mathgenerator.basic_math
1import random 2 3 4def absolute_difference(max_a=100, max_b=100): 5 r"""Absolute difference between two numbers 6 7 | Ex. Problem | Ex. Solution | 8 | --- | --- | 9 | $\|22-34\|=$ | $12$ | 10 """ 11 a = random.randint(-1 * max_a, max_a) 12 b = random.randint(-1 * max_b, max_b) 13 absDiff = abs(a - b) 14 15 return f'$|{a}-{b}|=$', f"${absDiff}$" 16 17 18def addition(max_sum=99, max_addend=50): 19 r"""Addition of two numbers 20 21 | Ex. Problem | Ex. Solution | 22 | --- | --- | 23 | $22+34=$ | $56$ | 24 """ 25 if max_addend > max_sum: 26 max_addend = max_sum 27 a = random.randint(0, max_addend) 28 # The highest value of b will be no higher than the max_sum minus the first number and no higher than the max_addend as well 29 b = random.randint(0, min((max_sum - a), max_addend)) 30 c = a + b 31 32 problem = f'${a}+{b}=$' 33 solution = f'${c}$' 34 return problem, solution 35 36 37def compare_fractions(max_val=10): 38 r"""Compare Fractions 39 40 | Ex. Problem | Ex. Solution | 41 | --- | --- | 42 | Which symbol represents the comparison between $\frac{1}{2}$ and $\frac{3}{4}$? | $>$ | 43 """ 44 a = random.randint(1, max_val) 45 b = random.randint(1, max_val) 46 c = random.randint(1, max_val) 47 d = random.randint(1, max_val) 48 49 while (a == b): 50 b = random.randint(1, max_val) 51 while (c == d): 52 d = random.randint(1, max_val) 53 54 first = a / b 55 second = c / d 56 57 if (first > second): 58 solution = ">" 59 elif (first < second): 60 solution = "<" 61 else: 62 solution = "=" 63 64 problem = rf"Which symbol represents the comparison between $\frac{{{a}}}{{{b}}}$ and $\frac{{{c}}}{{{d}}}$?" 65 return problem, solution 66 67 68def cube_root(min_no=1, max_no=1000): 69 r"""Cube Root 70 71 | Ex. Problem | Ex. Solution | 72 | --- | --- | 73 | What is the cube root of: $\sqrt[3]{125}=$ to 2 decimal places? | $5$ | 74 """ 75 b = random.randint(min_no, max_no) 76 a = b**(1 / 3) 77 78 return (rf"What is the cube root of: $\sqrt[3]{{{b}}}=$ to 2 decimal places?", f"${round(a, 2)}$") 79 80 81def divide_fractions(max_val=10): 82 r"""Divide Fractions 83 84 | Ex. Problem | Ex. Solution | 85 | --- | --- | 86 | $\frac{7}{9}\div\frac{4}{1}=$ | $\frac{7}{36}$ | 87 """ 88 a = random.randint(1, max_val) 89 b = random.randint(1, max_val) 90 91 while (a == b): 92 b = random.randint(1, max_val) 93 94 c = random.randint(1, max_val) 95 d = random.randint(1, max_val) 96 while (c == d): 97 d = random.randint(1, max_val) 98 99 def calculate_gcd(x, y): 100 while (y): 101 x, y = y, x % y 102 return x 103 104 tmp_n = a * d 105 tmp_d = b * c 106 107 gcd = calculate_gcd(tmp_n, tmp_d) 108 sol_numerator = tmp_n // gcd 109 sol_denominator = tmp_d // gcd 110 111 return rf'$\frac{{{a}}}{{{b}}}\div\frac{{{c}}}{{{d}}}=$', f'$\frac{{{sol_numerator}}}{{{sol_denominator}}}$' 112 113 114def division(max_a=25, max_b=25): 115 r"""Division 116 117 | Ex. Problem | Ex. Solution | 118 | --- | --- | 119 | $216\div24=$ | $9$ | 120 """ 121 a = random.randint(1, max_a) 122 b = random.randint(1, max_b) 123 124 divisor = a * b 125 dividend = random.choice([a, b]) 126 quotient = int(divisor / dividend) 127 128 return rf'${divisor}\div{dividend}=$', f'${quotient}$' 129 130 131def exponentiation(max_base=20, max_expo=10): 132 r"""Exponentiation 133 134 | Ex. Problem | Ex. Solution | 135 | --- | --- | 136 | $9^{5}=$ | $8$ | 137 """ 138 base = random.randint(1, max_base) 139 expo = random.randint(1, max_expo) 140 141 return f'${base}^{{{expo}}}=$', f'${base**expo}$' 142 143 144def factorial(max_input=6): 145 r"""Factorial 146 147 | Ex. Problem | Ex. Solution | 148 | --- | --- | 149 | $4! =$ | $24$ | 150 """ 151 a = random.randint(0, max_input) 152 n = a 153 b = 1 154 while a != 1 and n > 0: 155 b *= n 156 n -= 1 157 158 return f'${a}! =$', f'${b}$' 159 160 161def fraction_multiplication(max_val=10): 162 r"""Fraction Multiplication 163 164 | Ex. Problem | Ex. Solution | 165 | --- | --- | 166 | $\frac{3}{10}\cdot\frac{6}{7}=$ | $\frac{9}{35}$ | 167 """ 168 a = random.randint(1, max_val) 169 b = random.randint(1, max_val) 170 c = random.randint(1, max_val) 171 d = random.randint(1, max_val) 172 173 while (a == b): 174 b = random.randint(1, max_val) 175 176 while (c == d): 177 d = random.randint(1, max_val) 178 179 def calculate_gcd(x, y): 180 while (y): 181 x, y = y, x % y 182 return x 183 184 tmp_n = a * c 185 tmp_d = b * d 186 187 gcd = calculate_gcd(tmp_n, tmp_d) 188 189 problem = rf"$\frac{{{a}}}{{{b}}}\cdot\frac{{{c}}}{{{d}}}=$" 190 if (tmp_d == 1 or tmp_d == gcd): 191 solution = rf"$\frac{{{tmp_n}}}{{{gcd}}}$" 192 else: 193 solution = rf"$\frac{{{tmp_n//gcd}}}{{{tmp_d//gcd}}}$" 194 return problem, solution 195 196 197def fraction_to_decimal(max_res=99, max_divid=99): 198 r"""Fraction to Decimal 199 200 | Ex. Problem | Ex. Solution | 201 | --- | --- | 202 | $83\div80=$ | $1.04$ | 203 """ 204 a = random.randint(0, max_divid) 205 b = random.randint(1, min(max_res, max_divid)) 206 c = round(a / b, 2) 207 208 return rf'${a}\div{b}=$', f'${c}$' 209 210 211def greatest_common_divisor(numbers_count=2, max_num=10**3): 212 r"""Greatest Common Divisor of N Numbers ( GCD / HCF ) 213 214 | Ex. Problem | Ex. Solution | 215 | --- | --- | 216 | $GCD(488075608, 75348096)=$ | $8$ | 217 """ 218 219 def greatestCommonDivisorOfTwoNumbers(number1, number2): 220 number1 = abs(number1) 221 number2 = abs(number2) 222 while number2 > 0: 223 number1, number2 = number2, number1 % number2 224 return number1 225 226 numbers_count = max(numbers_count, 2) 227 numbers = [random.randint(0, max_num) 228 for _ in range(numbers_count)] 229 230 greatestCommonDivisor = greatestCommonDivisorOfTwoNumbers( 231 numbers[0], numbers[1]) 232 233 for index in range(1, numbers_count): 234 greatestCommonDivisor = greatestCommonDivisorOfTwoNumbers( 235 numbers[index], greatestCommonDivisor) 236 237 return f'$GCD({",".join(map(str, numbers))})=$', f"${greatestCommonDivisor}$" 238 239 240def is_composite(max_num=250): 241 r"""Is Composite 242 243 | Ex. Problem | Ex. Solution | 244 | --- | --- | 245 | Is $171$ composite? | Yes | 246 """ 247 a = random.randint(2, max_num) 248 249 problem = f"Is ${a}$ composite?" 