Class 6 · 6th standard · 2026-27

Class 6 maths worksheets, free, with every answer on the page

Three free Class 6 maths worksheets, with every question, every answer and the working printed on this page rather than behind a download. These are deliberately weighted towards integers and the first algebra rather than spread evenly across the syllabus, because those two ideas are where the year is actually won or lost - and where almost every Class 9 algebra difficulty turns out to have started. Every exercise opens with one question worked through, so a parent can help without teaching a different method from school.

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3 worksheets · 104 questions · every answer on the page · no sign-up · aligned to NCERT's Class 6 maths book is Ganita Prakash. Schools also use their own texts, so these sheets are written to the ideas rather than to one book's chapter order.

What these practise

Integers on the number line, including comparing two negatives
Adding and subtracting integers with a model rather than a memorised rule
Turning a word problem into a calculation with the right sign
Writing an algebraic expression from a sentence
Substituting a value into an expression
Reading an equation as a statement of balance
Simplifying fractions by spotting the HCF
Converting between fractions and decimals
The unitary method, including the cases where more means less

Last updated 2026-07-28

Free, with answers

The worksheets themselves

Every question is on this page, and so is every answer. Nothing is behind a sign-up, and there is no file to download unless you want one - use the print button on any sheet to save it as a PDF.

practice · medium · 25 min

Integers and the number line

Class 6 Maths · Integers · 34 questions with answers

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Integers are the first genuinely abstract idea in school maths - minus three of something that cannot be held. Most errors here are not carelessness but an unresolved confusion about the minus sign, which now means two different things at once.

Places any integer on a number line and compares two integers
Adds and subtracts integers using a model rather than a memorised rule
Explains why a particular answer is negative

Exercise 1 of 3 · 12 questions

Write each set in order, smallest first.

Write the answer · Warm-up

Here’s one done for you

3, -7, 0, 5, -2 → -7, -2, 0, 3, 5. On a number line, further left is always smaller. The second set catches most children: -18 is smaller than -3, because a larger digit after a minus sign means further left, not bigger. Drawing the line once fixes this permanently.

1)3, -7, 0, 5, -2
2)-12, -3, -18, -9
3)8, -8, 1, -1, 0
4)-45, 45, -54, 54
5)6, -6, 2, -11, 0
6)-30, -13, -25, -8
7)17, -17, -71, 71
8)-1, -100, -10, 0
9)9, -4, -9, 4, -14
10)-60, 16, -16, 60, 0
11)23, -32, -23, 32
12)-5, -50, 5, 50, -55

Answers

1) -7, -2, 0, 3, 5
2) -18, -12, -9, -3
3) -8, -1, 0, 1, 8
4) -54, -45, 45, 54
5) -11, -6, 0, 2, 6
6) -30, -25, -13, -8
7) -71, -17, 17, 71
8) -100, -10, -1, 0
9) -14, -9, -4, 4, 9
10) -60, -16, 0, 16, 60
11) -32, -23, 23, 32
12) -55, -50, -5, 5, 50

Exercise 2 of 3 · 12 questions

Work these out. Show the step.

Write the answer · Guided

Here’s one done for you

(-6) + 4 → start at -6 on the line and move 4 steps right, because adding moves right. You land on -2. For (-8) - (-5): subtracting a negative moves right, so start at -8 and move 5 right, giving -3. Teach the two moves - add goes right, subtract goes left, and a second minus flips the direction - rather than four separate rules.

1)(-6) + 4
2)5 + (-9)
3)(-3) - 7
4)(-8) - (-5)
5)12 + (-12)
6)(-4) - (-11)
7)(-15) + 8
8)7 + (-13)
9)(-9) - 6
10)(-20) - (-14)
11)(-11) + 11
12)(-5) - (-17)

Answers

1) -2
2) -4
3) -10
4) -3
5) 0
6) 7
7) -7
8) -6
9) -15
10) -6
11) 0
12) 12

Exercise 3 of 3 · 10 questions

Answer each one. Write the calculation, then the answer.

Write the answer · Practice

Here’s one done for you

Temperature 5, falls by 9 → 5 - 9 = -4, so -4 degrees. The maths is the easy part; turning the sentence into a calculation is the skill. Look for the word that tells you the direction - fell, rose, owes, down - and let it choose the sign before writing anything.

