Learn Foundational Math 1 by Building an Equation Solver
Each of these steps will lead you toward the Certification Project. First you have to copy the files and set them up in your Google Drive.
Make sure you are logged into your Google account, and copy this notebook to your own account. Click "File" (at the top of this page) and then click "Save a copy in Drive." The file will be in a folder called "Colab Notebooks" in your Google Drive.
Click on the little triangle next to the word "Step" to do that step. Once you complete a step, click the triangle to expand the next step.
Please run this code to get the library file from FreeCodeCamp. Each step will use this library to test your code. You do not need to edit anything; just run this code cell and wait a few seconds until it tells you to go on to the next step.
# You may need to run this cell at the beginning of each new session
!pip install requests
# This will just take a few seconds
import requests
# Get the library from GitHub
url = 'https://raw.githubusercontent.com/freeCodeCamp/cdn/main/build/math-cert-tests/math-code-test-a.py'
r = requests.get(url)
# Save the library in a local working directory
with open('math_code_test_a.py', 'w') as f:
f.write(r.text)
# Now you can import the library
import math_code_test_a as test
# This will tell you if the code works
test.step19()
Requirement already satisfied: requests in /usr/local/lib/python3.8/dist-packages (2.28.2) Requirement already satisfied: charset-normalizer<4,>=2 in /usr/local/lib/python3.8/dist-packages (from requests) (3.1.0) Requirement already satisfied: certifi>=2017.4.17 in /usr/lib/python3/dist-packages (from requests) (2019.11.28) Requirement already satisfied: idna<4,>=2.5 in /usr/lib/python3/dist-packages (from requests) (2.8) Requirement already satisfied: urllib3<1.27,>=1.21.1 in /usr/lib/python3/dist-packages (from requests) (1.25.8) WARNING: Running pip as the 'root' user can result in broken permissions and conflicting behaviour with the system package manager. It is recommended to use a virtual environment instead: https://pip.pypa.io/warnings/venv [notice] A new release of pip is available: 23.0.1 -> 23.1.2 [notice] To update, run: python3 -m pip install --upgrade pip Test passed. You can go on to the next step.
To help you get familiar with Colab notebooks, you will start with the basics. Python uses +, -, *, and / for the four math operations: add, subtract, multiply, and divide. When you add two numbers, the result is the sum. Use addition within the print statement to get the sum of a and b. To run the code, you can hit "shift" and "enter" or you can click the run button (the triangle inside a circle).
a=1
b=2
# Change the next line to print the sum of a and b
print(a+b)
# Only change code above this line
import math_code_test_a as test
test.step01(In[-1].split('# Only change code above this line')[0])
3 Code test passed Go on to the next step
When you subtract two numbers, the result is the difference. Use subtraction in the print statement to get the difference between c and d. Remember to use "shift" and "enter" to run the code.
c = 7
d = 3
# Change the next line to print the positive difference between c and d
print(c-d)
# Only change code above this line
import math_code_test_a as test
test.step02(In[-1].split('# Only change code above this line')[0])
4 Code test passed Go on to the next step
When you multiply numbers, the result is the product. Use multiplication within the print statement to get the product of e and f:
e = 2
f = 4
# Change the next line to print the product of e and f
print(e*f)
# Only change code above this line
import math_code_test_a as test
test.step03(In[-1].split('# Only change code above this line')[0])
8 Code test passed Go on to the next step
When you divide two numbers, the result is the quotient. Use division within the print statement to get the quotient of g and h:
g = 8
h = 4
# Change the next line
print(g/h)
# Only change code above this line
import math_code_test_a as test
test.step04(In[-1].split('# Only change code above this line')[0])
2.0 Code test passed Go on to the next step
User input comes in as a string, so you need to cast it as an integer or a float before doing any math. The code below asks for input and uses int() to cast it as an integer. Follow the model and cast the second variable as an integer. Then run the code an test it. (Remember to hit "enter" after you type each integer in the box.)
strA = input('Enter a positive integer: ')
intA = int(strA)
strB = input('Enter another positive integer: ')
# Change the next line but keep the variable name:
intB = int(strB)
print(intA+intB)
# Only change code above this line
import math_code_test_a as test
test.step05(In[-1].split('# Only change code above this line')[0])
9 Code test passed Go on to the next step
You can prompt for input and cast that input on the same line. Notice the nested functions in the first line of code. Follow that model to prompt for input and cast that input as an integer on the same line.