250 if a == 0 or a == 1: 251 return problem, "No" 252 for i in range(2, a): 253 if a % i == 0: 254 return problem, "Yes" 255 solution = "No" 256 257 return problem, solution 258 259 260def is_prime(max_num=100): 261 r"""Is Prime 262 263 | Ex. Problem | Ex. Solution | 264 | --- | --- | 265 | Is $37$ prime? | Yes | 266 """ 267 a = random.randint(2, max_num) 268 problem = f"Is ${a}$ prime?" 269 if a == 2: 270 return problem, "Yes" 271 if a % 2 == 0: 272 return problem, "No" 273 for i in range(3, a // 2 + 1, 2): 274 if a % i == 0: 275 return problem, "No" 276 solution = "Yes" 277 278 return problem, solution 279 280 281def multiplication(max_multi=12): 282 r"""Multiplication 283 284 | Ex. Problem | Ex. Solution | 285 | --- | --- | 286 | $10\cdot9=$ | $90$ | 287 """ 288 a = random.randint(0, max_multi) 289 b = random.randint(0, max_multi) 290 c = a * b 291 292 return rf'${a}\cdot{b}=$', f'${c}$' 293 294 295def percentage(max_value=99, max_percentage=99): 296 r"""Percentage of a number 297 298 | Ex. Problem | Ex. Solution | 299 | --- | --- | 300 | What is $45$% of $39$? | $17.55$ | 301 """ 302 a = random.randint(1, max_percentage) 303 b = random.randint(1, max_value) 304 problem = f"What is ${a}$% of ${b}$?" 305 percentage = a / 100 * b 306 formatted_float = "{:.2f}".format(percentage) 307 solution = f"${formatted_float}$" 308 309 return problem, solution 310 311 312def percentage_difference(max_value=200, min_value=0): 313 r"""Percentage difference between two numbers 314 315 | Ex. Problem | Ex. Solution | 316 | --- | --- | 317 | What is the percentage difference between $2$ and $10$? | $133.33$ | 318 """ 319 value_a = random.randint(min_value, max_value) 320 value_b = random.randint(min_value, max_value) 321 322 diff = 2 * (abs(value_a - value_b) / abs(value_a + value_b)) * 100 323 diff = round(diff, 2) 324 325 problem = f"What is the percentage difference between ${value_a}$ and ${value_b}$?" 326 solution = f'${diff}$%' 327 return problem, solution 328 329 330def percentage_error(max_value=100, min_value=-100): 331 r"""Percentage error 332 333 | Ex. Problem | Ex. Solution | 334 | --- | --- | 335 | Find the percentage error when observed value equals $32$ and exact value equals $81$. | $60.49$% | 336 """ 337 observed_value = random.randint(min_value, max_value) 338 exact_value = random.randint(min_value, max_value) 339 340 if observed_value * exact_value < 0: 341 observed_value *= -1 342 343 error = (abs(observed_value - exact_value) / abs(exact_value)) * 100 344 error = round(error, 2) 345 346 problem = f"Find the percentage error when observed value equals ${observed_value}$ and exact value equals ${exact_value}$." 