Fractions, decimals and percentages as one idea
A fraction, a decimal and a percentage can all describe the same amount. Choosing the easiest form for the job is what makes a calculation quick.
Lesson overview
What you'll learn in this lesson
Work interchangeably with terminating decimals and their corresponding fractions, and define percentage as 'number of parts per hundred'
Key learning points
- • Fraction to decimal
- • Percentage means per hundred
- • Facts worth owning
- • Which form to work in
This lesson at a glance
- 30 minutes
- 19 parts to scroll through
- 4 quick checks
- Marked quiz at the end
- Gentle pace: short sittings with pauses
Words to know
Scroll down — the lesson carries on below
Watch & discover
Part 1 of 19
Watch first
Fractions, decimals and percentages as one idea
An English teaching video on this topic from 1st Class Maths. Watch it, then scroll down for the lesson.
In a nutshell
Work interchangeably with terminating decimals and their corresponding fractions, and define percentage as 'number of parts per hundred'
What you already know
Part 2 of 19
Before we start
What you already know
You can simplify fractions and multiply and divide by 10, 100 and 1000.
Key words
Part 3 of 19
Key words
Words you'll need today
- terminating decimal
- A decimal that stops, such as 0.375.
- percentage
- A number of parts per hundred.
- equivalent
- Different in form but equal in value.
Learning cycle
Part 4 of 19
Learning cycle 1 of 2
Part 1 — Converting
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 5 of 19
Learn
Fraction to decimal
A fraction is a division: 3/8 means 3 ÷ 8 = 0.375. It terminates because 8 is made only of 2s. A denominator containing a 3 or 7, such as 1/3 or 2/7, never terminates — it recurs. So 3/8 = 0.375 exactly, but 1/3 = 0.333… forever.
Explore the idea
Part 6 of 19
Learn
Percentage means per hundred
37% is literally 37 per hundred, so 37/100 and 0.37. Converting a decimal to a percentage means multiplying by 100: 0.045 = 4.5%. Going back divides by 100. The word 'cent' is your reminder: hundred.
Quick check
Part 7 of 19
Quick check
Write 7/8 as a decimal.
Quick check
Part 8 of 19
Quick check
0.06 as a percentage is...
Reset break
Part 9 of 19
Pause
That's sitting 1 of 2 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Learning cycle
Part 10 of 19
Learning cycle 2 of 2
Part 2 — Choosing the easiest form
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 11 of 19
Learn
Facts worth owning
1/2 = 0.5 = 50%; 1/4 = 0.25 = 25%; 3/4 = 0.75 = 75%; 1/5 = 0.2 = 20%; 1/8 = 0.125 = 12.5%; 1/3 ≈ 0.333 = 33⅓%. Knowing these means you can find 75% of £48 mentally as three quarters: £36.
Explore the idea
Part 12 of 19
Learn
Which form to work in
Multiplying is easiest with decimals (0.15 × 60). Sharing and cancelling is easiest with fractions (2/3 of 24). Comparing amounts is easiest as percentages, because they all sit on the same scale out of 100. Convert first, then calculate — do not fight the form you were given.
Quick check
Part 13 of 19
Quick check
Which fraction does NOT terminate?
Quick check
Part 14 of 19
Quick check
Which is largest?
Common mix-ups
Part 15 of 19
Common mix-ups
Things people often get wrong
- Writing 0.045 as 45%.
- Assuming every fraction turns into a terminating decimal.
- Comparing 2/5 and 0.36 without converting to the same form.
Challenge round
Part 16 of 19
Game · Sort it
Which of these are true?
Drag each card into the right column. Tap a card first if dragging is fiddly.
True
Not true
Challenge round
Part 17 of 19
Game · Fill the gaps
Finish the sentences
Choose the word that belongs in each gap.
Multiplying is easiest with ____ (0.15 × 60).
Sharing and cancelling is easiest with ____ (2/3 of 24).
Mastery quiz
Part 18 of 19
Marked quiz
End of lesson quiz: Fractions, decimals and percentages as one idea
6 questions, marked with the reasoning shown. No timer.
1. 3/5 as a percentage is...
2. 12.5% as a fraction is...
3. 0.4 =
4. Find 75% of £64.
5. 1/3 as a decimal is...
6. Best form for comparing three amounts?
Lesson round-up
Part 19 of 19
Lesson round-up
Ready when you are
Quiz score
Not sat
Games
Not played
Points this lesson
0
Best run
0 in a row
Luna: 0 out of 4 on the practice checks. Only if you feel up to it — one more?
Ask LunaDo the work
Your written work for this lesson
This is the part you'd do in your book at school. Pick the pieces below, write here or on paper, and photograph anything you draw or work out.
The cost of a school trip
A school is planning a trip to a wildlife park. The coach costs £480 however many people go. Entry costs £9.50 for each pupil and each adult goes free. The school says every pupil must pay the same amount, and the trip must not lose money.
If 60 pupils go, the coach works out at £8 each, so the total for each pupil is £17.50. If only 40 pupils go, the coach works out at £12 each, so the price rises to £21.50. The teacher explains that the coach is a fixed cost and the entry is a cost per person — which is why the price per pupil changes when the number changes.
The school decides to charge £20 and to use anything left over for a second trip later in the year.
Written for Good Learning Co.
Reading questions
- Work out the total cost of the trip if 50 pupils go.
- Show why the price per pupil falls when more pupils go, using numbers.
- At £20 each, how many pupils must go before the trip makes money? Show your working.
Working out
Working outDo the practice questions on paper, showing every step — not just the answer. Mark them yourself and circle anything you got wrong.
10–15 questions
Worked example, explained
WritingCopy one question out and write underneath, in words, why each step works.
1 question, 4–5 sentences
Problem in words
Working outWrite your own real-life problem that uses today's method, then solve it.
1 problem + solution
Saved as you type.
Part 1 of 19 · Watch & discover