Class 6 maths · Original EZT practice
RS Aggarwal Class 6: original worked practice
A number pattern, a pictograph and a shape each need a different kind of check. Start with the rule the question gives you, show your working and explain how you know the result fits.
This page gives Class 6 students 12 original worked examples and 12 fresh self-check questions with explained answers. Use the EZT practice-skill index alongside your RS Aggarwal book to learn a method, not to look up its exercise answers.
Original EZT practice, not copied textbook exercises or a full-solutions service. Match the topic to your own book; editions vary. This is not an official chapter index, exercise map or claim about your current syllabus. Follow your school's topic list.
Bharati Bhawan lists Mathematics for Class 6 by R S Aggarwal. That source identifies the book, not the order of our practice topics. EZ Tuitions is not affiliated with the authors or publisher.
Choose, solve, check, then try a fresh question.
Before calculating, read the method prompt and name the condition that makes it useful. Write your own attempt. Open the steps only when you need them, and use the check to catch a wrong sign, unit or interpretation. Finish with the fresh question before reading its answer.
Make a number without losing the zero
Choose the method: The first digit of a six-digit number cannot be zero. Then compare place values from left to right.
EZT practice question
Use each digit 0, 2, 3, 5, 7 and 8 once to make the smallest six-digit number.
Show the worked solution
- Choose 2, the smallest non-zero digit, for the hundred-thousands place.
- Put the remaining digits in increasing order: 0, 3, 5, 7, 8.
- The number is 203578.
Answer: 203578
Check: The first digit is non-zero and all six given digits appear once. Any first digit above 2 would make a larger number.
Watch for this: Putting zero first makes a five-digit number, not a smaller six-digit number.
Now try it yourself
Use the same six digits once each to make the largest six-digit number.
Check your answer
875320
Put larger digits in higher place values: 8, 7, 5, 3, 2, 0. Changing any earlier digit to a smaller one reduces the number.
Explain what a pattern adds
Choose the method: Look for how many objects are added at each step, not only for the next total.
EZT practice question
A dot pattern has row lengths 1, 2, 3, 4 and 5. It has 15 dots altogether. One more row has 6 dots. How many dots are there now?
Show the worked solution
- The old five rows have 1 + 2 + 3 + 4 + 5 = 15 dots.
- The new row adds 6 dots, not 5.
- The new total is 15 + 6 = 21.
Answer: 21 dots
Check: Add all six row lengths: 1 + 2 + 3 + 4 + 5 + 6 = 21.
Watch for this: Adding the same amount at every step would describe a different pattern.
Now try it yourself
A square array has 6 dots in each of 6 equal rows. How many dots are in the array?
Check your answer
36 dots
Six equal rows of six dots give 6 × 6 = 36. This is a square array, not rows that grow from 1 to 6.
Prime and co-prime mean different things
Choose the method: A prime number has exactly two positive factors. Co-prime describes a pair whose only common positive factor is 1.
EZT practice question
Is 51 prime? Give a factor-based reason.
Show the worked solution
- The digit sum is 5 + 1 = 6, so 51 is divisible by 3.
- 51 = 3 × 17.
- It has factors besides 1 and itself, so it is composite.
Answer: No; 51 is composite because 51 = 3 × 17.
Check: 3 × 17 = 51, so the factorisation returns the original number.
Watch for this: Being odd does not make a number prime.
Now try it yourself
Are 8 and 15 co-prime, even though neither is prime?
Check your answer
Yes; their HCF is 1.
The factors of 8 are 1, 2, 4, 8. The factors of 15 are 1, 3, 5, 15. Only 1 occurs in both lists.
Use the right divisibility test
Choose the method: For divisibility by 9, test the digit sum. For divisibility by 4, test the last two digits.
EZT practice question
The three-digit number 34d is divisible by 9, where d is a single digit. Find d.
Show the worked solution
- The digit sum is 3 + 4 + d = 7 + d.
- For a digit d from 0 to 9, that sum is between 7 and 16.
- The only multiple of 9 in that interval is 9, so d = 2.
Answer: d = 2
Check: 342 = 9 × 38.
