Arithmetic operators

The seven operators, integer division and remainder, and the order they work in.

F1.9Programming basicsGCSE15 min

Covers OCR J277 2.2.1 Programming fundamentals · AQA 8525 3.2.3 Arithmetic operations in a programming language · Edexcel 1CP2 6.5.1 Arithmetic operators

Do this lesson in the simulator

Print it: worksheet (PDF) · answers (PDF) · as a web page

Robots are numbers all the way down: speeds, distances, angles, battery percentages. The symbols that do arithmetic are called operators, and this lesson is where you make Python do the working out for you.

The seven operators

# the two lines every program starts with: the commands, then the robot
from bugbot import *
connect()

print(17 + 5)     # addition: 22
print(17 - 5)     # subtraction: 12
print(17 * 5)     # multiplication: 85
print(17 / 5)     # division: 3.4
print(17 // 5)    # integer division: 3
print(17 % 5)     # modulus, the remainder: 2
print(5 ** 2)     # exponent, 5 to the power 2: 25

Run this in the simulator

The first four are the ones from maths, with * for times and / for divide. The last three are new.

Integer division and remainder

17 // 5 asks how many whole fives fit into 17: three. 17 % 5 asks what is left over: two. Together they are the division you did at primary school, 17 divided by 5 is 3 remainder 2.

# the two lines every program starts with: the commands, then the robot
from bugbot import *
connect()

seconds = 135
print(seconds // 60, "minutes and", seconds % 60, "seconds")

# % 2 is 0 for even numbers and 1 for odd ones
print(8 % 2, 9 % 2)

Run this in the simulator

Turning seconds into minutes and seconds, splitting sweets between a class, telling odd from even: // and % are more useful than they look.

Division as jumps along a number line. // counts the whole jumps that fit, % measures the bit left before the end. For 135 seconds that is 2 whole minutes, and 15 seconds left.

Division always gives a real number

# the two lines every program starts with: the commands, then the robot
from bugbot import *
connect()

print(20 / 5)
print(20 // 5)
print(10 / 3)
print(round(10 / 3, 2))

Run this in the simulator

20 / 5 printed 4.0, not 4: / always gives a float, even when the answer is whole. // gives an integer. round tidies a long float: the second argument is how many decimal places to keep.

Order of operations

Python follows the same order as maths: brackets first, then exponents, then multiply and divide (including // and %), then add and subtract.

# the two lines every program starts with: the commands, then the robot
from bugbot import *
connect()

print(2 + 3 * 4)
print((2 + 3) * 4)
print(2 * 3 ** 2)

Run this in the simulator

Predict all three before running. When in doubt, add brackets: they never hurt, and they show the reader what you meant.

Arithmetic with the robot

The robot's answers are numbers, so they can go straight into a calculation, and a calculation can go anywhere a function wants a number:

# the two lines every program starts with: the commands, then the robot
from bugbot import *
connect()

side = 20
print("a square of side", side, "cm covers", side ** 2, "square cm")

ahead = distance()
print("wall in", ahead, "cm; half way is", ahead / 2)
forward(50, distance=ahead / 2)
print("at", position())

Run this in the simulator

The drive went half the way to whatever was ahead. Numbers from sensors feeding into actions: that is most of robotics.

In the exam

Questions ask for the result of an expression, like 17 MOD 5, or which operator to use for a job, like finding out if a number is even. Integer division and modulus are the two people most often mix up, so be sure of both.

OCR 2.2.1

The Exam Reference Language writes the three new operators as words and a caret:

17 DIV 5    // 3
17 MOD 5    // 2
5 ^ 2       // 25

AQA 3.2.3

AQA lists addition, subtraction, multiplication, real division, and integer division including remainders. Pseudo-code writes the last two as words: 17 DIV 5 is 3 and 17 MOD 5 is 2.

Edexcel 6.5.1

Edexcel uses Python's operators and names them: real division /, quotient //, modulus % and exponentiation **.

Task: robot maths

Using only the numbers 17 and 5 in your calculations, print four lines: divide: 3.4, DIV: 3, MOD: 2 and power: 25 (the power is 5 to the power 2). Work each one out with an operator; do not type the answers. The robot must not drive.

# the two lines every program starts with: the commands, then the robot
from bugbot import *
connect()

print("divide:", 17 / 5)

Task: a third of the way

There is a wall ahead. Measure the distance to it and drive exactly a third of that distance forward. The program has to work out the third itself, so do not type in a distance.

# the two lines every program starts with: the commands, then the robot
from bugbot import *
connect()

ahead = distance()

Challenges

Print the distance ahead in metres instead of centimetres.
Ask for a number of seconds with input and print it as minutes and seconds.
Try -7 // 2 and -7 % 2. The answers surprise most people. Work out the rule Python is using.

Past paper questions on this

Real exam questions that test this, each worked through with a program you can run.