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Class 6 Math Practice Test Online

Class 6 Math introduces abstract thinking for the first time in a structured way, moving from simple arithmetic into working with negative numbers, fractions, ratios, and basic geometry through real, concrete situations rather than abstract drills.

Class 6Math

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Reviewed by Hari Narayana · Maths Faculty, GV Academy · 14+ years teaching Class 6-10 Math, reviewed for curriculum & exam alignment.Basic geometrical ideas, ratio-proportion steps, and whole number rules cross-checked for early logical development.

Last reviewed: August 2026

⚡ Quick quiz

Test yourself in under a minute: Class 6 Math Practice Test

Ratios, negative numbers, and one-step algebra equations get tested here, alongside perimeter and area problems for rectangles and squares.

1. Write the number 704,509 in words.
2. On a number line, which is smaller: -12 or -5?
3. In the expression 5x + 3, name the variable and the constant.
4. What do we call a straight path between two fixed endpoints, with a definite length?
5. Round off 68,215 to the nearest thousand.

💭 Think about this

Can you explain why -3 is greater than -7 using a number line, not just recite the rule?

Questions below are grouped by topic, pick the Math topics you want to practice, or swap in your own worksheet, notebook, or textbook questions any time.

Number System, Factors & Patterns

Covers reading, rounding and estimating large numbers, spotting number patterns, place value, prime/composite classification, common factors, and LCM by listing multiples.

📋 Quick referenceRounding, Primes & Factor Rules▶

Rounding
- Find your target place value, then look at the digit immediately to its right.
- Rounding to the 10s: check the ones digit. Rounding to the 100s: check the tens digit. Rounding to the 1,000s: check the hundreds digit.
- 5 or more: round up (add 1 to the target digit, replace the rest with zeros). 4 or less: round down (keep the target digit, replace the rest with zeros).
Primes & Composites
- A prime number can only be divided evenly by 1 and itself, nothing else (7 has no other factors).
- A composite number has at least one more factor besides 1 and itself (12 also splits evenly into 2, 3, 4, and 6).
HCF vs. LCM
- HCF: list the factors of each number and pick the biggest one they share.
- LCM: list multiples of each number and pick the first one that shows up in both lists.
Reading & Patterns
- Read a large number from the right in groups: ones, then thousands, then lakhs, then crores.
- To find a pattern's rule, check what changes from one term to the next (same amount added each time, or a multiplying pattern) across at least three terms before trusting it.

Building Number Sense Through Real Comparisons

For Parents

Teach rounding with a number line: show your child which thousand or hundred the number sits closer to, rather than just quoting the 'round up if 5 or more' rule.
Before adding exactly, round each number first and estimate the sum, so your child can catch a wrong answer later just by checking if it's close to the estimate.
Number patterns are best spotted by asking 'what did we do to get from one number to the next?' each time.
Tie factors and multiples to grouping real objects, since finding common factors is the same skill as figuring out how evenly two groups can both be split into equal smaller groups.

For Teachers

Watch for students who round correctly but then forget to use the rounded values in the estimate itself — have them write the rounded numbers down first, then add, so the two steps don't blur together.

1. Estimate the sum 3,876 + 5,102 by first rounding each number to the nearest hundred.
▶Reveal answer
About 9,000 (3,900 + 5,100)
Rounding 3,876 to the nearest hundred gives 3,900, and rounding 5,102 gives 5,100. Adding these rounded numbers gives a quick estimate of 9,000, close to the exact answer of 8,978.
2. Look at the pattern 5, 10, 20, 40, ___. What is the next number, and what is the rule?
▶Reveal answer
80; the rule is multiply the previous number by 2
Checking how each number changes from the one before it shows a clear rule: 5 to 10 doubles, 10 to 20 doubles, and 20 to 40 doubles. Following the same rule, 40 doubled gives 80.
3. In the number 47,239, what is the place value of the digit 2?
▶Reveal answer
200 (hundreds place)
Counting the digits from the right, the digit 2 sits in the hundreds place. So its place value is 2 x 100 = 200.
4. Is 87 a prime number or a composite number? Explain using its factors.
▶Reveal answer
Composite, 87 = 3 x 29, so it has factors other than 1 and itself.
A prime number has only two factors: 1 and itself. Since 87 can be divided evenly by 3 and 29 (3 x 29 = 87), it has more than two factors, making it composite.
5. Find all the common factors of 20 and 30.
▶Reveal answer
1, 2, 5, and 10
List all factors of each number separately, then pick out the ones appearing in both lists. Twenty's factors are 1, 2, 4, 5, 10, 20 and thirty's are 1, 2, 3, 5, 6, 10, 15, 30. The numbers common to both are 1, 2, 5, and 10.
6. Find the LCM of 9 and 12 by listing their multiples.
▶Reveal answer
36
Listing out multiples of each number until a common one appears works well for small numbers: multiples of 9 are 9, 18, 27, 36 and multiples of 12 are 12, 24, 36. The first number appearing in both lists is 36.
7. Find the HCF of 16 and 24 by listing their factors.
▶Reveal answer
8
Sixteen's factors are 1, 2, 4, 8, 16 and twenty-four's are 1, 2, 3, 4, 6, 8, 12, 24. The highest number appearing in both lists is 8, so that is the HCF.

