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📘 Class 6 maths · session 1 of 13 · 60 minutes

Fractions

Fractions one idea at a time: what a fraction means, equivalent fractions with fraction bars, comparing, then adding, subtracting and multiplying. Each idea is practised at three levels before the next.

🖨 Practice sheet

A complete lesson · 60 minutes

Teach it, see it, practise it, all on this page.

Open this page with your learner and work down it, or press Teach this lesson to go through it one step at a time on a big screen. Every section has something to do.

See the teacher's plan
  1. Warm-up4 min
  2. Meaning8 min
  3. Equivalent fractions10 min
  4. Comparing8 min
  5. Operations8 min
  6. Party recipe7 min
  7. Pizza party6 min
  8. Fraction detective5 min
  9. Quiz3 min
  10. Set the project1 min

By the end you can

  • Explain what the numerator and denominator of a fraction mean
  • Make equivalent fractions and write a fraction in its simplest form
  • Compare two fractions, even when the denominators are different
  • Add, subtract and multiply fractions and check the answer with a picture

Before you start

  • Times tables up to 10 × 10
  • Finding factors and common multiples of small numbers

Have ready

  • Paper and a pencil
  • Two strips of paper the same length (for folding)
  • This page open on a screen
  • A printed practice sheet (optional)

Class 6 · CBSE, ICSE and state boards

Warm-up · think first

Asha and Ben share a chocolate bar with 6 equal pieces. Asha eats 2 pieces. Ben eats one third of the bar. Who ate more?

Show the answer

They ate the same amount. Two pieces out of six is 2/6, and one third of six pieces is also two pieces, so 2/6 = 1/3.

Teacher tip: Before you show the answer, ask everyone to vote: Asha, Ben or the same? Then ask one person from each side to explain.

Part 1 of 4 · learn, see, practise

What a fraction means

A fraction names equal parts of a whole. In 3/4 the denominator 4 says the whole is cut into 4 equal parts, and the numerator 3 says how many parts we have.

A proper fraction like 3/5 is less than 1. An improper fraction like 7/4 is 1 or more, and can be written as a mixed number: 7 ÷ 4 = 1 remainder 3, so 7/4 = 1 3/4.

Example 1

A pizza is cut into 8 equal slices and you eat 3. What fraction did you eat?

  1. The whole is cut into 8 equal parts: the denominator is 8.
  2. You have 3 of them: the numerator is 3.

Answer: 3/8

Example 2

Write 7/4 as a mixed number, and 2 3/5 as an improper fraction.

  1. 7 ÷ 4 = 1 remainder 3, so 7/4 = 1 3/4.
  2. 2 3/5: two wholes are 10 fifths, plus 3 fifths is 13 fifths.

Answer: 1 3/4 and 13/5

Practise it

Start with the warm-up and go as far as you can. The stretch questions are meant to be hard.

Warm-up

Warm-up

Core

Core

Stretch 🔥

Stretch 🔥

Answers (for the teacher)
  1. 5/12
  2. 13/5
  3. 3 5/6
  4. 1/3
  5. 3/8
  6. 3/5

Part 2 of 4 · learn, see, practise

Equivalent fractions and simplest form

Multiply or divide the numerator and denominator by the same number and the value does not change: 2/3 = 4/6 = 8/12.

To write a fraction in its simplest form, divide both by their highest common factor (HCF).

Example 1

Simplify 18/24.

  1. The HCF of 18 and 24 is 6.
  2. 18 ÷ 6 = 3 and 24 ÷ 6 = 4.

Answer: 3/4

Example 2

Find the missing number: 2/3 = ?/12.

  1. 3 became 12: it was multiplied by 4.
  2. Multiply the top by 4 too: 2 × 4 = 8.

Answer: 8

Fraction bars: see it, then say it

Change the top and bottom numbers of each fraction. The bars redraw so you can see the size, and the panel below compares, adds and simplifies for you.

  1. Make the two bars exactly the same length using different numbers.
  2. Make fraction A bigger than fraction B, but give A the smaller denominator.
  3. Make two fractions that add up to exactly 1.
  4. Make fraction A equal to 3/4 using a denominator of 8 or more.

Practise it

Start with the warm-up and go as far as you can. The stretch questions are meant to be hard.

Warm-up

Warm-up

Core

Core

Stretch 🔥

Stretch 🔥

Answers (for the teacher)
  1. 2/3
  2. 16
  3. 3/4
  4. 6/10
  5. 35
  6. 2/3

Part 3 of 4 · learn, see, practise

Comparing and ordering fractions

Same denominator: the bigger numerator is bigger. Same numerator: the smaller denominator is bigger (bigger pieces).