347 solution = f'${error}$%' 348 return problem, solution 349 350 351def power_of_powers(max_base=50, max_power=10): 352 r"""Power of Powers 353 354 | Ex. Problem | Ex. Solution | 355 | --- | --- | 356 | Simplify $18^{10^{8}}$ | $18^{80}$ | 357 """ 358 base = random.randint(1, max_base) 359 power1 = random.randint(1, max_power) 360 power2 = random.randint(1, max_power) 361 step = power1 * power2 362 363 problem = f"Simplify ${base}^{{{power1}^{{{power2}}}}}$" 364 solution = f"${base}^{{{step}}}$" 365 return problem, solution 366 367 368def square(max_square_num=20): 369 r"""Square 370 371 | Ex. Problem | Ex. Solution | 372 | --- | --- | 373 | $17^2=$ | $289$ | 374 """ 375 a = random.randint(1, max_square_num) 376 b = a ** 2 377 378 return f'${a}^2=$', f'${b}$' 379 380 381def square_root(min_no=1, max_no=12): 382 r"""Square Root 383 384 | Ex. Problem | Ex. Solution | 385 | --- | --- | 386 | $\sqrt{64}=$ | $8$ | 387 """ 388 b = random.randint(min_no, max_no) 389 a = b ** 2 390 391 return rf'$\sqrt{{{a}}}=$', f'${b}$' 392 393 394def simplify_square_root(max_variable=100): 395 r"""Simplify Square Root 396 397 | Ex. Problem | Ex. Solution | 398 | --- | --- | 399 | $\sqrt{63}$ | $3\sqrt{7}$ | 400 """ 401 y = x = random.randint(1, max_variable) 402 factors = {} 403 f = 2 404 while x != 1: 405 if x % f == 0: 406 if f not in factors: 407 factors[f] = 0 408 factors[f] += 1 409 x /= f 410 else: 411 f += 1 412 a = b = 1 413 for i in factors.keys(): 414 if factors[i] & 1 == 0: 415 a *= i ** (factors[i] // 2) 416 else: 417 a *= i ** ((factors[i] - 1) // 2) 418 b *= i 419 if a == 1 or b == 1: 420 return simplify_square_root(max_variable) 421 else: 422 return rf'$\sqrt{{{y}}}$', rf'${a}\sqrt{{{b}}}$' 423 424 425def subtraction(max_minuend=99, max_diff=99): 426 r"""Subtraction of two numbers 427 428 | Ex. Problem | Ex. Solution | 429 | --- | --- | 430 | $54-22=$ | $32$ | 431 """ 432 a = random.randint(0, max_minuend) 433 b = random.randint(max(0, (a - max_diff)), a) 434 c = a - b 435 436 return f'${a}-{b}=$', f'${c}$'
def
absolute_difference(max_a=100, max_b=100):
5def absolute_difference(max_a=100, max_b=100): 6 r"""Absolute difference between two numbers 7 8 | Ex. Problem | Ex. Solution | 9 | --- | --- | 10 | $\|22-34\|=$ | $12$ | 11 """ 12 a = random.randint(-1 * max_a, max_a) 13 b = random.randint(-1 * max_b, max_b) 14 absDiff = abs(a - b) 15 16 return f'$|{a}-{b}|=$', f"${absDiff}$"
Absolute difference between two numbers
| Ex. Problem | Ex. Solution |
|---|---|
| $|22-34|=$ | $12$ |
def
addition(max_sum=99, max_addend=50):
19def addition(max_sum=99, max_addend=50): 20 r"""Addition of two numbers 21 22 | Ex. Problem | Ex. Solution | 23 | --- | --- | 24 | $22+34=$ | $56$ | 25 """ 26 if max_addend > max_sum: 27 max_addend = max_sum 28 a = random.randint(0, max_addend) 29 # The highest value of b will be no higher than the max_sum minus the first number and no higher than the max_addend as well 30 b = random.randint(0, min((max_sum - a), max_addend)) 31 c = a + b 32 33 problem = f'${a}+{b}=$' 34 solution = f'${c}$' 35 return problem, solution
Addition of two numbers
| Ex. Problem | Ex. Solution |
|---|---|
| $22+34=$ | $56$ |
def
compare_fractions(max_val=10):