Watch for this: The last digit alone does not decide divisibility by 9.
Now try it yourself
Is 7284 divisible by 4? Is it divisible by 9?
Check your answer
Divisible by 4, but not by 9.
The last two digits form 84, which is divisible by 4. The digit sum is 21, which is not divisible by 9.
Split a product into friendly parts
Choose the method: Use the distributive property to change the calculation without changing its value.
EZT practice question
Calculate 25 × 36 by splitting 36 into 30 + 6.
Show the worked solution
- Write 25 × 36 = 25 × (30 + 6).
- Multiply both parts: 25 × 30 = 750 and 25 × 6 = 150.
- Add the products: 750 + 150 = 900.
Answer: 900
Check: 36 ÷ 4 = 9 and 25 × 4 = 100, so 25 × 36 = 100 × 9 = 900.
Watch for this: Adding 25 only once after multiplying by 30 would leave out five groups of 25.
Now try it yourself
Calculate 48 × 99 using 99 = 100 - 1.
Check your answer
4752
48 × 99 = 48 × 100 - 48 × 1 = 4800 - 48 = 4752.
A change can cross zero
Choose the method: A rise moves to the right on a number line; a fall moves to the left.
EZT practice question
A temperature rises from -3°C to 5°C. By how many degrees does it rise?
Show the worked solution
- From -3°C to 0°C is a rise of 3°C.
- From 0°C to 5°C is a rise of another 5°C.
- The total rise is 3 + 5 = 8°C.
Answer: 8°C
Check: The final temperature is -3 + 8 = 5°C.
Watch for this: 5 - 3 = 2 ignores the distance from -3 to zero.
Now try it yourself
Start at -4 on a number line and move 6 units left. Where do you finish?
Check your answer
-10
Moving left subtracts 6: -4 - 6 = -10.
Compare equal-sized fractional units
Choose the method: Rewrite fractions with a common denominator so the units being counted have the same size.
EZT practice question
Find 5/6 - 1/3 in simplest form.
Show the worked solution
- Write 1/3 as 2/6.
- Subtract equal-sized sixths: 5/6 - 2/6 = 3/6.
- Simplify 3/6 to 1/2.
Answer: 1/2
Check: 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
Watch for this: Subtracting the denominators would change the fractional unit.
Now try it yourself
Which is greater: 3/4 or 5/8?
Check your answer
3/4 is greater.
3/4 = 6/8, and six eighths is greater than five eighths.
Tenths and hundredths must line up
Choose the method: Use a zero placeholder when needed to keep equal place values together.
EZT practice question
One length is 2.05 m and another is 0.7 m. Find their total length.
Show the worked solution
- Write 0.7 m as 0.70 m.
- Add 2.05 + 0.70 = 2.75.
- The total length is 2.75 m.
Answer: 2.75 m
Check: In centimetres, 205 + 70 = 275 cm, which is 2.75 m.
Watch for this: Writing 0.7 as 0.07 would turn seven tenths into seven hundredths.
Now try it yourself
Which is larger: 1.2 or 1.19?
Check your answer
1.2 is larger.
Write 1.2 as 1.20. Twenty hundredths is greater than nineteen hundredths, so 1.20 > 1.19.
Connect a turn to an angle
Choose the method: A full turn measures 360°. Name the angle after finding its measure.
EZT practice question
A pointer turns through one quarter of a full turn. How many degrees does it turn, and what type of angle is that?
Show the worked solution
- A full turn is 360°.
- One quarter is 360° ÷ 4 = 90°.
- An angle of 90° is a right angle.
Answer: 90°; a right angle
Check: Four quarter-turns total 4 × 90° = 360°.
Watch for this: A quarter-turn is not 45°; eight turns of 45° make a full turn.
Now try it yourself
A pointer turns through three quarters of a full turn. Find the angle turned through and classify it.
Check your answer
270°; a reflex angle
Three quarters of 360° is 270°. It is greater than 180° and less than 360°, so it is reflex. The question asks for the whole turn made, not the smaller angle between the final and initial directions.
Equal boundaries need not enclose equal areas
Choose the method: Perimeter counts boundary length; area counts square units inside.
