# 7B: Math

**Source**: https://cscircles.cemc.uwaterloo.ca/7b-math/
**Parent**: https://cscircles.cemc.uwaterloo.ca/

*Lesson 7 has three parts A, B, C which can be completed in any order.*

So far, we have performed math calculations using Python's operators `+`,  `-`, `*`, `/` and the functions `max` and `min`. In this lesson we will see some more operators and functions and learn how to perform more complex calculations.

## Math Operators

We have already seen how to use operators for addition (`a + b`), subtraction (`a - b`), multiplication (`a * b`) and division (`a / b`). We will now learn about three additional operators.

- The **power** operator `a ** b` computes `ab` (`a` multiplied by itself `b` times). For example, `2 ** 3` produces `8` (which is 2×2×2).
- The **integer division** operator `a // b` computes the "quotient" of `a` divided by `b` and ignores the remainder. For example, `14 // 3` produces `4`.
- The **modulus** operator `a % b` computes the remainder when `a` is divided by `b`. For example, `14 % 3` produces `2`.

Example

The power, integer division, and modulus operators

print(2 \*\* 3)
print(14 // 3)
print(14 % 3)

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Coding Exercise: Eggsactly

Egg cartons each hold exactly 12 eggs. Write a program which reads an integer number of eggs from `input()`, then prints out two numbers: how many cartons can be filled by these eggs, and how many eggs will be left over. For example, the output corresponding to `27` eggs is

```
2\
3
```

since `27` eggs fill `2` cartons, leaving `3` eggs left over. Hint

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The modulus operator is used for a variety of tasks. It can be used to answer questions like these ones:

- If the time now is 10 o'clock, what will be the time 100 hours from now? (requires modulus by 12)
- Will the year 2032 be a leap year? ([requires modulus by 4, 100, and 400](http://en.wikipedia.org/wiki/Leap_year))

Checking leap years is an example of divisibility testing; in the next exercise we ask you to write a program that performs divisibility testing in general.

Coding Exercise: Divisibility

Write a program that reads two positive integers `a` and `b` on separate lines. If `a` is divisible by `b`, print the message "divisible". Otherwise, print the message "not divisible". For example, when the input is

```
14\
3
```

the program should print "not divisible". Hint

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