38def compare_fractions(max_val=10): 39 r"""Compare Fractions 40 41 | Ex. Problem | Ex. Solution | 42 | --- | --- | 43 | Which symbol represents the comparison between $\frac{1}{2}$ and $\frac{3}{4}$? | $>$ | 44 """ 45 a = random.randint(1, max_val) 46 b = random.randint(1, max_val) 47 c = random.randint(1, max_val) 48 d = random.randint(1, max_val) 49 50 while (a == b): 51 b = random.randint(1, max_val) 52 while (c == d): 53 d = random.randint(1, max_val) 54 55 first = a / b 56 second = c / d 57 58 if (first > second): 59 solution = ">" 60 elif (first < second): 61 solution = "<" 62 else: 63 solution = "=" 64 65 problem = rf"Which symbol represents the comparison between $\frac{{{a}}}{{{b}}}$ and $\frac{{{c}}}{{{d}}}$?" 66 return problem, solution
Compare Fractions
| Ex. Problem | Ex. Solution |
|---|---|
| Which symbol represents the comparison between $\frac{1}{2}$ and $\frac{3}{4}$? | $>$ |
def
cube_root(min_no=1, max_no=1000):
69def cube_root(min_no=1, max_no=1000): 70 r"""Cube Root 71 72 | Ex. Problem | Ex. Solution | 73 | --- | --- | 74 | What is the cube root of: $\sqrt[3]{125}=$ to 2 decimal places? | $5$ | 75 """ 76 b = random.randint(min_no, max_no) 77 a = b**(1 / 3) 78 79 return (rf"What is the cube root of: $\sqrt[3]{{{b}}}=$ to 2 decimal places?", f"${round(a, 2)}$")
Cube Root
| Ex. Problem | Ex. Solution |
|---|---|
| What is the cube root of: $\sqrt[3]{125}=$ to 2 decimal places? | $5$ |
def
divide_fractions(max_val=10):
82def divide_fractions(max_val=10): 83 r"""Divide Fractions 84 85 | Ex. Problem | Ex. Solution | 86 | --- | --- | 87 | $\frac{7}{9}\div\frac{4}{1}=$ | $\frac{7}{36}$ | 88 """ 89 a = random.randint(1, max_val) 90 b = random.randint(1, max_val) 91 92 while (a == b): 93 b = random.randint(1, max_val) 94 95 c = random.randint(1, max_val) 96 d = random.randint(1, max_val) 97 while (c == d): 98 d = random.randint(1, max_val) 99 100 def calculate_gcd(x, y): 101 while (y): 102 x, y = y, x % y 103 return x 104 105 tmp_n = a * d 106 tmp_d = b * c 107 108 gcd = calculate_gcd(tmp_n, tmp_d) 109 sol_numerator = tmp_n // gcd 110 sol_denominator = tmp_d // gcd 111 112 return rf'$\frac{{{a}}}{{{b}}}\div\frac{{{c}}}{{{d}}}=$', f'$\frac{{{sol_numerator}}}{{{sol_denominator}}}$'
Divide Fractions
| Ex. Problem | Ex. Solution |
|---|---|
| $\frac{7}{9}\div\frac{4}{1}=$ | $\frac{7}{36}$ |
def
division(max_a=25, max_b=25):
115def division(max_a=25, max_b=25): 116 r"""Division 117 118 | Ex. Problem | Ex. Solution | 119 | --- | --- | 120 | $216\div24=$ | $9$ | 121 """ 122 a = random.randint(1, max_a) 123 b = random.randint(1, max_b) 124 125 divisor = a * b 126 dividend = random.choice([a, b]) 127 quotient = int(divisor / dividend) 128 129 return rf'${divisor}\div{dividend}=$', f'${quotient}$'
Division
| Ex. Problem | Ex. Solution |
|---|---|
| $216\div24=$ | $9$ |
def
exponentiation(max_base=20, max_expo=10):
132def exponentiation(max_base=20, max_expo=10): 133 r"""Exponentiation 134 135 | Ex. Problem | Ex. Solution | 136 | --- | --- | 137 | $9^{5}=$ | $8$ | 138 """ 139 base = random.randint(1, max_base) 140 expo = random.randint(1, max_expo) 141 142 return f'${base}^{{{expo}}}=$', f'${base**expo}$'
Exponentiation
| Ex. Problem | Ex. Solution |
|---|---|
| $9^{5}=$ | $8$ |
def
factorial(max_input=6):