intA = int(input('Enter an integer: '))
# Change the next line but keep the variable name:
intB = int(input('Enter an integer: '))
print(intA+intB)
# Only change code above this line
import math_code_test_a as test
test.step06(In[-1].split('# Only change code above this line')[0])
7 Code test passed Go on to the next step
A float number allows decimal places. When prompting for a number as input, casting that as a float is usually the best choice. Follow the model below to prompt for input and cast that input as a float on the same line.
a = float(input('Enter a number: '))
# Change the next line but keep the variable name:
b = float(input('Enter a number: '))
print(a/b)
# Only change code above this line
import math_code_test_a as test
test.step07(In[-1].split('# Only change code above this line')[0])
0.1270789360751789 Code test passed Go on to the next step
You may have heard of the order of operations and the acronym PEMDAS, which reminds you of the correct order. This means that you do what is in Parentheses first, then simplify Exponents. You then do all of the Multiplication and Division together, as long as you work from left to right and simplify them in order. The same is true of Addition and Subtraction: work from left to right and simplify the one the comes up next. Python knows the order of operations. In the following code, Python will calculate the actual_answer correctly. Notice the use of ** to indicate an exponent. Do the arithmetic in your head (no writing code) and change the your_answer variable, then run the code to see if your_answer matches the actual_answer.
actual_answer = (1+4*2-14/2)**3
# Put your answer on the following line:
your_answer = 8
print('Actual answer is ', actual_answer)
print('Your answer is ', your_answer)
# Only change code above this line
import math_code_test_a as test
test.step08(your_answer)
Actual answer is 8.0 Your answer is 8 Code test passed Go on to the next step
A remainder is what is left over when you try to divide two numbers and it doesn’t divide evenly. The remainder of 10 / 4 is 2 because 4 goes into 10 two whole times, with 2 left over. The modulus (%) operator will output the remainder, so 10 % 4 will return 2. Use the modulus operator to find the remainder of a divided by b:
a = 14
b = 6
# Change this line
print(a%b)
# Only change code above this line
import math_code_test_a as test
test.step09(In[-1].split('# Only change code above this line')[0])
2 Code test passed Go on to the next step
Use an if statement with the modulus operator to find out if one number is a factor of another. For example, to see if 5 is a factor of 20, you can test if 20 % 5 == 0. If there's no remainder, the second number is a factor of the first. Remember that Python comparisons use == to test values. Remember that the if statement ends in a colon (:) and the resulting block is indented four spaces. Finish the code below to print "true" if test_factor is a factor of number and print "false" if it is not.
number = int(input('Enter an integer: '))
test_factor = int(input('Enter an integer to see if it’s a factor: '))
# Change the next line to test the factor:
if number % test_factor == 0:
print('true')
else:
print('false')
# Only change code above this line
import math_code_test_a as test
test.step10(In[-1].split('# Only change code above this line')[0])
true Code test passed Go on to the next step
Now you will find all of the factors of a number. This code has a loop with a variable, test_factor, that iterates through a defined range. Remember that the first line defining the loop ends in a colon (:) and each line in the loop requires a four-space indent. Change the if statement to find all the factors of number.
number = int(input('Enter an integer: '))
# Only change the if statement:
for test_factor in range(1, number+1):
if number % test_factor == 0:
print(test_factor)
# Only change code above this line
import math_code_test_a as test
test.step11(In[-1].split('# Only change code above this line')[0])
1 2 3 4 6 8 12 24 Code test passed Go on to the next step
A prime number is a number whose only factors are 1 and itself. The number 5 is prime because its only factors are 1 and 5, but the 6 is not prime because it has 1, 2, 3, and 6 as factors. Any number that is not a prime is a composite. For each iteration in the loop, test_number will be a possible factor. Change the if statement so that the code prints "composite" if number is not prime.
number = int(input("Enter a positive integer: "))
prime_or_comp = "prime"
for test_number in range(2,number):
# Change the if statement to test one factor here:
if number % test_number == 0:
prime_or_comp = "composite"
break
print(prime_or_comp)
# Only change code above this line
import math_code_test_a as test
test.step12(In[-1].split('# Only change code above this line')[0])
composite Code test passed Go on to the next step
A reciprocal is a number "flipped." The reciprocal of $\frac{2}{3}$ is $\frac{3}{2}$ and the reciprocal of 5 is $\frac{1}{5}$ because whole numbers have denominators of 1. You can multiply a number by its reciprocal to get 1, so 5 * $\frac{1}{5}$ = 1 and $\frac{2}{3}$ * $\frac{3}{2}$ = 1. To get the reciprocal of a number, take 1 divided by that number. Trying to get the reciprocal of zero will lead to a "divide by zero" error. Use a print statement to output the reciprocal of n as a decimal.
