#
# This program adds, subtracts, multiplies, divides two fractions and simplifies the result.
# Author: Arvin Javaheripur
#
# Copyright 2021 Arvin Javaheripur
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
#
import math
def is_integer(num):
result = False
try:
if (isinstance(num, int)):
result = True
elif (isinstance(num, float)):
result = False
elif (isinstance(num, str)):
int(num)
result = True
except:
result = False
return result
def lcm(x, y):
x = abs(x)
y = abs(y)
temp = 0
if x > y:
temp = x
x = y
y = temp
result = x
while (result % y) != 0:
result += x
return int(result)
# main
is_valid = False
inp_fraction1 = ""
while not is_valid:
inp_fraction1 = input("Enter the first fraction (\u00B1x1/y1): ")
inp_fraction1_splitted = inp_fraction1.split("/", 1)
if len(inp_fraction1_splitted) == 1:
inp_fraction1_splitted.append("1")
if is_integer(inp_fraction1_splitted[0]) and is_integer(inp_fraction1_splitted[1]) and (int(inp_fraction1_splitted[1]) != 0):
is_valid = True
else:
print("Invalid fraction!")
numerator1 = int(inp_fraction1_splitted[0])
denominator1 = int(inp_fraction1_splitted[1])
if denominator1 < 0:
numerator1 *= -1
denominator1 *= -1
print(f"{inp_fraction1} changed to {numerator1}/{denominator1}")
is_valid = False
inp_fraction2 = ""
while not is_valid:
inp_fraction2 = input("Enter the second fraction (\u00B1x2/y2): ")
inp_fraction2_splitted = inp_fraction2.split("/", 1)
if len(inp_fraction2_splitted) == 1:
inp_fraction2_splitted.append("1")
if is_integer(inp_fraction2_splitted[0]) and is_integer(inp_fraction2_splitted[1]) and (int(inp_fraction2_splitted[1]) != 0):
is_valid = True
else:
print("Invalid fraction!")
numerator2 = int(inp_fraction2_splitted[0])
denominator2 = int(inp_fraction2_splitted[1])
if denominator2 < 0:
numerator2 *= -1
denominator2 *= -1
print(f"{inp_fraction2} changed to {numerator2}/{denominator2}")
lcm = lcm(denominator1, denominator2)
result_numerator_addition = int(lcm/denominator1*numerator1 + lcm/denominator2*numerator2)
result_denominator_addition = lcm
result_numerator_subtraction = int(lcm/denominator1*numerator1 - lcm/denominator2*numerator2)
result_denuminator_subtraction = lcm
result_numerator_multiplication = int(numerator1*numerator2)
result_denominator_multiplication = denominator1*denominator2
result_numerator_division = int(numerator1*denominator2)
result_denominator_division = denominator1*numerator2
if result_denominator_division < 0:
result_numerator_division *= -1
result_denominator_division *= -1
final_result_addition = f"{numerator1}/{denominator1} + {numerator2}/{denominator2} = {result_numerator_addition}/{result_denominator_addition}"
final_result_subtraction = f"{numerator1}/{denominator1} - {numerator2}/{denominator2} = {result_numerator_subtraction}/{result_denuminator_subtraction}"
final_result_multiplication = f"{numerator1}/{denominator1} * {numerator2}/{denominator2} = {result_numerator_multiplication}/{result_denominator_multiplication}"
if result_denominator_division == 0:
final_result_division = f"{numerator1}/{denominator1} \u00F7 {numerator2}/{denominator2} = \u221E"
else:
final_result_division = f"{numerator1}/{denominator1} \u00F7 {numerator2}/{denominator2} = {result_numerator_division}/{result_denominator_division}"
prime_numbers = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31]
simplified_numerator1 = result_numerator_addition
simplified_denominator1 = result_denominator_addition
i = 0
while i < len(prime_numbers):
if (simplified_numerator1 % prime_numbers[i]) == 0 and (simplified_denominator1 % prime_numbers[i]) == 0:
simplified_numerator1 //= prime_numbers[i]
simplified_denominator1 //= prime_numbers[i]
else:
i += 1
simplified_numerator2 = result_numerator_subtraction
simplified_denominator2 = result_denuminator_subtraction
i = 0
while i < len(prime_numbers):
if (simplified_numerator2 % prime_numbers[i]) == 0 and (simplified_denominator2 % prime_numbers[i]) == 0:
simplified_numerator2 //= prime_numbers[i]
simplified_denominator2 //= prime_numbers[i]
else:
i += 1
simplified_numerator3 = result_numerator_multiplication
simplified_denominator3 = result_denominator_multiplication
i = 0
while i < len(prime_numbers):