145def factorial(max_input=6): 146 r"""Factorial 147 148 | Ex. Problem | Ex. Solution | 149 | --- | --- | 150 | $4! =$ | $24$ | 151 """ 152 a = random.randint(0, max_input) 153 n = a 154 b = 1 155 while a != 1 and n > 0: 156 b *= n 157 n -= 1 158 159 return f'${a}! =$', f'${b}$'
Factorial
| Ex. Problem | Ex. Solution |
|---|---|
| $4! =$ | $24$ |
def
fraction_multiplication(max_val=10):
162def fraction_multiplication(max_val=10): 163 r"""Fraction Multiplication 164 165 | Ex. Problem | Ex. Solution | 166 | --- | --- | 167 | $\frac{3}{10}\cdot\frac{6}{7}=$ | $\frac{9}{35}$ | 168 """ 169 a = random.randint(1, max_val) 170 b = random.randint(1, max_val) 171 c = random.randint(1, max_val) 172 d = random.randint(1, max_val) 173 174 while (a == b): 175 b = random.randint(1, max_val) 176 177 while (c == d): 178 d = random.randint(1, max_val) 179 180 def calculate_gcd(x, y): 181 while (y): 182 x, y = y, x % y 183 return x 184 185 tmp_n = a * c 186 tmp_d = b * d 187 188 gcd = calculate_gcd(tmp_n, tmp_d) 189 190 problem = rf"$\frac{{{a}}}{{{b}}}\cdot\frac{{{c}}}{{{d}}}=$" 191 if (tmp_d == 1 or tmp_d == gcd): 192 solution = rf"$\frac{{{tmp_n}}}{{{gcd}}}$" 193 else: 194 solution = rf"$\frac{{{tmp_n//gcd}}}{{{tmp_d//gcd}}}$" 195 return problem, solution
Fraction Multiplication
| Ex. Problem | Ex. Solution |
|---|---|
| $\frac{3}{10}\cdot\frac{6}{7}=$ | $\frac{9}{35}$ |
def
fraction_to_decimal(max_res=99, max_divid=99):
198def fraction_to_decimal(max_res=99, max_divid=99): 199 r"""Fraction to Decimal 200 201 | Ex. Problem | Ex. Solution | 202 | --- | --- | 203 | $83\div80=$ | $1.04$ | 204 """ 205 a = random.randint(0, max_divid) 206 b = random.randint(1, min(max_res, max_divid)) 207 c = round(a / b, 2) 208 209 return rf'${a}\div{b}=$', f'${c}$'
Fraction to Decimal
| Ex. Problem | Ex. Solution |
|---|---|
| $83\div80=$ | $1.04$ |
def
greatest_common_divisor(numbers_count=2, max_num=1000):
212def greatest_common_divisor(numbers_count=2, max_num=10**3): 213 r"""Greatest Common Divisor of N Numbers ( GCD / HCF ) 214 215 | Ex. Problem | Ex. Solution | 216 | --- | --- | 217 | $GCD(488075608, 75348096)=$ | $8$ | 218 """ 219 220 def greatestCommonDivisorOfTwoNumbers(number1, number2): 221 number1 = abs(number1) 222 number2 = abs(number2) 223 while number2 > 0: 224 number1, number2 = number2, number1 % number2 225 return number1 226 227 numbers_count = max(numbers_count, 2) 228 numbers = [random.randint(0, max_num) 229 for _ in range(numbers_count)] 230 231 greatestCommonDivisor = greatestCommonDivisorOfTwoNumbers( 232 numbers[0], numbers[1]) 233 234 for index in range(1, numbers_count): 235 greatestCommonDivisor = greatestCommonDivisorOfTwoNumbers( 236 numbers[index], greatestCommonDivisor) 237 238 return f'$GCD({",".join(map(str, numbers))})=$', f"${greatestCommonDivisor}$"
Greatest Common Divisor of N Numbers ( GCD / HCF )
| Ex. Problem | Ex. Solution |
|---|---|
| $GCD(488075608, 75348096)=$ | $8$ |
def
is_composite(max_num=250):