n = float(input('Enter a number: '))
# Write your code here
print(1/n)
# Only change code above this line
import math_code_test_a as test
test.step13(In[-1].split('# Only change code above this line')[0])
0.04 Code test passed Go on to the next step
The code below asks for two integers, separated by a comma, then splits the input at the comma. Notice the input remains a string, then the split() function creates an array with two elements. Finish the following code to cast the two variables a and b as float numbers, then divide the two numbers and print the result.
nums = input('Enter two numbers, separated by a comma: ')
sp = nums.split(",")
# Use the next line as a model:
a = float(sp[0])
# Change the next line to cast the number as a float:
b = float(sp[1])
# Change the print statement:
print(a/b)
# Only change code above this line
import math_code_test_a as test
test.step14(In[-1].split('# Only change code above this line')[0])
0.375 Code test passed Go on to the next step
One factor multiplied by itself will produce a square number, so a number raised to an exponent of 2 is that number squared (like calculating the area of a square). Python uses ** to indicate exponents. Complete the code to print the square of the input.
n = float(input('Enter a number to square: '))
# Change this line of code:
print(n**2)
# Only change code above this line
import math_code_test_a as test
test.step15(In[-1].split('# Only change code above this line')[0])
441.0 Code test passed Go on to the next step
You can find the square root of a number with the sqrt() function. To use this function, you need to import the math library. This library enables you to use many functions, as you will see in later steps. To get the square root of x, you would write math.sqrt(x). Complete the code to print the square root of a number.
import math
n = float(input('Enter a number to find the square root: '))
# Change the next line of code:
print(math.sqrt(n))
# Only change code above this line
import math_code_test_a as test
test.step16(In[-1].split('# Only change code above this line')[0])
4.795831523312719 Code test passed Go on to the next step
Thefloor() function drops any decimals and sometimes is called the integer part of a number. Complete the code to print the floor of a number. Notice you import math and use math.floor(n)
import math
n = float(input('Enter a number with decimal places: '))
# Change the next line of code:
print(math.floor(n))
# Only change code above this line
import math_code_test_a as test
test.step17(In[-1].split('# Only change code above this line')[0])
32 Code test passed Go on to the next step
This step will combine a few things you have already done. Remember that a square number is an integer that is the result of multiplying another integer by itself. Just as you created a loop to find factors of an integer, here you will find the greatest factor that is a perfect square. For example, 2 is a factor of 16, but 2 is not a square number, while 4 is a factor and it is a square number, but it is not the greatest square factor. The greatest square factor of 16 is 16. The greatest square factor of 32 is 16. Complete if statement in the loop to find the greatest square factor of a number.
import math
n = int(input('Enter an integer to find the greatest square factor: '))
max_factor = 1
upper_limit = math.floor(math.sqrt(n)) + 1
# Change one line in this loop:
for maybe_factor in range(1,upper_limit):
if n % (maybe_factor**2) == 0:
max_factor = maybe_factor
# Keep this print statement:
print(max_factor**2)
# Only change code above this line
import math_code_test_a as test
test.step18(In[-1].split('# Only change code above this line')[0])
9 Code test passed Go on to the next step
Building upon your code from the previous step, this code will divide out the greatest square factor of a number. You don't need to change anything; just run the code below a few times, inputting different numbers each time.
import math
n = int(input('Enter an integer to factor: '))
upper_limit = math.floor(math.sqrt(n)) + 1
square_root = 1
max_factor = 1
other_factor = 1
# Notice what the loop is doing here
for maybe_factor in range(1, upper_limit):
# Check for square factors
if n % (maybe_factor**2) == 0:
# Find the greatest square factor
max_factor = maybe_factor**2
# Divide out the greatest square factor
other_factor = n/max_factor
# Display the results
print("", n, " = ", max_factor, " * ", other_factor)
# Only change code above this line
import math_code_test_a as test
test.step19()
4336 = 16 * 271.0 Test passed. You can go on to the next step.
The last four steps prepared you for this. To factor a square root, you want to divide out any perfect square factors. For example:
$\sqrt{12}$ = $\sqrt{4 * 3}$ = 2$\sqrt{3}$
Because 4 is a square number, the square root of 4 is now outside the radical.
