Using arithmetic operators

What you'll learn

How to use Python arithmetic operators: +, -, *, /, %, // and **.
The difference between division, integer division and modulus.
How Python decides the order of calculations in an expression.
How to write short program statements that calculate and store numeric results.

Arithmetic in programs

A program often needs to calculate values: scores, totals, averages, positions, costs, distances, file sizes, and more. In Python 3, you write these calculations using arithmetic operators.

Definition

Arithmetic operators and expressions

An arithmetic operator is a symbol that tells the computer to perform a calculation. An operand is a value or variable that the operator works on. An arithmetic expression is a piece of code that combines operands and operators to produce a numeric result.

For example, in score + 10, the operator is +, and the operands are score and 10.

A variable is a named storage location in a program. You can store the result of a calculation in a variable using assignment, written with = in Python.

For example: total = price * quantity

This means: calculate price * quantity, then store the result in total.

The arithmetic operators you need

Operation	Python operator	Example	Result	Meaning
Addition	`+`	`7 + 2`	`9`	Adds values
Subtraction	`-`	`7 - 2`	`5`	Takes one value away from another
Multiplication	`*`	`7 * 2`	`14`	Multiplies values
Division	`/`	`7 / 2`	`3.5`	Gives a real-number answer
Integer division	`//`	`7 // 2`	`3`	Gives the whole-number quotient
Modulus	`%`	`7 % 2`	`1`	Gives the remainder
Exponentiation	`<strong>`	`2 </strong> 3`	`8`	Raises a number to a power

Common Mistake

Writing maths symbols instead of Python symbols

Python does not understand 2x, 2^3, or a written divide sign. Write 2 * x, 2 ** 3, and 7 / 2 instead.

Assignment: storing a calculated result

In Python, assignment uses =. The expression on the right is evaluated first, then the answer is stored in the variable on the left.

For example:

score = 12
score = score + 5

The second line may look strange at first, because score appears on both sides. In programming, this means “take the old value of score, add 5, then store the new value back into score”.

Example

Updating a score

Start with the current value: score stores 12.
Evaluate the right-hand side of score = score + 5: this becomes 12 + 5, which gives 17.
Store the result back into the variable, so score now stores 17 instead of 12.

Key Idea

Assignment is not a maths equation

In Python, score = score + 5 is valid because = means “store this value”, not “these two sides are already equal”.

Multiplication, division and real answers

Multiplication uses *. Division uses /.

In Python 3, / gives a float, which is Python’s name for a number that may have a decimal part. So 8 / 2 gives 4.0, not just 4.

That matters when the rest of your program expects a whole number.

Common Mistake

Expecting division to give an integer

7 / 2 gives 3.5. If you want the whole-number part of the answer, use integer division: 7 // 2 gives 3.

Integer division and modulus

Integer division and modulus are a pair. They are useful when you are splitting something into equal groups.

Definition

Integer division and modulus

Integer division using // gives the whole-number quotient. Modulus using % gives the remainder after division.

For positive whole numbers, they fit this pattern: dividend equals divisor times quotient plus remainder.

For example, 29 // 6 gives 4, because 6 fits into 29 four complete times. Then 29 % 6 gives 5, because 5 is left over.

Example

Finding full groups and remainders

Suppose 29 students are put into groups of 6. Use integer division to find the number of full groups: 29 // 6 gives 4.
Use modulus to find how many students are left over: 29 % 6 gives 5.
Check the result using the relationship $\times 4 + 5$ , so there are 4 full groups and 5 students left over.

Tip

When modulus is useful

Modulus is useful for “left over” questions. For example, number % 2 gives 0 when a whole number divides exactly by 2, so it can help detect even numbers.

Common Mistake

Dividing by zero

You cannot use /, // or % with zero as the divisor. For example, 10 / 0 causes a Python error because division by zero is undefined.

Exponentiation: powers

Exponentiation means raising a number to a power. In Python, use **.