241def is_composite(max_num=250): 242 r"""Is Composite 243 244 | Ex. Problem | Ex. Solution | 245 | --- | --- | 246 | Is $171$ composite? | Yes | 247 """ 248 a = random.randint(2, max_num) 249 250 problem = f"Is ${a}$ composite?" 251 if a == 0 or a == 1: 252 return problem, "No" 253 for i in range(2, a): 254 if a % i == 0: 255 return problem, "Yes" 256 solution = "No" 257 258 return problem, solution
Is Composite
| Ex. Problem | Ex. Solution |
|---|---|
| Is $171$ composite? | Yes |
def
is_prime(max_num=100):
261def is_prime(max_num=100): 262 r"""Is Prime 263 264 | Ex. Problem | Ex. Solution | 265 | --- | --- | 266 | Is $37$ prime? | Yes | 267 """ 268 a = random.randint(2, max_num) 269 problem = f"Is ${a}$ prime?" 270 if a == 2: 271 return problem, "Yes" 272 if a % 2 == 0: 273 return problem, "No" 274 for i in range(3, a // 2 + 1, 2): 275 if a % i == 0: 276 return problem, "No" 277 solution = "Yes" 278 279 return problem, solution
Is Prime
| Ex. Problem | Ex. Solution |
|---|---|
| Is $37$ prime? | Yes |
def
multiplication(max_multi=12):
282def multiplication(max_multi=12): 283 r"""Multiplication 284 285 | Ex. Problem | Ex. Solution | 286 | --- | --- | 287 | $10\cdot9=$ | $90$ | 288 """ 289 a = random.randint(0, max_multi) 290 b = random.randint(0, max_multi) 291 c = a * b 292 293 return rf'${a}\cdot{b}=$', f'${c}$'
Multiplication
| Ex. Problem | Ex. Solution |
|---|---|
| $10\cdot9=$ | $90$ |
def
percentage(max_value=99, max_percentage=99):
296def percentage(max_value=99, max_percentage=99): 297 r"""Percentage of a number 298 299 | Ex. Problem | Ex. Solution | 300 | --- | --- | 301 | What is $45$% of $39$? | $17.55$ | 302 """ 303 a = random.randint(1, max_percentage) 304 b = random.randint(1, max_value) 305 problem = f"What is ${a}$% of ${b}$?" 306 percentage = a / 100 * b 307 formatted_float = "{:.2f}".format(percentage) 308 solution = f"${formatted_float}$" 309 310 return problem, solution
Percentage of a number
| Ex. Problem | Ex. Solution |
|---|---|
| What is $45$% of $39$? | $17.55$ |
def
percentage_difference(max_value=200, min_value=0):
313def percentage_difference(max_value=200, min_value=0): 314 r"""Percentage difference between two numbers 315 316 | Ex. Problem | Ex. Solution | 317 | --- | --- | 318 | What is the percentage difference between $2$ and $10$? | $133.33$ | 319 """ 320 value_a = random.randint(min_value, max_value) 321 value_b = random.randint(min_value, max_value) 322 323 diff = 2 * (abs(value_a - value_b) / abs(value_a + value_b)) * 100 324 diff = round(diff, 2) 325 326 problem = f"What is the percentage difference between ${value_a}$ and ${value_b}$?" 327 solution = f'${diff}$%' 328 return problem, solution
Percentage difference between two numbers
| Ex. Problem | Ex. Solution |
|---|---|
| What is the percentage difference between $2$ and $10$? | $133.33$ |
def
percentage_error(max_value=100, min_value=-100):
331def percentage_error(max_value=100, min_value=-100): 332 r"""Percentage error 333 334 | Ex. Problem | Ex. Solution | 335 | --- | --- | 336 | Find the percentage error when observed value equals $32$ and exact value equals $81$. | $60.49$% | 337 """ 338 observed_value = random.randint(min_value, max_value) 339 exact_value = random.randint(min_value, max_value) 340 341 if observed_value * exact_value < 0: 342 observed_value *= -1 343 344 error = (abs(observed_value - exact_value) / abs(exact_value)) * 100 345 error = round(error, 2) 346 347 problem = f"Find the percentage error when observed value equals ${observed_value}$ and exact value equals ${exact_value}$." 348 solution = f'${error}$%' 349 return problem, solution