You will import sympy and symbols to use the radical ($\sqrt{x}$) in the output. Use the code from the previous step (without changing much). Your goal is to ask for a number and output the factored square root. The radical formatting (using sympy and symbols) is already done for you.
import math
import sympy
from sympy import symbols
n = int(input('Without the radical, enter a square root to factor: '))
# Use these variables
upper_limit = math.floor(math.sqrt(n)) + 1
max_factor = 1
other_factor = 1
square_root = 1
# Notice what the loop is doing here
for maybe_factor in range(1, upper_limit):
if n % (maybe_factor**2) == 0:
max_factor = maybe_factor**2
# Divide out the greatest square factor
other_factor = n/max_factor
# Output - keep this:
square_root = int(math.sqrt(max_factor))
other_factor = int(other_factor)
output = square_root*sympy.sqrt(other_factor)
# Only change code above this line
import math_code_test_a as test
test.step20()
output
Test passed. This is this your factored square root:
If you only want a certain number of decimal places, use the round() function. This takes two arguments: the number to round and the number of decimal places, so round(2.468, 2) will return 2.47. To round a large number instead of a decimal number, make the second argument negative, so round(2345, -3) will return 2000. Finish the code below so that it prints the first number rounded to the nearest million (six zeros) and the second number rounded to 3 decimal places.
a = 14588132
b = 0.006538298336
# Write your code here
print(round(a, -6))
print(round(b, 3))
# Only change code above this line
import math_code_test_a as test
test.step21(In[-1].split('# Only change code above this line')[0])
15000000 0.007 Code test passed Go on to the next step
To convert a decimal number to a fraction, let $x$ = the number of decimal places. The basic fraction is the number (without the decimal point) over 10$^{x}$. Example: 0.2 = $\frac{2}{10}$ and 0.34 = $\frac{34}{100}$ and 0.567 = $\frac{567}{1000}$. In some cases, you may be able to reduce that fraction. Because "percent" means "out of 100" the percent refers to the first two decimal places. Complete the code to ask for a decimal input, then print the fraction and the percent. Hint: The exponent variable gives you the number of decimal places.
import math
digits = input("Enter a decimal number to convert: ")
exponent = int(len(digits))-1
n = float(digits)
# Change the values of these three variables
numerator = int(n*10**exponent)
denominator = 10**exponent
percent = (numerator/denominator)*100
# Output - keep this
print("The decimal is ", n)
print("The fraction is ", numerator, "/", denominator)
print("The percent is ", percent, " %")
# Only change code above this line
import math_code_test_a as test
test.step22(n,numerator,denominator,percent,exponent)
The decimal is 0.2342341 The fraction is 2342341 / 10000000 The percent is 23.42341 % Code test passed Go on to the next step
To execute a block of code with one command, define a function with the def command and the name of the function. Notice everything in the function is indented 4 spaces. Run the following code to see an example. Then change the function name to fun() and also change the name where you call the function. Run the code again.
# Define a function
def fun():
print("This is in the function")
# Other code not in the function
print("This is outside the function")
# Call the function
fun()
print("Back outside the function")
# Only change code above this line
import math_code_test_a as test
test.step23(In[-1].split('# Only change code above this line')[0])
This is outside the function This is in the function Back outside the function Code test passed Go on to the next step
A function can take input (called an "argument") and do something with that input. Use def to define the function, and include a variable in the parentheses to represent the argument. Indent everything that is a part of the function. When calling the function, pass the argument to it in the parentheses. Run the following code to see this example. Then change the input() variable name to nombre and also change that variable name in the argument when you call the function. Run the code again.
# Define a function
def greeting(name):
print("Hello ", name)
nombre = input("What is your name? \n")
# Call the function
greeting(nombre)
# Only change code above this line
import math_code_test_a as test
test.step24(In[-1].split('# Only change code above this line')[0])
Hello Python Code test passed You can go on to the next step
To pass more than one argument to a function, separate the arguments with commas. Run the code to see the example, then add a third argument to the function and run it again. The third variable is already in the code. Change three lines of code to use that variable: (1) the argument when you call the function, (2) the argument when you define the function, (3) the sum line within in the function definition.
# Define function
def add(a,b, c):
# Use c for the third variable
sum = a+b+c
print("The sum is ", sum)
first = float(input("Enter a number: \n"))
second= float(input("Enter another number: \n"))
third = 3
# Call the function
add(first,second, third)
# Only change code above this line
import math_code_test_a as test
test.step25(In[-1].split('# Only change code above this line')[0])
The sum is 555.0 Code test passed You can go on to the next step
Instead of including a print() statement within the function, the function can return a value right where you call it. To make the function return a value, use the return statement. Run the following code to see an example, then change the return statement to multiply by 3 instead of 2 and run the code again.