if (simplified_numerator3 % prime_numbers[i]) == 0 and (simplified_denominator3 % prime_numbers[i]) == 0:
simplified_numerator3 //= prime_numbers[i]
simplified_denominator3 //= prime_numbers[i]
else:
i += 1
simplified_numerator4 = result_numerator_division
simplified_denominator4 = result_denominator_division
if result_denominator_division != 0:
i = 0
while i < len(prime_numbers):
if (simplified_numerator4 % prime_numbers[i]) == 0 and (simplified_denominator4 % prime_numbers[i]) == 0:
simplified_numerator4 //= prime_numbers[i]
simplified_denominator4 //= prime_numbers[i]
else:
i += 1
final_result1 = final_result_addition
final_result2 = final_result_subtraction
final_result3 = final_result_multiplication
final_result4 = final_result_division
# simplification
result1_is_whole = False
if simplified_denominator1 == 1:
simplified_result1 = f"{int(simplified_numerator1)}"
result1_is_whole = True
elif (simplified_numerator1 % simplified_denominator2) == 0:
simplified_result1 = f"{int(simplified_numerator1 / simplified_denominator1)}"
result1_is_whole = True
else:
simplified_result1 = f"{int(simplified_numerator1)}/{int(simplified_denominator1)}"
if simplified_denominator1 != result_denominator_addition:
final_result1 += " = " + simplified_result1
result2_is_whole = False
if simplified_denominator2 == 1:
simplified_result2 = f"{int(simplified_numerator2)}"
result2_is_whole = True
elif (simplified_numerator2 % simplified_denominator2) == 0:
simplified_result2 = f"{int(simplified_numerator2 / simplified_denominator2)}"
result2_is_whole = True
else:
simplified_result2 = f"{int(simplified_numerator2)}/{int(simplified_denominator2)}"
if simplified_denominator2 != result_denuminator_subtraction:
final_result2 += " = " + simplified_result2
result3_is_whole = False
if simplified_denominator3 == 1:
simplified_result3 = f"{int(simplified_numerator3)}"
result3_is_whole = True
elif (simplified_numerator3 % simplified_denominator3) == 0:
simplified_result3 = f"{int(simplified_numerator3 / simplified_denominator3)}"
result3_is_whole = True
else:
simplified_result3 = f"{int(simplified_numerator3)}/{int(simplified_denominator3)}"
if simplified_denominator3 != result_denominator_multiplication:
final_result3 += " = " + simplified_result3
result4_is_whole = False
if simplified_denominator4 == 1:
simplified_result4 = f"{int(simplified_numerator4)}"
result4_is_whole = True
elif simplified_denominator4 == 0:
simplified_result4 = ""
result4_is_whole = True
elif (simplified_numerator4 % simplified_denominator4) == 0:
simplified_result4 = f"{int(simplified_numerator4 / simplified_denominator4)}"
result4_is_whole = True
else:
simplified_result4 = f"{int(simplified_numerator4)}/{int(simplified_denominator4)}"
if simplified_denominator4 != result_denominator_division:
final_result4 += " = " + simplified_result4
# convert to mixed number
if not result1_is_whole and simplified_numerator1 > simplified_denominator1:
mixed_num_fraction1 = f"{simplified_numerator1 % simplified_denominator1}/{simplified_denominator1}"
mixed_num1 = f"{simplified_numerator1 // simplified_denominator1} {mixed_num_fraction1}"
final_result1 += f" = {mixed_num1}"
if not result2_is_whole and simplified_numerator2 > simplified_denominator2:
mixed_num_fraction2 = f"{simplified_numerator2 % simplified_denominator2}/{simplified_denominator2}"
mixed_num2 = f"{simplified_numerator2 // simplified_denominator2} {mixed_num_fraction2}"
final_result2 += f" = {mixed_num2}"
if not result3_is_whole and simplified_numerator3 > simplified_denominator3:
mixed_num_fraction3 = f"{simplified_numerator3 % simplified_denominator3}/{simplified_denominator3}"
mixed_num3 = f"{simplified_numerator3 // simplified_denominator3} {mixed_num_fraction3}"
final_result3 += f" = {mixed_num3}"
if not result4_is_whole and simplified_numerator4 > simplified_denominator4:
mixed_num_fraction4 = f"{simplified_numerator4 % simplified_denominator4}/{simplified_denominator4}"
mixed_num4 = f"{simplified_numerator4 // simplified_denominator4} {mixed_num_fraction4}"
final_result4 += f" = {mixed_num4}"
print(final_result1)
print(final_result2)
print(final_result3)
print(final_result4)
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