Integers, Fractions, Decimals & Ratio

Tests integer comparison and arithmetic, comparing and adding/subtracting fractions, converting improper fractions to mixed numbers, decimal addition, simplifying ratios, and the unitary method.

📋 Quick referenceInteger, Fraction & Ratio Rules▶

On a number line, further right always means larger, even for negatives (-2 is greater than -5).
Fractions can only be compared or added once their bottom numbers match, so rewrite them with the same denominator first.
A ratio simplifies the same way as a fraction: divide both terms by their HCF.
Unitary method: find the value of ONE item first, then multiply for however many are needed.

Connecting Negative Numbers, Fractions and Ratios to Real Life

For Parents

Ground negative numbers in real contexts like a thermometer reading below zero, money owed, or a submarine's depth below sea level, rather than as abstract symbols.
Encourage your child to always ask 'can I make these two fractions have the same bottom number?' before comparing or adding fractions.
Decimal addition trips up many children simply because the decimal points aren't lined up; writing decimals in a column with the points aligned removes this error almost entirely.
Practice the unitary method, finding the value of one item before scaling up, as one of the most useful problem-solving habits at this level.

For Teachers

A frequent error on integer comparison is treating '-8' as bigger than '-3' because 8 is bigger than 3 — a quick number-line sketch on the board before the test usually clears this up faster than repeating the rule verbally.

1. A lift starts at the ground floor (0) and goes down 3 floors, then down 2 more. Which floor is it on now?
▶Reveal answer
Floor -5 (5 floors below the ground floor)
Going down means subtracting, so we work out 0 - 3 - 2 = -5. The negative sign shows the lift is below the ground floor, in the basement levels.
2. Find the value of: 15 - (-6) + (-4).
▶Reveal answer
17
Subtracting a negative number is the same as adding its positive value, so 15 - (-6) becomes 15 + 6 = 21, and then 21 + (-4) = 17. Rewriting double negatives as addition first prevents sign mistakes.
3. Arrange in descending order: -3, 7, -9, 0, 4.
▶Reveal answer
7, 4, 0, -3, -9
Descending order means largest to smallest. Positive numbers come before zero, and negative numbers farther from zero (like -9) are smaller than ones closer to zero (like -3), giving 7, 4, 0, -3, -9.
4. Which fraction is smaller: 2/3 or 5/9?
▶Reveal answer
5/9
To compare fractions with different denominators, convert them to the same denominator first: 2/3 = 6/9. Since 5/9 is less than 6/9, 5/9 is the smaller fraction.
5. Subtract the fractions: 5/6 - 1/3.
▶Reveal answer
1/2
To subtract fractions with different denominators, first convert to a common denominator: 1/3 becomes 2/6. Then subtract the numerators: 5/6 - 2/6 = 3/6, which simplifies to 1/2.
6. Convert the improper fraction 9/4 into a mixed number.
▶Reveal answer
2 1/4
To convert an improper fraction to a mixed number, divide the numerator by the denominator: 9 divided by 4 is 2, with a remainder of 1. This gives the whole number 2 and the fraction 1/4.
7. Add the decimals: 7.35 + 4.8.
▶Reveal answer
12.15
When adding decimals, line up the decimal points first so digits of the same place value are added together. Adding a trailing zero to 4.8, making it 4.80, makes this lining-up easier: 7.35 + 4.80 = 12.15.
8. Write the ratio of 24 to 40 in its simplest form.
▶Reveal answer
3:5
To simplify a ratio, divide both numbers by their highest common factor. The HCF of 24 and 40 is 8, so dividing both gives 3:5.
9. Divide Rs. 800 between two workers in the ratio 3:5.
▶Reveal answer
Rs. 300 and Rs. 500
The ratio 3:5 has 8 total parts, so each part is worth 800 divided by 8, which is Rs. 100. The first worker gets 3 parts (Rs. 300) and the second gets 5 parts (Rs. 500).
10. If 5 notebooks cost Rs. 125, find the cost of 8 notebooks using the unitary method.
▶Reveal answer
Rs. 200
Using the unitary method, first find the cost of one notebook: 125 divided by 5 is Rs. 25. Then multiply by 8 to find the cost of 8 notebooks: 25 x 8 = Rs. 200.