Examples:

2 ** 3 means 2 cubed, giving 8.
5 ** 2 means 5 squared, giving 25.
10 ** 3 gives 1000.

This is useful in Computer Science. For example, 8 bits can represent 2 ** 8 different unsigned values, which is 256 values.

Operator precedence: the order of calculation

Operator precedence means the order Python uses when an expression contains more than one operator.

Python does not simply calculate from left to right every time. Some operators are done before others. Brackets are done first, then exponentiation, then multiplication/division-related operators, then addition and subtraction.

Arithmetic operator precedence in Python

Example

Evaluating a mixed expression

In 2 + 3 * 4 <strong> 2, exponentiation has the highest precedence after brackets, so calculate 4 </strong> 2 first. The expression becomes 2 + 3 * 16.
Multiplication is done before addition, so calculate 3 * 16. The expression becomes 2 + 48.
Finally, calculate the addition. The result is 50.

Operators on the same precedence level are usually evaluated from left to right. For GCSE programming, the safest habit is to use brackets whenever the intended order might not be obvious.

Using brackets to control the result

Brackets force Python to calculate part of an expression first. This can completely change the answer.

For example:

10 + 6 // 4 gives 11, because 6 // 4 is calculated first and gives 1.
(10 + 6) // 4 gives 4, because the bracketed addition is calculated first.

Key Idea

Brackets make your intention clear

Even when Python would calculate the expression correctly without brackets, adding brackets can make your program easier to read and reduce mistakes.

Writing arithmetic with user input

If a program asks the user to type a value using input(), Python receives it as a string, which means text. To do arithmetic, convert it to a number first.

Use:

int(...) for whole numbers, such as age = int(input("Age: "))
float(...) for numbers that may contain decimals, such as price = float(input("Price: "))

Then you can calculate with the value:

quantity = int(input("Quantity: "))
price = float(input("Price of one item: "))
total = quantity * price

Common Mistake

Forgetting to convert input

If you write quantity = input("Quantity: "), the value is text. Convert it with int() before using arithmetic, otherwise your calculation may fail or behave unexpectedly.

Choosing the right operator

A good way to choose the correct operator is to translate the problem into what you want the computer to calculate.

If the problem says...	You probably need...	Example
“total”, “more”, “increase by”	`+`	`score = score + bonus`
“difference”, “decrease by”, “left after taking away”	`-`	`lives = lives - 1`
“each”, “per item”, “repeated groups”	`*`	`cost = price * quantity`
“share equally with possible decimals”	`/`	`average = total / count`
“number of full groups”	`//`	`boxes = items // items_per_box`
“left over” or “remainder”	`%`	`left_over = items % items_per_box`
“squared”, “cubed”, “power of”	`<strong>`	`area = side </strong> 2`

Exam technique

In the exam

Decide whether the question needs a real-number division answer using /, or a whole-number quotient and remainder using // and %.
When an expression has several operators, apply precedence carefully: brackets, powers, multiplication/division/integer division/modulus, then addition/subtraction.
Use Python syntax exactly: * for multiplication, ** for powers, and meaningful variable names for calculated values.

Self review

Check yourself

What is the difference between 17 / 5, 17 // 5 and 17 % 5?
Why does 2 + 3 * 4 not give the same result as (2 + 3) * 4?
What conversion might you need if a number has been entered using input()?

Using arithmetic operators

What you'll learn

How to use Python arithmetic operators: +, -, *, /, %, // and **.
The difference between division, integer division and modulus.
How Python decides the order of calculations in an expression.
How to write short program statements that calculate and store numeric results.

Arithmetic in programs

A program often needs to calculate values: scores, totals, averages, positions, costs, distances, file sizes, and more. In Python 3, you write these calculations using arithmetic operators.

Definition

Arithmetic operators and expressions

For example, in score + 10, the operator is +, and the operands are score and 10.