1)The temperature was 5 degrees and fell by 9 degrees. What is it now?
2)A lift is on the 3rd floor and goes down 7 floors. Where is it?
3)A submarine at -120 m rises 45 m. What is its depth now?
4)Rahul owes 250 rupees and then earns 400. What is his position?
5)A town was at 8 degrees at noon and dropped 14 degrees by night. What was the night temperature?
6)A diver at -30 m goes down another 25 m. What depth is she at?
7)A basement lift starts at -2 and rises 9 floors. Which floor is it on?
8)Meera has 180 rupees and spends 260. What is her position?
9)A mountain peak is 2,400 m above sea level and a mine is 350 m below it. What is the difference in height?
10)The temperature rose from -6 degrees to 7 degrees. By how much did it rise?

Answers

1) 5 - 9 = -4, so it is -4 degrees.
2) 3 - 7 = -4, so it is 4 floors below ground.
3) -120 + 45 = -75, so it is at -75 m.
4) -250 + 400 = 150, so he has 150 rupees.
5) 8 - 14 = -6, so it was -6 degrees.
6) -30 - 25 = -55, so she is at -55 m.
7) -2 + 9 = 7, so it is on the 7th floor.
8) 180 - 260 = -80, so she owes 80 rupees.
9) 2,400 - (-350) = 2,750 m.
10) 7 - (-6) = 13, so it rose by 13 degrees.

While your child works

Draw the number line every single time for the first fortnight, even for questions your child gets right. The model has to become automatic before the rules can be trusted.
-18 being smaller than -3 is the single most common error. It is worth checking specifically before moving on.
In word problems, underline the direction word first. That one habit fixes most of the sign errors.

Open the Integers worksheet on its own page

practice · medium · 25 min

The first algebra: letters for numbers

Class 6 Maths · Algebra · 36 questions with answers

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A letter in algebra is a number we have not been told yet - not a label for an object. Getting that framing right in Class 6 is what makes Class 8 equations feel like reasoning instead of like following steps.

Writes an expression from a sentence
Substitutes a value into an expression correctly
Reads an equation as a statement of balance rather than an instruction

Exercise 1 of 3 · 12 questions

Write an expression for each. Use n for the unknown number.

Write the answer · Warm-up

Here’s one done for you

Five more than a number → n + 5. Careful with 'three less than a number': it is n - 3, not 3 - n. English puts the 3 first and the maths puts it second, and that reversal catches almost every child at least once.

1)Five more than a number
2)Twice a number
3)Three less than a number
4)A number divided by four
5)Two more than three times a number
6)Seven less than half a number
7)Ten more than a number
8)Five times a number
9)A number decreased by nine
10)One third of a number
11)Four more than twice a number
12)Six less than five times a number

Answers

1) n + 5
2) 2n
3) n - 3
4) n ÷ 4 or n/4
5) 3n + 2
6) n/2 - 7
7) n + 10
8) 5n
9) n - 9
10) n/3
11) 2n + 4
12) 5n - 6

Exercise 2 of 3 · 12 questions

Find the value when n = 6.

Write the answer · Guided

Here’s one done for you

4n when n = 6 → 4 × 6 = 24. The letter simply stands in for 6, so replace it and calculate. Note that n - 11 gives -5, which is a perfectly good answer - children often assume they have made a mistake when the result is negative, and that is where the integers work above pays off.

1)n + 9
2)4n
3)n - 11
4)2n + 3
5)3n - 8
6)n/2 + 5
7)5n - 6
8)n × n
9)(n + 4)/2
10)10 - n
11)2(n + 1)
12)n/3 + 7

Answers

1) 15
2) 24
3) -5
4) 15
5) 10
6) 8
7) 24
8) 36
9) 5
10) 4
11) 14
12) 9

Exercise 3 of 3 · 12 questions

Find the value of the letter that makes each statement true.

Write the answer · Practice

Here’s one done for you

x + 7 = 15 → the equals sign means both sides are worth the same. Something plus 7 is 15, so x is 8. Do not teach 'move it across and change the sign' yet - at Class 6 the useful question is 'what would make this true?', and that keeps the balance idea intact for Class 8.

1)x + 7 = 15
2)5y = 40
3)a - 9 = 4
4)3m + 2 = 17
5)p/4 = 6
6)x + 13 = 20
7)7y = 63
8)b - 14 = 6
9)4m - 5 = 23
10)q/6 = 5
11)2k + 9 = 25
12)c + 2.5 = 8

Answers

1) x = 8
2) y = 8
3) a = 13
4) m = 5
5) p = 24
6) x = 7
7) y = 9
8) b = 20
9) m = 7
10) q = 30
11) k = 8
12) c = 5.5

While your child works

Never explain 3a + 2a as three apples plus two apples. It works for a term and then makes a × a = a² impossible to understand.
'Three less than a number' is n - 3, not 3 - n. English and maths put the numbers in opposite orders and this reversal catches nearly everyone.
Read the equals sign aloud as 'is the same as'. It stops a child treating an equation as an instruction to compute.