Introduction to Algebra

Checks identifying variables and constants in an expression, writing an algebraic expression from a word phrase, and solving simple one-step equations.

📋 Quick referenceAlgebra Basics▶

A term's coefficient is the number multiplying the variable (in 3x, the coefficient is 3).
Whatever operation you do to one side of an equation, do the exact same thing to the other side.
To solve for x, undo whatever was done to it: undo addition/subtraction first, then multiplication/division.

Making the Jump from Arithmetic to Algebra

For Parents

Ask your child to describe a word phrase like 'four less than a number' before writing it symbolically, since translating language to symbols is the actual new skill here, not the arithmetic itself.
For one-step equations, keep coming back to the same idea: whatever you do to one side, you must also do to the other side, to keep the two sides balanced like a see-saw.
Reframe solving y - 5 = 12 as 'what number, with 5 taken away, gives 12?' — a question your child could likely already answer without knowing it's called algebra.

For Teachers

Have students read the word phrase aloud before writing the expression — the ones who skip straight to symbols are the ones most likely to reverse a subtraction (writing '5 - x' when the phrase means 'x - 5').

1. Write an algebraic expression for: '7 more than twice a number y.'
▶Reveal answer
2y + 7
'Twice a number y' means the number is multiplied by 2, giving 2y. '7 more than' that means adding 7, so the full expression is 2y + 7.
2. Solve for x: x + 9 = 17.
▶Reveal answer
x = 8
To find x, do the opposite of adding 9, which is subtracting 9, from both sides: 17 - 9 = 8. Checking the answer, 8 + 9 does equal 17.
3. Solve for y: 4y = 28.
▶Reveal answer
y = 7
To find y, do the opposite of multiplying by 4, which is dividing by 4, on both sides: 28 divided by 4 is 7. Checking the answer, 4 x 7 does equal 28.

Geometry, Mensuration & Data Handling

Measures line and shape identification, angle types, symmetry, perimeter and area of rectangles and squares, and reading tally marks, pictographs, and bar graphs.

📋 Quick referencePerimeter, Area & Angle Rules▶

Perimeter vs. Area
- Perimeter: the distance measured around the outer edge of a shape.
- Area: the amount of space covered inside a shape.
Rectangle
- Perimeter = 2 × (length + width).
- Area = length × width.
Square
- Perimeter = 4 × side.
- Area = side × side.
Angle Types
- Acute angle: narrower than a square corner, so under 90°.
- Use a book corner as a check when an angle looks exactly square.
- Obtuse angle: wider than a square corner but still short of a straight line, so somewhere between 90° and 180°.
Symmetry, Lines & Data
- A shape has line symmetry if you can fold it along a line and both halves land exactly on top of each other.
- Mark any visible ends on a drawn path, then decide whether the path stops at both ends, at one end, or continues past both.
- In a tally chart, every fifth mark is drawn as a diagonal stroke across the previous four, making groups of 5 easy to count.
- On a bar graph or pictograph, always check what one unit of height (or one picture symbol) stands for before reading off any value.

Seeing Shapes and Data as Everyday Objects

For Parents

Tie geometry to objects your child already knows: a ray is like a torch beam starting at one point and going on forever, parallel lines are railway tracks.
Keep perimeter and area straight by remembering what each one measures: perimeter is the distance walked around the edge, area is the space covered inside.
Practice angle classification by estimating first, is this angle smaller than a right angle (a book's corner), the same, or bigger, before measuring precisely with a protractor.
For data questions, have your child write out the totals or comparisons in a simple sentence first, like 'the red bar is 4 taller than the blue bar', before treating it as a pure number problem.

For Teachers

Students frequently swap perimeter and area formulas under time pressure — a fast in-class check is asking them to name the unit first (cm vs. cm²) before doing the calculation, since the unit reveals which formula is needed.