A variable is a named storage location in a program. You can store the result of a calculation in a variable using assignment, written with = in Python.

For example: total = price * quantity

This means: calculate price * quantity, then store the result in total.

The arithmetic operators you need

Operation	Python operator	Example	Result	Meaning
Addition	`+`	`7 + 2`	`9`	Adds values
Subtraction	`-`	`7 - 2`	`5`	Takes one value away from another
Multiplication	`*`	`7 * 2`	`14`	Multiplies values
Division	`/`	`7 / 2`	`3.5`	Gives a real-number answer
Integer division	`//`	`7 // 2`	`3`	Gives the whole-number quotient
Modulus	`%`	`7 % 2`	`1`	Gives the remainder
Exponentiation	`<strong>`	`2 </strong> 3`	`8`	Raises a number to a power

Common Mistake

Writing maths symbols instead of Python symbols

Python does not understand 2x, 2^3, or a written divide sign. Write 2 * x, 2 ** 3, and 7 / 2 instead.

Assignment: storing a calculated result

In Python, assignment uses =. The expression on the right is evaluated first, then the answer is stored in the variable on the left.

For example:

score = 12
score = score + 5

The second line may look strange at first, because score appears on both sides. In programming, this means “take the old value of score, add 5, then store the new value back into score”.

Example

Updating a score

Start with the current value: score stores 12.
Evaluate the right-hand side of score = score + 5: this becomes 12 + 5, which gives 17.
Store the result back into the variable, so score now stores 17 instead of 12.

Key Idea

Assignment is not a maths equation

In Python, score = score + 5 is valid because = means “store this value”, not “these two sides are already equal”.

Multiplication, division and real answers

Multiplication uses *. Division uses /.

In Python 3, / gives a float, which is Python’s name for a number that may have a decimal part. So 8 / 2 gives 4.0, not just 4.

That matters when the rest of your program expects a whole number.

Common Mistake

Expecting division to give an integer

7 / 2 gives 3.5. If you want the whole-number part of the answer, use integer division: 7 // 2 gives 3.

Integer division and modulus

Integer division and modulus are a pair. They are useful when you are splitting something into equal groups.

Definition

Integer division and modulus

Integer division using // gives the whole-number quotient. Modulus using % gives the remainder after division.

For positive whole numbers, they fit this pattern: dividend equals divisor times quotient plus remainder.

For example, 29 // 6 gives 4, because 6 fits into 29 four complete times. Then 29 % 6 gives 5, because 5 is left over.

Example

Finding full groups and remainders

Suppose 29 students are put into groups of 6. Use integer division to find the number of full groups: 29 // 6 gives 4.
Use modulus to find how many students are left over: 29 % 6 gives 5.
Check the result using the relationship $\times 4 + 5$ , so there are 4 full groups and 5 students left over.

Tip

When modulus is useful

Modulus is useful for “left over” questions. For example, number % 2 gives 0 when a whole number divides exactly by 2, so it can help detect even numbers.

Common Mistake

Dividing by zero

You cannot use /, // or % with zero as the divisor. For example, 10 / 0 causes a Python error because division by zero is undefined.

Exponentiation: powers

Exponentiation means raising a number to a power. In Python, use **.

Examples:

2 ** 3 means 2 cubed, giving 8.
5 ** 2 means 5 squared, giving 25.
10 ** 3 gives 1000.

This is useful in Computer Science. For example, 8 bits can represent 2 ** 8 different unsigned values, which is 256 values.

Operator precedence: the order of calculation

Operator precedence means the order Python uses when an expression contains more than one operator.

Arithmetic operator precedence in Python

Example

Evaluating a mixed expression

In 2 + 3 * 4 <strong> 2, exponentiation has the highest precedence after brackets, so calculate 4 </strong> 2 first. The expression becomes 2 + 3 * 16.
Multiplication is done before addition, so calculate 3 * 16. The expression becomes 2 + 48.
Finally, calculate the addition. The result is 50.