Open the Algebra worksheet on its own page

practice · medium · 25 min

Fractions, decimals and ratio

Class 6 Maths · Fractions, decimals and ratio · 34 questions with answers

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Class 6 treats fractions and decimals as two ways of writing the same quantity rather than as two topics, and introduces ratio - which compares two quantities without producing a third. The unitary method learned here reappears as percentage, speed and most word problems for years.

Simplifies a fraction by spotting a common factor
Converts between a fraction and a decimal
Uses the unitary method on an unfamiliar problem

Exercise 1 of 3 · 12 questions

Write each fraction in its simplest form.

Write the answer · Warm-up

Here’s one done for you

18/24 → divide both by 6, giving 3/4. Six is the HCF of 18 and 24, so one step is enough. A child dividing by 2 and then by 3 gets the same answer more slowly - and that is fine, but spotting the HCF is what the Class 6 factors chapter was for. Five of these six simplify to 3/4, which is worth noticing.

1)18/24
2)45/60
3)36/48
4)27/36
5)50/75
6)42/56
7)30/45
8)64/80
9)21/28
10)60/72
11)35/63
12)48/54

Answers

1) 3/4
2) 3/4
3) 3/4
4) 3/4
5) 2/3
6) 3/4
7) 2/3
8) 4/5
9) 3/4
10) 5/6
11) 5/9
12) 8/9

Exercise 2 of 3 · 12 questions

Convert between fractions and decimals.

Write the answer · Guided

Here’s one done for you

3/4 as a decimal → 3 ÷ 4 = 0.75. A fraction is a division waiting to happen, which is the whole idea Class 6 is trying to establish. For 0.6 as a fraction: 0.6 is six tenths, so 6/10, which simplifies to 3/5 - and the simplifying step is where marks are lost.

1)1/2 as a decimal
2)3/4 as a decimal
3)0.25 as a fraction
4)0.6 as a fraction
5)1/5 as a decimal
6)0.75 as a fraction
7)1/4 as a decimal
8)2/5 as a decimal
9)0.8 as a fraction
10)0.05 as a fraction
11)3/10 as a decimal
12)1.5 as a fraction

Answers

1) 0.5
2) 0.75
3) 1/4
4) 3/5
5) 0.2
6) 3/4
7) 0.25
8) 0.4
9) 4/5
10) 1/20
11) 0.3
12) 3/2 (or 1 1/2)

Exercise 3 of 3 · 10 questions

Use the unitary method. Show the 'one' step.

Write the answer · Practice

Here’s one done for you

5 pens cost 60 → one pen costs 60 ÷ 5 = 12, so 8 pens cost 12 × 8 = 96. Always find the value of one first. The second question is the tricky kind - more workers means fewer days, so one worker takes 4 × 12 = 48 days, and 6 workers take 48 ÷ 6 = 8. Ask 'should the answer be bigger or smaller?' before calculating.

1)If 5 pens cost 60 rupees, what do 8 pens cost?
2)If 4 workers finish a job in 12 days, how long for 6 workers?
3)A recipe for 6 people needs 300 g of rice. How much for 10 people?
4)If 3 books weigh 1.2 kg, what do 7 books weigh?
5)If 5 pens cost 60 rupees, what do 15 pens cost?
6)If 8 identical bricks weigh 12 kg, what do 20 bricks weigh?
7)A car travels 240 km on 16 litres. How far on 25 litres?
8)If 6 shirts need 9 m of cloth, how much cloth for 10 shirts?
9)If 4 taps fill a tank in 30 minutes, how long would 5 taps take?
10)If 9 kg of rice costs 630 rupees, what does 4 kg cost?

Answers

1) One pen costs 12, so 8 pens cost 96 rupees.
2) One worker would take 48 days, so 6 workers take 8 days.
3) One person needs 50 g, so 10 people need 500 g.
4) One book weighs 0.4 kg, so 7 books weigh 2.8 kg.
5) One pen costs 12, so 15 pens cost 180 rupees.
6) One brick weighs 1.5 kg, so 20 bricks weigh 30 kg.
7) One litre gives 15 km, so 25 litres give 375 km.
8) One shirt needs 1.5 m, so 10 shirts need 15 m.
9) One tap would take 120 minutes, so 5 taps take 24 minutes.
10) One kg costs 70, so 4 kg costs 280 rupees.

