Programming arithmetic operators

Computer Science · Python

14 counters, 3 people: one division, three answers

Step through a tiny program. Watch the same 14 and 3 give you three different values depending on the operator.

Which line tells you how many counters each person gets? Which one tells you how many are left on the table?

 1  number = 14 / 3
 2  counters_each = 14 // 3
 3  counters_remaining = 14 % 3

Computer Science · Python

Which operation is it?

Sort each expression by the operation its operator performs.

7 of 7 still to sort.

Pick an expression, then pick the operation its symbol performs. Watch the lookalikes.

Predict, then check

Modulo as a test, not just a remainder in a story.

A program stores 7 in number and then evaluates number % 2. What value comes out?

What you need to know

• An operator is a symbol or word that tells the computer to perform a specific calculation or action.
• In Python, + adds, - subtracts, * multiplies, / divides, and ** is exponentiation.
• An arithmetic expression results in a numeric value. For example, score ** 2 is score to the power of two.
• Have a goMaya insists that 4 ** 2 is 8, because 'two stars is just times two'. Is she right? What is it really?

  No. 4 ** 2 is 16: four to the power of two.

  ** is exponentiation, so it raises 4 to the power of two. Multiplying 4 by two would be 4 * 2, which is 8.

• Python follows the order of operations: brackets, indices, multiplication and division, then addition and subtraction (read left to right).
• Have a goNo calculator, no scrolling: what does 2 + 3 * 4 evaluate to? Commit, then reveal.

  14

  Multiplication comes before addition, so 3 * 4 = 12 is done first, then 2 + 12 = 14. Going strictly left to right would wrongly give 20.

• An expression can use values stored in variables, but a variable must be assigned a value before it is used.
• Real division, /, divides the entire value, so there is no remainder: 14 / 3 gives 4.666…, a decimal result.
• Integer division (also called floor division) discards any remainder and leaves a whole number. Python writes it //, so 14 // 3 gives 4.
• Modulo (MOD) returns only the remainder. Python writes it %, so 14 % 3 gives 2: 3 goes into 14 four times with 2 left over.
• Have a goOver to you: what do 17 // 5 and 17 % 5 give?

  3 and 2.

  5 goes into 17 three times (that uses 15), leaving 2 over. // keeps the 3 and % keeps the 2.

• // and % work as a pair: // says how many each person gets, and % says how many are left over.
• Modulo also tests for odd numbers: if number % 2 evaluates to 1, the number is odd.

The big picture

Python has +, -, *, / and ** for arithmetic, and three different kinds of division: / keeps the whole value, // throws the remainder away and % keeps only the remainder. Python also works in a set order of operations, and a variable needs a value before an expression can use it.

⚠ Watch out

Believing there is only one kind of division, or that Python always works a line from left to right. Real division, integer division and modulo give different values, and the order of operations decides what is worked out first.

Memory hook

One division, three operators: / is the whole answer, // is how many each person gets, % is the counters left on the table.

Check yourself

Without scrolling back: a teacher shares 25 pencils between 6 pupils. Which operator tells you how many each pupil gets, which tells you how many are left over, and what are the two values?