random denominator "b" from set B
b = random(B)               

# Generate the second fraction
# Choose another random numerator "c" from 1 to 9
c = random(1,9)   
# Define set "D" of denominators coprime with "c", different from "b"                  
D = { d with d in 2..9 where gcd(c,d)=1 && d!=b } 
# Choose random denominator "d" from set "D"
d = random(D)                  

# Calculate the sum of the two irreducible fractions
# The solution the students will calculate
sol = a/b + c/d                     

Solving linear equations with integer solutions

Consider creating a linear equation with random coefficients, ensuring that the solution is an integer.

# Generate a quadratic equation ax^2 + bx + c = 0
 with integer/rational solutions by ensuring discriminant is a perfect square.

# Generate random values for the coefficients
a = random([-10..10]/[0])
b = random([-10..10]/[0])
c = random([-10..10]/[0])

# Ensure the discriminant=b^2-4*a*c is a perfect square. If not, regenerate value "c". 

while square?(b^2-4*a*c) == false
do c = random([-10..10]/[0])


# At this point, we have a valid quadratic equation with rational solutions
solution1 = (-b + sqrt(discriminant)) / (2*a)
solution2 = (-b - sqrt(discriminant)) / (2*a)

r():= random([-10..10]/[0])
a=r()
b=r()
c=r()

Greatest common divisor of two random integers

Consider creating an exercise where students must calculate the GCD of two random integers.

# Randomly select target GCD between 2 and 10
target_gcd = random(2,10)

# Select two random integers that are coprime (so gcd=1)
repeat
  m = random(2,10)
  n = random([2,10]/[m])
until gcd(m, n) == 1

# Generate integers ensuring exact GCD is target_gcd
x = m * target_gcd
y = n * target_gcd

# Students should find the gcd of "x" and "y"
solution = target_gcd

Division with no remainder (exact division)

Consider creating an exercise where students divide two integers, ensuring that the result is an exact integer without remainder

# Select a random divisor from 2 to 12
divisor = random(2,12)

# Choose a random integer quotient between 2 and 10
quotient = random(2,10)

# Compute dividend ensuring exact division
dividend = divisor * quotient

# Students perform the division: dividend ÷ divisor
solution = quotient