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
- 21 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 21
Visual introductionPicture this
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.
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 21
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 21
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.
Reset break
Part 4 of 21
Pause
That's sitting 1 of 5 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 5 of 21
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 6 of 21
Quick check
Part 7 of 21
Reset break
Part 8 of 21
Pause
That's sitting 2 of 5 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 9 of 21
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.
Explore the idea
Part 10 of 21
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 11 of 21
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.
Reset break
Part 12 of 21
Pause
That's sitting 3 of 5 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.
Quick check
Part 13 of 21
Quick check
Part 14 of 21
Explore the idea
Part 15 of 21
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).
Reset break
Part 16 of 21
Pause
That's sitting 4 of 5 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.
Challenge round
Part 17 of 21
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 18 of 21
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.
Challenge round
Part 19 of 21
Game · Recall cards
Increase 240 by 15%.
Card 1 of 4
Mastery quiz
Part 20 of 21
Marked quiz
End of lesson quiz: Fractions, decimals and percentages in one system
4 questions, marked with the reasoning shown. No timer.
1. Increase 240 by 15%.
2. A count drops from 200 to 150. The percentage decrease is…
3. Which multiplier applies a 7% decrease?
4. Write 3/8 as a percentage.
Lesson round-up
Part 21 of 21
Lesson round-up
Ready when you are
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Ask LunaPart 1 of 21 · Watch & discover
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Work interchangeably with terminating decimals and their corresponding fractions, and define percentage as 'number of parts per hundred'