# define the function
def multiplied(number):
return number*3
a = float(input("Enter a number: \n"))
print("Your number multiplied = ", multiplied(a))
# Only change code above this line
import math_code_test_a as test
test.step26(In[-1].split('# Only change code above this line')[0])
Your number multiplied = 966.0 Code test passed You can go on to the next step
In Algebra, X often refers to the unknown number in an equation. To find the value of x we use algebra rules to get to x = [some number]. SymPy is a Python library to work with symbolic math. The following code works to solve an equation set equal to zero. Run the code and remember to use Python syntax to enter an equation (with "x" as the variable) and see the solution.
import sympy
from sympy import symbols
from sympy.solvers import solve
x = symbols('x')
eq = input('Enter an equation to solve for x: 0 = ')
print(len(solve(eq,x)))
print("x = ", solve(eq,x)[0])
# Only change code above this line
import math_code_test_a as test
test.step27(In[-1].split('# Only change code above this line')[0])
2 x = -16/23 - sqrt(53610)*I/23 If you didn't get a syntax error, you are ready for the project
Building upon what you did in previous steps, define a different function for each of the following:
# Write your code here
import re
import sympy
from sympy import symbols
from sympy.solvers import solve
def arithematic():
print("Enter an equation comprising only of numbers seprated by aithematic operators:")
eq = input()
if (re.search("^(\s?[0-9]+\s?[+-\\\*]\s?)+[0-9]+$", eq)):
result = eval(eq)
print(f'{eq} = {result}')
else:
print("Error: equation is not in accepted format")
def get_smallest_prime_factor(num):
if (num % 2 == 0 and num != 2):
return 2
for i in range(3, int(num/2)+1, 2):
if num % i == 0:
return i
return 1
def is_prime():
try:
num = int(input("Type a natural number to test if it a prime number:"))
except Exception as e:
print("Error:", e)
return
smallest_prime_factor = get_smallest_prime_factor(num)
if (smallest_prime_factor == 1):
print(f"{num} is a prime number.")
else:
print(f"{num} is not a prime number and is divisible by {smallest_prime_factor}")
def prime_factorization():
try:
num = int(input("Type a natural number to find it's prime factors:"))
except Exception as e:
print("Error:", e)
factors = []
new_num = num
while True:
factor = get_smallest_prime_factor(new_num)
if (factor == 1):
factors.append(int(new_num))
break
else:
factors.append(factor)
new_num /= factor
print(f"Prime factors of {num} are:")
print(' x '.join([str(n) for n in factors]))
def simplify_sqrt():
try:
sqrt = int(input("Input a radical/square root number (without symbol) to find it's simplified form:"))
except Exception as e:
print("Error:", e)
return
maybe_factor = 2
max_factor = 1
while (maybe_factor**2 <= sqrt):
if (sqrt % maybe_factor**2 == 0):
max_factor = maybe_factor
maybe_factor += 1
return max_factor*sympy.sqrt(int(sqrt/max_factor**2))
def solve_for_x():
try:
eq = input("Type an equation to solve for x. 0 = ")
x = symbols("x")
solutions = solve(eq, x)
for s in solutions:
print("x =", s)
except BaseException as e:
print(f"Error: {e}")
# This step does not have test
Use print statements to create a menu that displays a numbered list of options. Then prompt for user input to choose an option. Use an if statement to print a different message for each option in the menu.
# Write your code here
from IPython.display import display
options = [("Simple calculations", arithematic),
("Check if a number is prime", is_prime),
("Prime factorize a number", prime_factorization),
("Find simplified form of a square root", simplify_sqrt),
("Solve an euqation for X", solve_for_x)]
def print_menu():
print("What would you like to do?")
for i in range(len(options)):
print(f"{i+1}: {options[i][0]}")
# This step does not have test
Now put it all together to build a multi-function calculator. Use the menu and the functions you created in the previous steps. Define one more function of your own. Create the menu so that the user input will run a function.
# Write your code here
print_menu()
try:
selected = int(input())
except BaseException as e:
print("Error:", e)
if selected < 1 or selected > len(options):
print("Error: Invalid option selected")
elif selected == 4: # for pretty printing sqrt symbol
display(options[selected-1][1]())
else:
options[selected-1][1]()
# This step does not have test
What would you like to do? 1: Simple calculations 2: Check if a number is prime 3: Prime factorize a number 4: Find simplified form of a square root 5: Solve an euqation for X