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Fair shares: fractions with roti
What you will learn: Split a whole into equal parts and compare fractions.
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The mystery
Three rotis, four hungry people. How can everyone get exactly the same amount?
Dadi has three rotis left and four hungry people: Tara, Tanmay, Dhruv and Dadi herself. Tanmay reaches for a whole one. "Stop!" says Tara. "Everyone must get exactly the same." Three rotis, four people. How do you cut them so that every share is equal?
Small test at the end: scroll down to the end of this page for five short questions that check what you have learnt. Tap an answer, then press Check answer. Go to the questions ↓
Safety: Use paper rotis. A grown-up does the cutting. Read the safety box before you start making.
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Your first guess
Before we work it out: how much roti do you think each person gets?
Make a prediction and write one reason for it. It's okay to change your mind.
Less than half a roti
Hold on to that guess. You will check it in "Watch the idea work".
Exactly half a roti
Hold on to that guess. You will check it in "Watch the idea work".
More than half, but less than a whole roti
Hold on to that guess. You will check it in "Watch the idea work".
A whole roti each
Hold on to that guess. You will check it in "Watch the idea work".
Not sure
That is fine. Picture 3 rotis and 4 plates. Is there enough for everyone to get a whole roti?
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Understand the basics
Before we share the rotis: what does "equal" mean?
Show me
Two rotis, each cut into four pieces. In the first, the pieces are different sizes. In the second, all four pieces are the same size.
Only the second roti is cut into quarters. A quarter is one of four equal parts. Four pieces are not enough: they must be the same size.
Let me try
Tap the roti that is cut into true quarters.
Roti A
Not this one. It has four pieces, but the bottom two are much smaller than the top two.
Roti B
Yes! You noticed that every piece is the same size. That is what makes these quarters.
Explain it another way
Think of sharing a bar of chocolate with three friends. If you snap off one big piece for yourself and three tiny pieces for them, everyone has "a piece", but it is not fair.
Fair means every piece is the same size. When a whole is cut into 4 equal pieces, each piece is called a quarter, and we write it 1/4.
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Try it on the strips
Each bar is one roti. Cut all three rotis the same way and see whether the four people get fair shares.
The strips need JavaScript. You can do the same on paper: draw 3 bars of the same length.
Which numbers of parts give everyone the same?
With 4 parts, how many pieces does each person get, and what is one piece called?
No screen? Draw three long bars of the same length on paper, mark each into 4 equal parts, and colour each person's pieces in a different colour.
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The idea
A fraction means equal parts of one whole. In 3/4, the bottom number (4) says how many equal parts the whole is cut into; the top number (3) says how many parts you have.
The parts must be equal. A roti torn into one big and three tiny pieces is not cut into quarters.
With the same-sized whole, more parts means smaller parts: 1/8 is smaller than 1/4, which is smaller than 1/2.
Sharing 3 rotis among 4 people: cut each roti into 4 quarters. That makes 12 quarters, and each person gets 3 of them: 3/4 of a roti.
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Watch the idea work: sharing three rotis among four
- Cut each of the 3 rotis into 4 equal quarters: 3 × 4 = 12 quarters.
- Share the 12 quarters among 4 people: 12 ÷ 4 = 3 quarters each.
- Three quarters is written 3/4.
Each person gets 3/4 of a roti.
Look back at your first guess and your reason. Were you close?
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Spot the mistake
Tanmay got 3 pieces and says, "I have 3/4 of a roti." Dhruv also got 3 pieces, but his came from a roti cut into 8 equal parts. Dhruv says, "Then I have 3/4 too." Is Dhruv right?
Decide, and write one reason for it. Then tap the answer closest to yours.
Yes: they both have 3 pieces
Count is not enough. Look at how big each piece is. Dhruv's pieces are eighths, which are half the size of quarters.
No: Dhruv has 3/8, because his pieces are eighths
Test it: on the strips, colour 3 pieces of a roti cut into 8 and 3 pieces of a roti cut into 4. Which covers more? Each eighth is half a quarter.
Yes: 3 pieces is always 3/4
Three pieces are three quarters only when each piece is a quarter of the whole.
Not sure
Use the strips above: cut into 8 and colour 3 pieces of one roti. Compare with 3 pieces from 4 parts.
Why it matters
The bottom number of a fraction says how many equal parts the whole was cut into. Three pieces can be 3/4, 3/8 or 3/6: it depends on the size of each piece.
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A new problem, on your own
A new problem, on your own: 5 rotis, 6 people. How much does each person get? Try it on the strips or on paper, then write your method in one sentence.
The strips need JavaScript. You can do the same on paper: draw 5 bars of the same length.
Check your method
Cut each roti into 6 equal parts: 5 × 6 = 30 pieces. 30 ÷ 6 = 5 pieces each. Each piece is 1/6, so everyone gets 5/6 of a roti.
The same rule as before: sharing 5 among 6 gives 5/6, just as sharing 3 among 4 gave 3/4.
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Make it real
Safety first
Use paper rotis. A grown-up does the cutting.
