Fractions, decimals and percentages in one system
Fractions, decimals and percentages describe the same quantities in three notations. Fluent students choose the notation that makes the question easiest, rather than sticking with the one they were given.
Part of your national curriculum
- Number: Work interchangeably with terminating decimals and their corresponding fractions, and define percentage as 'number of parts per hundred'
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
- • Converting without guessing
- • Which denominators terminate
- • Multipliers do the work
- • Comparing mixed notation
This lesson at a glance
- 30 minutes
- 17 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 17
Watch first
Fractions, decimals and percentages in one system
An English teaching video on this topic from Smile and Learn - English. 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'
Learning cycle
Part 2 of 17
Learning cycle 1 of 2
Part 1 · Converting without guessing
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 3 of 17
Learn
Converting without guessing
A fraction is a division, so 7/8 = 7 ÷ 8 = 0.875. Multiplying a decimal by 100 gives the percentage: 0.875 = 87.5%. Going back, a percentage is parts per hundred, so 87.5% = 87.5/100 = 875/1000 = 7/8 after cancelling.
Explore the idea
Part 4 of 17
Learn
Which denominators terminate
A fraction in its simplest form gives a terminating decimal exactly when its denominator has only 2s and 5s as prime factors. That is why halves, quarters, fifths, eighths and twentieths terminate, while thirds, sevenths and ninths recur. Predicting this before dividing saves time and prevents rounding errors.
Quick check
Part 5 of 17
Quick check
Write 7/8 as a percentage.
Quick check
Part 6 of 17
Quick check
Which fraction gives a recurring decimal?
Learning cycle
Part 7 of 17
Learning cycle 2 of 2
Part 2 · Multipliers do the work
A short piece of teaching, then a check to make sure it has landed.
Reset break
Part 8 of 17
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.
Explore the idea
Part 9 of 17
Learn
Multipliers do the work
Finding 15% of £80 as 0.15 × 80 is faster and less error-prone than splitting into 10% and 5%, and the same multiplier handles increases and decreases: a 15% increase is × 1.15, a 15% decrease is × 0.85. Multipliers also chain, so two successive 10% rises are × 1.1 × 1.1 = × 1.21, not a 20% rise.
Explore the idea
Part 10 of 17
Learn
Comparing mixed notation
To order 3/5, 0.58 and 62%, convert everything to one notation: 0.6, 0.58, 0.62. The ordering is then obvious. Comparing without converting is the single most common source of error in this topic.
Quick check
Part 11 of 17
Quick check
The multiplier for a 35% decrease is
Quick check
Part 12 of 17
Quick check
Order smallest first: 3/5, 0.58, 62%.
Explore the idea
Part 13 of 17
Worked example
Worked answer: a price rises 20% then falls 20%. Is it back where it started? (3 marks)
A rise of 20% multiplies by 1.2 and a fall of 20% multiplies by 0.8 (1). The combined multiplier is 1.2 × 0.8 = 0.96 (1). The final price is therefore 96% of the original, a 4% overall fall, because the decrease is calculated on the larger, increased amount (1).
Challenge round
Part 14 of 17
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 15 of 17
Game · Fill the gaps
Finish the sentences
Choose the word that belongs in each gap.
A fraction in its simplest form gives a ____ decimal exactly when its denominator has only 2s and 5s as prime factors.
Mastery quiz
Part 16 of 17
Marked quiz
End of lesson quiz: Fractions, decimals and percentages in one system
4 questions, marked with the reasoning shown. No timer.
1. Write 7/8 as a percentage.
2. Which fraction gives a recurring decimal?
3. The multiplier for a 35% decrease is
4. Order smallest first: 3/5, 0.58, 62%.
Lesson round-up
Part 17 of 17
Lesson round-up
Ready when you are
Quiz score
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Games
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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 17 · Watch & discover
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Work interchangeably with terminating decimals and their corresponding fractions, and define percentage as 'number of parts per hundred'