Percentage error
| Ex. Problem | Ex. Solution |
|---|---|
| Find the percentage error when observed value equals $32$ and exact value equals $81$. | $60.49$% |
def
power_of_powers(max_base=50, max_power=10):
352def power_of_powers(max_base=50, max_power=10): 353 r"""Power of Powers 354 355 | Ex. Problem | Ex. Solution | 356 | --- | --- | 357 | Simplify $18^{10^{8}}$ | $18^{80}$ | 358 """ 359 base = random.randint(1, max_base) 360 power1 = random.randint(1, max_power) 361 power2 = random.randint(1, max_power) 362 step = power1 * power2 363 364 problem = f"Simplify ${base}^{{{power1}^{{{power2}}}}}$" 365 solution = f"${base}^{{{step}}}$" 366 return problem, solution
Power of Powers
| Ex. Problem | Ex. Solution |
|---|---|
| Simplify $18^{10^{8}}$ | $18^{80}$ |
def
square(max_square_num=20):
369def square(max_square_num=20): 370 r"""Square 371 372 | Ex. Problem | Ex. Solution | 373 | --- | --- | 374 | $17^2=$ | $289$ | 375 """ 376 a = random.randint(1, max_square_num) 377 b = a ** 2 378 379 return f'${a}^2=$', f'${b}$'
Square
| Ex. Problem | Ex. Solution |
|---|---|
| $17^2=$ | $289$ |
def
square_root(min_no=1, max_no=12):
382def square_root(min_no=1, max_no=12): 383 r"""Square Root 384 385 | Ex. Problem | Ex. Solution | 386 | --- | --- | 387 | $\sqrt{64}=$ | $8$ | 388 """ 389 b = random.randint(min_no, max_no) 390 a = b ** 2 391 392 return rf'$\sqrt{{{a}}}=$', f'${b}$'
Square Root
| Ex. Problem | Ex. Solution |
|---|---|
| $\sqrt{64}=$ | $8$ |
def
simplify_square_root(max_variable=100):
395def simplify_square_root(max_variable=100): 396 r"""Simplify Square Root 397 398 | Ex. Problem | Ex. Solution | 399 | --- | --- | 400 | $\sqrt{63}$ | $3\sqrt{7}$ | 401 """ 402 y = x = random.randint(1, max_variable) 403 factors = {} 404 f = 2 405 while x != 1: 406 if x % f == 0: 407 if f not in factors: 408 factors[f] = 0 409 factors[f] += 1 410 x /= f 411 else: 412 f += 1 413 a = b = 1 414 for i in factors.keys(): 415 if factors[i] & 1 == 0: 416 a *= i ** (factors[i] // 2) 417 else: 418 a *= i ** ((factors[i] - 1) // 2) 419 b *= i 420 if a == 1 or b == 1: 421 return simplify_square_root(max_variable) 422 else: 423 return rf'$\sqrt{{{y}}}$', rf'${a}\sqrt{{{b}}}$'
Simplify Square Root
| Ex. Problem | Ex. Solution |
|---|---|
| $\sqrt{63}$ | $3\sqrt{7}$ |
def
subtraction(max_minuend=99, max_diff=99):
426def subtraction(max_minuend=99, max_diff=99): 427 r"""Subtraction of two numbers 428 429 | Ex. Problem | Ex. Solution | 430 | --- | --- | 431 | $54-22=$ | $32$ | 432 """ 433 a = random.randint(0, max_minuend) 434 b = random.randint(max(0, (a - max_diff)), a) 435 c = a - b 436 437 return f'${a}-{b}=$', f'${c}$'
Subtraction of two numbers
| Ex. Problem | Ex. Solution |
|---|---|
| $54-22=$ | $32$ |