Keep it safe:
- Use paper circles, not real food, for the folding and cutting.
- A grown-up does any cutting with scissors or a knife.
You will need
- Paper circlesDraw round a bowl and cut out 4 circles. A grown-up does the cutting.
- A pencil and ruler
- ColoursTo shade your share.
Time: About 35 minutes.
Try it
Fold into halves.
Fold one paper roti exactly in half. Open it: 2 equal parts. Label each 1/2.
Fold into quarters.
Fold a second roti in half, then in half again: 4 equal parts. Label each 1/4.
Fold into eighths.
Fold a third roti three times: 8 equal parts. Label each 1/8.
Compare.
Lay one 1/2, one 1/4 and one 1/8 on top of each other. Which is biggest?
Share three among four.
Draw 3 rotis, cut each into quarters on paper, and colour each person's share in a different colour.
What you make (paper or offline)
Your fraction sheet
Labelled halves, quarters and eighths.
A drawing of 3 rotis shared among 4, with each share coloured.
One comparison sentence, such as "1/4 is bigger than 1/8 because..."
Make it on paper. Keep it with you. Nothing to upload.
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Check yourself
Five questions about what this page teaches. Choose an answer and press Check answer, or open "See the answer and why". Nothing is saved or sent: your choices stay on this screen and disappear when you leave or reload the page.
See the answer and why
- A. You cannot compare fractions Not this one. With same-sized wholes you can: fewer parts means bigger parts.
- B. They are the same size Not this one. Half of a roti is two quarters, so a half is bigger than a quarter.
- C. 1/4 Not this one. 4 is a bigger number, but cutting into more parts makes each part smaller.
- D. 1/2 Correct. The same roti cut into fewer equal parts gives bigger parts.
See the answer and why
- A. 4 rotis Not this one. There are only 2 rotis in all.
- B. 1/4 of a roti Not this one. That would be sharing just 1 roti among 4.
- C. 2 rotis Not this one. That would need 8 rotis for 4 people.
- D. 1/2 of a roti Correct. Cut each roti into 4 quarters: 8 quarters ÷ 4 people = 2 quarters each, which is 1/2.
See the answer and why
- A. Yes, because there are 4 pieces Not this one. Four pieces are only quarters if all four are the same size.
- B. No: quarters must be equal parts Correct. A fraction needs equal parts. His pieces are not equal.
- C. Yes, if he eats the big piece first Not this one. The order of eating does not change the sizes.
- D. No, because quarters need 8 pieces Not this one. 8 equal pieces would be eighths, not quarters.
See the answer and why
- A. It depends on who cut it Not this one. If the eighths are equal, 5 of them is always more than 3.
- B. They are equal Not this one. Both have eighths, but 5 parts is more than 3 parts.
- C. 5/8 Correct. Both are eighths, so the one with more parts, 5, is more.
- D. 3/8 Not this one. 3 eighths is fewer parts than 5 eighths.
See the answer and why
- A. 2/6 of the roti Correct. The roti has 6 equal parts and you ate 2 of them.
- B. 2/8 of the roti Not this one. The roti was cut into 6 parts, not 8.
- C. 6/2 of the roti Not this one. That is upside down. The bottom number is the number of parts in the whole.
- D. 4/6 of the roti Not this one. 4/6 is what is left, not what you ate.
Explain your discovery
Why must the parts be equal?
Where else do you share things into equal parts?
Try another situation
- Share 5 rotis among 4 people. How much does each get?
- Fold a paper strip into thirds. Is 1/3 bigger or smaller than 1/4?
Come back tomorrow
Come back to this tomorrow, without looking: a 3 metre ribbon is shared equally among 4 children for a school display. How long is each piece?
Try it from memory first: nothing is saved, so write your answer on paper.
Check your answer
3/4 of a metre each, which is 75 cm. It is the same idea as the rotis: 3 shared among 4 is 3/4.
If you got it, you can use the idea anywhere: rotis, ribbon, water or money. If not, come back to "Try it on the strips".
For grown-upsTap a heading to open it. A short safety line is near the top, and the full safety box comes just before the hands-on steps.
Before you start
- Draw and cut out four paper circles of the same size.
Questions that help
- "Are all the pieces the same size?"
- "Which is bigger, and how can you show it?"
What's really going on
The common confusion is thinking 1/4 is bigger than 1/2 because 4 is bigger than 2. Folding the same-sized paper shows the opposite.
Sharing 3 among 4 shows that a fraction can also mean a division: 3 ÷ 4 = 3/4.
Other ways to do it
- Use paper strips of the same length instead of circles.
For teachersLearning aims, classroom ideas and what to look for.
Learning aims
- Understand fractions as equal parts of a whole.
- Compare unit fractions and fractions with the same denominator.
Subject links
- Mathematics: fractions and division.
- Everyday life: fair sharing.
These links are general. They have not been checked against a specific board syllabus.
In the classroom
- Groups share different numbers of paper rotis among 4 and compare answers.
What to look for
- Insists on equal parts.
- Explains why more parts means smaller parts.