While your child works

The 'find one first' step must be written down, not done mentally. It is where the method mark is and where errors become visible.
For the workers question, ask 'more workers - should it take longer or less time?' before any calculation. That check catches the commonest ratio error.
If simplifying is slow, the gap is factors and HCF from earlier in Class 6, not fractions.

Open the Fractions, decimals and ratio worksheet on its own page

What makes Class 6 maths different?

Everything in primary could be pictured. Three apples shared between four children is a drawing. From Class 6 that stops being true, and three ideas arrive that cannot be drawn the same way:

Integers - minus three of something that cannot be held.
Algebra - a letter standing where a number should be.
Ratio - a comparison between two quantities that does not produce a third.

The practical consequence catches most families out. Abstract reasoning uses working memory, and so does arithmetic that is not yet automatic. A child rebuilding 7 × 8 in the middle of a factorisation has less capacity left for the factorisation itself - so they fail at the new thing while the actual bottleneck is the old one. This is why fixing tables in Class 6 often improves algebra marks, which looks like a coincidence and is not.

Full detail on the year is on our Class 6 maths page, and why marks drop in Class 6 covers the wider transition.

How should we use these at home?

Twenty-five minutes each, once or twice a week, and expect the integers sheet to take longest. Every exercise opens with a worked example showing one question done with the reasoning visible - not just the answer.

Draw the number line every time for the first fortnight, even on questions your child gets right. The model has to become automatic before the sign rules can be trusted.
Insist the working is written down. From Class 6 the method carries marks of its own, and a child who computes mentally and writes only the answer is discarding marks they earned.
Check arithmetic fluency first. If simplifying fractions is slow, the gap is tables rather than fractions.
Let your child mark their own work. Every answer is on the page for exactly that.

Where do Class 6 children usually stall?

Four places, and only one of them is about the Class 6 syllabus.

Thinking -18 is bigger than -3. A larger digit after a minus sign means further left, not bigger. Worth checking specifically.
Getting integer answers right without being able to explain them. A memorised sign rule holds until Class 7 multiplication of negatives, then stops working silently.
Writing 3 - n for 'three less than a number'. English and maths put the numbers in opposite orders, and this reversal catches nearly everyone once.
Slow arithmetic underneath everything else. The most common real cause, and the one that looks like a Class 6 problem while being a Class 4 one - see making tables stick.

Questions parents ask

Class 6 Maths worksheets - your questions

Are these Class 6 maths worksheets free?

Yes. Every question, every answer and the working are on this page, with no sign-up, no email wall and no account. The printable version puts the answers on a separate final sheet.

Do these include an answer key?

Yes, with the working shown rather than just the final answer - so a parent who is unsure of the current method can follow it, and a stuck child can restart without asking.

Why is Class 6 maths suddenly harder?

Because it asks for reasoning about quantities that cannot be pictured - negatives, letters standing for unknowns, ratios. If arithmetic is still effortful there is no working memory left for that, so the failure shows up at the new topic while the bottleneck is the old one.

My child gets integer questions right but cannot explain them.

They have memorised a rule for signs rather than built a model. It holds until Class 7, when multiplication and division of negatives arrive and the rule silently stops working. Go back to the number line now - it is much cheaper than fixing it in Class 8.

How should I explain algebra to a Class 6 child?

A letter is a number we have not been told yet. Avoid 'a stands for apples' - it works for a term and then makes a × a = a² impossible, because three apples times two apples is not six apples of anything.

My child simplifies fractions very slowly. What is wrong?

Usually nothing about fractions. Spotting a common factor requires tables to be automatic, and if they are not, every simplification becomes a search. Fix the fluency and the fractions speed up on their own.

Are these matched to NCERT?

They are written to the ideas Class 6 covers rather than to one book's chapter order, so they work whether your school uses NCERT's Ganita Prakash or its own text.

Can I print these worksheets?

Yes. They print cleanly on A4 with the answers on a separate final page, and nothing needs to be downloaded or signed up for.

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Class 6 maths worksheets, free, with every answer on the page

The worksheets themselves

Integers and the number line

The first algebra: letters for numbers

Fractions, decimals and ratio

Class 6 Maths - the guide

What makes Class 6 maths different?

How should we use these at home?

Where do Class 6 children usually stall?

Class 6 Maths worksheets - your questions

Worksheets are free. So is the first class.

Book a free assessment