1. What do we call a part of a line that starts at one point and goes on forever in one direction, like a torch beam?
▶Reveal answer
Ray
A ray has one fixed starting point but no endpoint, since it keeps going endlessly in a single direction. Think of a road that begins at a signpost and stretches on to the horizon with no end in sight.
2. How many edges does a cube have?
▶Reveal answer
12
A cube has 12 straight edges, the lines where two of its 6 square faces meet. Counting the edges of a dice or a box is an easy way to check this in real life.
3. An angle that measures exactly 90 degrees is called what?
▶Reveal answer
Right angle
A right angle measures exactly 90 degrees, the same as the corner of a book or a square piece of paper. Angles smaller than this are acute, and angles larger are obtuse.
4. How many lines of symmetry does an equilateral triangle have?
▶Reveal answer
3
An equilateral triangle has 3 equal sides and 3 equal angles, and it can be folded along 3 different lines, one from each corner to the middle of the opposite side, to make two matching halves.
5. Find the perimeter of a square with side 15 cm.
▶Reveal answer
60 cm
The perimeter of a square is 4 times the length of one side, since all four sides are equal. Here, 4 x 15 = 60 cm.
6. Find the area of a rectangle with length 18 cm and breadth 10 cm.
▶Reveal answer
180 sq. cm
The area of a rectangle is length x breadth, so 18 x 10 = 180 square centimetres.
7. A rectangular garden is 20 m long and 12 m wide. Find the cost of fencing it at Rs. 15 per metre.
▶Reveal answer
Rs. 960
Fencing goes around the outside, so first find the perimeter: 2 x (20 + 12) = 2 x 32 = 64 m. Multiplying by the rate gives the total cost: 64 x 15 = Rs. 960.
8. The tally marks |||| || stand for what number?
▶Reveal answer
7
Tally marks are grouped in fives, with the fifth mark drawn across the first four. Here there is one full group of five plus two more marks, giving 5 + 2 = 7.
9. In a pictograph, each apple symbol stands for 10 fruits sold. If Monday has 4 symbols, how many fruits were sold that day?
▶Reveal answer
40 fruits
In a pictograph, the total is found by multiplying the number of symbols by the value each symbol represents. Here, 4 symbols x 10 fruits each = 40 fruits.
10. A bar graph shows Friday's sales were 25 and Saturday's were 18. Which day sold more, and by how many?
▶Reveal answer
Friday sold more, by 7
Comparing the two values directly, Friday's 25 is 7 more than Saturday's 18. Reading a bar graph is really just comparing the heights of the bars, which represent these exact numbers.

Where students at this level usually slip

When comparing fractions with different denominators, many children compare the numerators alone and assume 5/9 is bigger than 2/3 just because 5 is bigger than 2 — converting both to a common denominator first removes this mistake completely.
Ratio and unitary-method word problems are often lost to the right method with an arithmetic slip, or the wrong method with correct arithmetic — double-checking by asking 'does this answer make sense for the situation?' catches both kinds of errors.

Frequently asked questions

What math skills should a Class 6 child have?

Comparing and calculating with negative numbers, adding and comparing fractions and decimals, simplifying ratios, writing simple algebraic expressions and solving one-step equations, and finding the perimeter and area of basic shapes like rectangles and squares.

Why does my child struggle with negative numbers specifically?

Negative numbers are the first idea where 'more' doesn't always mean bigger, since -2 is greater than -5 even though 5 is bigger than 2 without the sign. This breaks a rule children have relied on since they started counting, so it usually takes steady repetition, not more explanation, before it feels automatic.

Explore more for Class 6

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Move between subjects in the same class to build a fuller revision routine.

Math learning ladder — Middle (Class 6-8)

See where Class 6 Math fits in the middle (class 6-8) years, and jump straight to the next step.

📍 You are here
Class 6
Integers, Ratios & Introductory Algebra
The jump from Class 5: introduces negative numbers, ratio and the unitary method, and the first algebraic variables and equations, the first year of middle-school math.
Class 7
Rational Numbers, Exponents & Algebraic Expressions
Extends Class 6 further: integers become rational numbers, exponents and algebraic expressions enter the picture, and triangle geometry and proportional comparison bring in multi-step problems in place of single-step arithmetic.
Open test →
Class 8
Roots, Factorisation & Applied Percentages
Class 7's algebra and geometry get real-world application here: square/cube roots, algebraic factorisation, and percentage-based problems like profit/loss and simple interest, the last middle-school milestone before Class 9 board-prep math.
Open test →

Mastering Class 6 Math today builds a strong foundation, making next year's complex concepts feel effortless and natural.

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