EZT practice question
A rectangle is 9 cm long and 4 cm wide. Find its perimeter and area.
Show the worked solution
- Its perimeter is 9 + 4 + 9 + 4 = 26 cm.
- Its area is 9 × 4 = 36 cm².
- Use cm for perimeter and cm² for area.
Answer: Perimeter 26 cm; area 36 cm²
Check: The perimeter has two lengths and two widths; the area can be counted as 4 rows of 9 unit squares.
Watch for this: Multiplying length by width finds area, not perimeter.
Now try it yourself
A second rectangle is 8 cm by 5 cm. Does it have the same perimeter and area as the first?
Check your answer
Same perimeter, 26 cm; different area, 40 cm².
2 × (8 + 5) = 26 cm, but 8 × 5 = 40 cm². Equal perimeter does not force equal area.
Read the key before counting symbols
Choose the method: Each symbol stands for a stated number of objects; a half-symbol stands for half that number.
EZT practice question
In a pictograph, one complete star represents 4 library books. A row shows 3 complete stars and half a star. How many books does the row represent?
Show the worked solution
- Three complete stars represent 3 × 4 = 12 books.
- Half a star represents 4 ÷ 2 = 2 books.
- The row represents 12 + 2 = 14 books.
Answer: 14 books
Check: 14 ÷ 4 = 3.5, matching three and a half stars.
Watch for this: Counting symbols as books ignores the pictograph key.
Now try it yourself
A class of 24 students each votes for one game. Chess gets 8 votes and badminton gets 10. All the other votes go to football. How many votes does football get?
Check your answer
6 votes
The two known groups use 8 + 10 = 18 votes. The remaining group has 24 - 18 = 6. Each student votes once, so the groups do not overlap.
A mirror line and a turn are different tests
Choose the method: Reflection symmetry means matching across a line; rotational symmetry means matching after a turn smaller than a full turn.
EZT practice question
For a rectangle that is not a square, how many lines of reflection symmetry are there, and what is its rotational symmetry order?
Show the worked solution
- There is a reflection line through the midpoints of each pair of opposite sides: two lines.
- A half-turn makes the rectangle coincide with itself. A quarter-turn does not, because the side lengths differ.
- There are two matching positions during a full turn, counting the full-turn position, so the rotational order is 2.
Answer: 2 reflection lines; rotational order 2
Check: Its diagonals are not reflection lines unless the rectangle is a square.
Watch for this: A shape can have rotational symmetry without each line through its centre being a mirror line.
Now try it yourself
For a square, give the number of reflection lines and the rotational symmetry order.
Check your answer
4 reflection lines; rotational order 4
Two midpoint lines and two diagonals are reflection lines. The square matches after 90°, 180°, 270° and 360°, giving rotational order 4.
Know the rule but lose track of the steps?
Bring your Class 6 maths book, your school topic list and a question you attempted. Ask a tutor to explain the choice of method and test it with a different problem. Agree the lesson topics, schedule and fee before starting.
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Questions about this practice page
- Are these official RS Aggarwal Class 6 exercise answers?
- No. These are original EZT practice questions with worked steps, checks and fresh questions. They are not reproduced textbook exercises, an exercise-number answer key or an official publisher resource.
- Does the practice index follow my book chapter order?
- Not necessarily. Editions and school topic lists vary. This is a selected EZT skill index, not a verified publisher table of contents or exercise map. Match the topic to your own book before using a practice pair.
- How should I use a worked example?
- Try it first, then compare your method with the steps. Use the check to catch a wrong unit or rule. Solve the fresh question without opening its answer; explain why the method applies, rather than copying the result.
- Does this cover the complete Class 6 maths syllabus?
- No. It covers selected number, shape and data skills, including some revision. Follow your school topic list for the full course. A topic appearing here does not mean every Class 6 school teaches it in the same term.
- What should I bring to a tutor if I am stuck?
- Bring your own book, the question and your attempted steps. Mark the first step you cannot explain. Ask for a different practice question to test your understanding, and agree lesson topics, schedule and fee before starting.