Otherwise make the denominators the same, or cross-multiply: a/b is bigger than c/d when a × d is bigger than b × c.

Example 1

Which is greater, 3/4 or 5/7?

  1. Cross-multiply: 3 × 7 = 21 and 5 × 4 = 20.
  2. 21 > 20, so 3/4 is greater.

Answer: 3/4

Example 2

Put 1/2, 2/5 and 3/4 in order from smallest.

  1. Use the denominator 20: 10/20, 8/20 and 15/20.
  2. Order the numerators: 8, 10, 15.

Answer: 2/5, 1/2, 3/4

Practise it

Start with the warm-up and go as far as you can. The stretch questions are meant to be hard.

Warm-up

Warm-up

Core

Core

Stretch 🔥

Stretch 🔥

Answers (for the teacher)
  1. 3/5
  2. 1/4
  3. 5/8
  4. 3/5
  5. 5/12
  6. 3/4, 7/9, 5/6

Part 4 of 4 · learn, see, practise

Adding, subtracting and multiplying

To add or subtract, make the denominators the same, then add or subtract only the numerators. Simplify at the end.

To multiply, multiply the numerators and multiply the denominators. "Of" means multiply: 3/4 of 20 = 3/4 × 20 = 15.

Example 1

2/3 + 1/6 = ?

  1. The LCM of 3 and 6 is 6, so 2/3 = 4/6.
  2. 4/6 + 1/6 = 5/6.

Answer: 5/6

Example 2

3/4 × 2/5 = ?

  1. Tops: 3 × 2 = 6. Bottoms: 4 × 5 = 20.
  2. 6/20 simplifies to 3/10.

Answer: 3/10

Practise it

Start with the warm-up and go as far as you can. The stretch questions are meant to be hard.

Warm-up

Warm-up

Core

Core

Core

Stretch 🔥

Stretch 🔥

Answers (for the teacher)
  1. 3/5
  2. 1/4
  3. 11/12
  4. 7/12
  5. 1/2
  6. 4 1/6
  7. 18

Watch out

Common mistakes

Adding the denominators

1/2 + 1/3 is not 2/5. Make the parts the same size first: 3/6 + 2/6 = 5/6.

Stopping before the simplest form

6/12 is not finished: divide by the HCF to get 1/2.

Bigger denominator, bigger fraction?

1/8 is smaller than 1/4: more parts means smaller parts.

Class activity 1 of 3

Party recipe

A recipe for 4 people uses 3/4 cup of sugar, 1/2 cup of butter, 2 1/4 cups of flour and 2/3 cup of milk. Rewrite it for 6 people.

  1. 6 people is 6/4 = 3/2 of the recipe, so multiply every amount by 3/2.
  2. Turn mixed numbers into improper fractions before multiplying.
  3. Simplify and write answers bigger than 1 as mixed numbers.

Answers (for the teacher)
  1. 1 1/8
  2. 3/4
  3. 3 3/8
  4. 1

Class activity 2 of 3

Pizza party

3 pizzas are each cut into 8 equal slices. Riya eats 3/8 of a pizza, Kabir eats 5/8 of a pizza and Asha eats 1 1/4 pizzas.

  1. Add what the three ate (use eighths).
  2. Take it away from 3 whole pizzas.
  3. Share the leftover equally between 3 friends.

Answers (for the teacher)
  1. 2 1/4
  2. 3/4
  3. 6
  4. 1/4

Class activity 3 of 3

Fraction detective

Each clue describes exactly one fraction. Find it.

  1. Write what each clue tells you about the numerator and denominator.
  2. Use equivalent fractions to find the numbers.
  3. Check your fraction against every clue.

Answers (for the teacher)
  1. 14/21
  2. 15/25
  3. 7/24
  4. 3/4

Quiz · 10 questions

Check what you learned

Pick an answer to see if it is right and why. Your best score is saved on this device.

1Which fraction is equivalent to 3/4?
Show the answer

6/8. Multiply the top and the bottom by 2: 3 × 2 = 6 and 4 × 2 = 8.

2What is 24/36 in its simplest form?
Show the answer

2/3. The highest common factor of 24 and 36 is 12, and 24 ÷ 12 = 2, 36 ÷ 12 = 3.

3Which is greater, 5/8 or 3/5?
Show the answer

5/8. Cross-multiply: 5 × 5 = 25 and 3 × 8 = 24. 25 is bigger, so 5/8 is greater.

