Number System (Classes VI-VIII)
If you are sitting CTET Paper II with Maths and Science, the number system is where you bank easy marks. It anchors the whole upper-primary syllabus, and the paper draws on it twice: a handful of straight computation items (an HCF here, an integer rule there) and, more interestingly, the pedagogy questions that describe a child making a very specific error and ask what is going on inside that child's head. That second kind is what separates candidates who scraped 60 percent in school maths from those who clear the cut-off. You are not being asked to be a calculator; you are being asked to read a wrong answer like a diagnosis. Why does a Class 6 child insist that -5 is bigger than -2? Why does another write 0.7 as smaller than 0.65? This chapter walks the six strands of the upper-primary number system, but every recap is tied to the misconception CTET hangs the question on and the way a thoughtful teacher would unpick it. Get the maths right, learn the typical child errors, and this is the most predictable section on the paper.
Topics
⚡ Smart tips & memory hooks
Memory hooks and exam-smart tips to lock this chapter in and answer CTET MCQs quickly and accurately.
- HCF takes the LOWEST powers of common primes; LCM takes the HIGHEST powers of all primes. (HCF is small, LCM is large.)
- Word-problem signals: largest size / greatest that fits both -> HCF; meet again / ring together / smallest common -> LCM.
- Use HCF(a,b) x LCM(a,b) = a x b to find one when you know the other.
- Integer signs for x and division: like signs -> +, unlike signs -> -. For addition, same signs add, different signs subtract.
- Decimals: pad with zeros so all have the same number of places (0.7 = 0.70), then compare like whole numbers.
- Exponents with the SAME base: multiply -> add powers, divide -> subtract powers; and any non-zero base to the power 0 is 1.
⚠️ Common mistakes & traps
CTET loves to test these exact confusions. Internalise each trap before exam day.
- Swapping HCF and LCM, or computing HCF by multiplying all common factors instead of the lowest prime powers.
- Saying -5 is greater than -2 by comparing magnitudes and ignoring the number line.
- Adding fractions by adding numerators AND denominators (1/2 + 1/3 = 2/5) instead of using a common denominator.
- Longer-is-larger in decimals: judging 0.65 greater than 0.7 because it has more digits.
- Reading 3^2 as 3 x 2 = 6, or writing a^2 x a^3 = a^6 by multiplying the exponents.
- Thinking a rational number must be a proper fraction, so excluding integers like 5 or -3 (which are 5/1 and -3/1).
📈 CTET exam insight & PYQ analysis
🎴 Flashcards — instant recall
Tap a card to reveal the answer. Drill these until they are automatic.
📌 Quick revision
Chapter test
📚 Want the full concept lesson?
This chapter gives you the CTET-focused recap, pedagogy and exam-style practice. For the underlying concept taught step by step — worked from the ground up with diagrams — open the matching lesson in our school Maths course.
🏆 Vidaara CTET success checklist
You have truly mastered Number System (Classes VI-VIII) when you can tick every box below.
- Recall every formula in this chapter without looking them up
- Solve each topic’s practice set with at least 80% accuracy
- Use the chapter shortcuts to cut your solving time in half
- Spot and avoid every common trap listed above
- Score 80%+ on the timed chapter test
📋 Chapter mastery scorecard
Track where you stand. Aim for the target before moving to the next chapter.
| Skill checkpoint | Target |
|---|---|
| Concept theory & formulas understood | 100% |
| Topic practice sets attempted (6 topics) | 6/6 |
| Best topic-test score | — → 80%+ |
| Chapter test score | — → 80%+ |
| Flashcards drilled to instant recall | 12 cards |
Key Concepts — Quick Reference
HCF, LCM and divisibility (the workhorses)
| HCF | Highest common factor = product of the LOWEST powers of common primes |
|---|---|
| LCM | Lowest common multiple = product of the HIGHEST powers of all primes present |
| Key identity | HCF(a,b) x LCM(a,b) = a x b (for any two numbers) |
| Divisibility by 3 / 9 | Divisible if the digit sum is divisible by 3 / by 9 |
Integers, fractions and exponents
| Integer signs | Two like signs -> +, two unlike signs -> - (for x and division) |
|---|---|
| Adding fractions | Take the LCM of denominators, then add the numerators only |
| Laws of exponents | a^m x a^n = a^(m+n); a^m / a^n = a^(m-n); a^0 = 1 |
| Squares and cubes | Square = n x n (area model); cube = n x n x n (volume model) |