GCSE · Computer Science · AQA · Spec 8525

Real division

Share 7 pizzas between 2 people and each gets three and a half, not three. A program doing real division agrees: 7 / 2 is 3.5.

Computer Science · Programming

Where do these answers land?

No calculator yet. Drag each division to where you think its answer lands. On a whole number, or between two?

Computer Science · Programming

Real division inside a program

This program averages four test marks. Step through it and keep an eye on the Variables panel.

Stop when line 6 lights up and total holds 29. Before you press Next, predict: will average hold 7, or something else?

 1  score1 ← 7
 2  score2 ← 8
 3  score3 ← 6
 4  score4 ← 8
 5  count ← 4
 6  total ← score1 + score2 + score3 + score4
 7  average ← total / count
 8  OUTPUT average

Variables

score1=7

Output

Step 1: score1 stores 7.

1 / 8

Use Next to go one line at a time and watch the Variables panel update.

Step 1 of 8: score1 stores 7..

Computer Science · Programming

Spot the slip in this trace

This program turns a time in seconds into minutes. A student has written what each line stores. Which line did they get wrong?

A student's trace — which line goes wrong?

Computer Science · Programming

Your turn: write the division

Complete a program that shares a bill of 18 equally between 4 people and outputs each person's share.

  1. bill ← 18
  2. people ← 4
  3. missing step
Which line is step 3?

WHAT YOU'VE LEARNED

A quick recap of today's lesson.

7 / 2 is 3.5, not 3 — real division keeps the whole answer, fractional part and all.

What you need to know

  • Real division divides one number by another and gives the full answer, keeping any fractional part (the part after the decimal point).
  • In the pseudo-code in this lesson, real division is written with /, for example average ← total / count.
  • Dividing two whole numbers can give an answer that isn't whole: 7 / 2 = 3.5 and 3 / 4 = 0.75.
  • When a division comes out exactly, the answer is a whole number: 10 / 5 = 2.
  • Order matters: bill / people shares the bill between the people, but people / bill gives a completely different value.

The big picture

Real division divides one number by another and keeps the full answer, including any part after the decimal point: 7 / 2 gives 3.5, not 3. In a program you write it with /, store the result in a variable, and can predict that value before the program runs.

Key points

1To predict a real division result, find how many whole times it goes in, then turn what's left over into a fraction: 9 / 4 is 2 with 1 left over, and 1 / 4 = 0.25, so 9 / 4 = 2.25.
2When you trace a program, a variable that stores a real division result holds the full value. Write 7.25, not 7.
3Divide by the variable (count, people) rather than a fixed number, so the program still works when the data changes.
4Not every programming language treats / the same way when both numbers are whole, so check which kind of division your language is doing. In this lesson, / always means real division.

Worked example

Problem

A program stores distance ← 45 and laps ← 6, then runs lapLength ← distance / laps. What value does lapLength store?

⚠ Watch out

Chopping the answer down to a whole number, for example writing 29 / 4 as 7 instead of 7.25. Real division keeps the fractional part. Giving only the whole-number part is a separate operation (integer division), so don't mix the two up.

🧠

Memory hook

Nothing gets chopped: 7 / 2 lands at 3.5, between the tick marks, not on the 3.

✓

Check yourself

No calculator: what does x store after x ← 11 / 4? Work out how many whole times 4 goes in, then what the leftover is worth.

Flashcards

(7)
What does real division do?
Divides one number by another and keeps the fractional part of the answer. For example, 7 / 2 = 3.5.
What symbol does this lesson's pseudo-code use for real division?
/ (a forward slash), as in average ← total / count.
Can dividing two whole numbers give an answer that isn't whole?
Yes. 1 / 4 = 0.25 and 11 / 2 = 5.5.
When does real division give a whole-number answer?
When the division comes out exactly, for example 12 / 4 = 3. The fractional part is then zero.
total ← 17 and count ← 2. What does total / count give?
8.5. The .5 is kept.
What is the difference between bill / people and people / bill?
bill / people shares the bill between the people. people / bill divides the other way round and gives a different, wrong value for a share.
Does every programming language treat / as real division?
No. In some languages, dividing two whole numbers with / behaves differently, so check which kind of division your language is doing.

Tap any card to flip it, or use Study as deck to go through them one at a time. In the full lesson these run as a spaced-repetition deck — you rate each card Hard, Good or Easy and the tricky ones keep coming back until they stick.

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