41/4 + 2/3 = ?
Show the answer

11/12. Use twelfths: 1/4 = 3/12 and 2/3 = 8/12, so the sum is 11/12.

55/6 − 1/4 = ?
Show the answer

7/12. Use twelfths: 10/12 − 3/12 = 7/12.

62/5 × 3/4 = ?
Show the answer

3/10. Multiply tops and bottoms: 6/20, which simplifies to 3/10.

7Write 13/4 as a mixed number.
Show the answer

3 1/4. 13 ÷ 4 = 3 with remainder 1, so 13/4 = 3 1/4.

8A pizza is cut into 8 equal slices. Riya eats 3 slices and Kabir eats 2. What fraction of the pizza is left?
Show the answer

3/8. 5 of the 8 slices are eaten, so 3 slices are left: 3/8.

9Which fraction is the smallest?
Show the answer

1/5. With the same numerator, more parts means smaller parts, so 1/5 is the smallest.

10What is 3/4 of 20?
Show the answer

15. One quarter of 20 is 5, so three quarters is 15.

After class · project

Fraction recipe card

Pick a simple recipe your family makes for 4 people (lemonade, a sandwich, a salad, a smoothie). Rewrite it so it serves 2 people and 6 people.

What to make: One recipe card (paper or a photo of it) with three columns: 4 people, 2 people, 6 people.

Stretch: Find the price of each ingredient and work out the cost of one serving.

How it is marked

Look forDone well when
Correct amountsEvery amount for 2 and 6 people is right
Simplest formFractions are simplified and improper fractions are mixed numbers
PicturesTwo fraction-bar drawings match the amounts
ExplainingThe sentence about 3/2 makes sense to someone else

Project template

Copy it onto paper or print the practice sheet.

Recipe: ______________________
Ingredient | 4 people | 2 people (× 1/2) | 6 people (× 3/2)
__________ | ________ | ________ | ________
__________ | ________ | ________ | ________
__________ | ________ | ________ | ________
Fraction-bar drawings for two amounts:
Why multiplying by 3/2 gives the amounts for 6 people: ____________________

Homework

Practise at home

Try each on paper, then tap to see the answer and working. Or print the practice sheet.

  1. Simplify 45/60.

    3/4 (divide by 15)

  2. Which is bigger, 7/12 or 5/8?

    5/8 (14/24 against 15/24)

  3. 3/8 + 5/12 = ?

    19/24 (9/24 + 10/24)

  4. A tank holds 60 litres and is 2/3 full. How many litres are in it?

    40 litres

  5. Write 4 2/7 as an improper fraction.

    30/7

For parents and teachers

The 60-minute lesson plan

Use it as it is, or stretch any part over two sessions. Each row links to the part of the page you need.

TimePartThe teacherThe learner
0–4 minWarm-upAsk the chocolate question and take a vote.Vote and explain.
4–12 minMeaningFold a paper strip; show the examples step by step.Practise to the stretch.
12–22 minEquivalent fractionsUse the fraction bars for the tasks.Practise; simplify 84/126.
22–30 minComparingCross-multiply on the board.Practise; halfway stretch.
30–38 minOperationsShow one example per operation.Practise to 3/4 of 3/5 of 40.
38–45 minParty recipeRemind them: multiply by 3/2.Scale the recipe.
45–51 minPizza partyDraw the 3 pizzas in eighths.Solve all four.
51–56 minFraction detectiveSet as homework if short.Solve the clues.
56–59 minQuizRun part of the quiz as an exit ticket.Answer.
59–60 minSet the projectShow the recipe template.Pick a recipe.

Questions to ask

  • Why can we not add the denominators when we add fractions?
  • How can 4/8 be the same size as 1/2 when the numbers are bigger?
  • Which is bigger, 1/8 or 1/4? Show it with the bars.
  • When you multiply by a fraction smaller than 1, does the answer get bigger or smaller? Why?

If it feels hard

Stay with halves, quarters and eighths, and use the bars for every question before writing anything.

If it feels easy

Ask for three different fractions between 1/3 and 1/2, and a reason why there is always another one in between.

FAQ

Fractions: questions

How do you teach fractions in Class 6?

One idea at a time: meaning, equivalent fractions, comparing, then operations, with fraction bars to see each idea and practice after every step.

How do you add fractions with different denominators?

Make the denominators equal using the LCM, then add the numerators and keep the denominator, and simplify at the end.

Is there a printable fractions worksheet?

Yes. The practice sheet for this lesson has every question with space to work and an answer key on its own page.

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