Operators on the same precedence level are usually evaluated from left to right. For GCSE programming, the safest habit is to use brackets whenever the intended order might not be obvious.

Using brackets to control the result

Brackets force Python to calculate part of an expression first. This can completely change the answer.

For example:

10 + 6 // 4 gives 11, because 6 // 4 is calculated first and gives 1.
(10 + 6) // 4 gives 4, because the bracketed addition is calculated first.

Key Idea

Brackets make your intention clear

Even when Python would calculate the expression correctly without brackets, adding brackets can make your program easier to read and reduce mistakes.

Writing arithmetic with user input

If a program asks the user to type a value using input(), Python receives it as a string, which means text. To do arithmetic, convert it to a number first.

Use:

int(...) for whole numbers, such as age = int(input("Age: "))
float(...) for numbers that may contain decimals, such as price = float(input("Price: "))

Then you can calculate with the value:

quantity = int(input("Quantity: "))
price = float(input("Price of one item: "))
total = quantity * price

Common Mistake

Forgetting to convert input

If you write quantity = input("Quantity: "), the value is text. Convert it with int() before using arithmetic, otherwise your calculation may fail or behave unexpectedly.

Choosing the right operator

A good way to choose the correct operator is to translate the problem into what you want the computer to calculate.

If the problem says...	You probably need...	Example
“total”, “more”, “increase by”	`+`	`score = score + bonus`
“difference”, “decrease by”, “left after taking away”	`-`	`lives = lives - 1`
“each”, “per item”, “repeated groups”	`*`	`cost = price * quantity`
“share equally with possible decimals”	`/`	`average = total / count`
“number of full groups”	`//`	`boxes = items // items_per_box`
“left over” or “remainder”	`%`	`left_over = items % items_per_box`
“squared”, “cubed”, “power of”	`<strong>`	`area = side </strong> 2`

Exam technique

In the exam

Decide whether the question needs a real-number division answer using /, or a whole-number quotient and remainder using // and %.
When an expression has several operators, apply precedence carefully: brackets, powers, multiplication/division/integer division/modulus, then addition/subtraction.
Use Python syntax exactly: * for multiplication, ** for powers, and meaningful variable names for calculated values.

Self review

Check yourself

What is the difference between 17 / 5, 17 // 5 and 17 % 5?
Why does 2 + 3 * 4 not give the same result as (2 + 3) * 4?
What conversion might you need if a number has been entered using input()?

Using arithmetic operators

What you'll learn

Arithmetic in programs

The arithmetic operators you need

Assignment: storing a calculated result

Multiplication, division and real answers

Integer division and modulus

Exponentiation: powers

Operator precedence: the order of calculation

Using brackets to control the result

Writing arithmetic with user input

Choosing the right operator

You've reached the end

Using arithmetic operators

What you'll learn

Arithmetic in programs

The arithmetic operators you need

Assignment: storing a calculated result

Multiplication, division and real answers

Integer division and modulus

Exponentiation: powers

Operator precedence: the order of calculation

Using brackets to control the result

Writing arithmetic with user input

Choosing the right operator

You've reached the end

Using arithmetic operators

What you'll learn

Arithmetic in programs

The arithmetic operators you need

Assignment: storing a calculated result

Multiplication, division and real answers

Integer division and modulus

Exponentiation: powers

Operator precedence: the order of calculation

Using brackets to control the result

Writing arithmetic with user input

Choosing the right operator

You've reached the end

Using arithmetic operators Revision Guide

Using arithmetic operators

What you'll learn

Arithmetic in programs

The arithmetic operators you need

Assignment: storing a calculated result

Multiplication, division and real answers

Integer division and modulus

Exponentiation: powers

Operator precedence: the order of calculation

Using brackets to control the result

Writing arithmetic with user input

Choosing the right operator

You've reached the end

Using arithmetic operators Revision Guide