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Number System (Classes VI-VIII) — 25-Question Test
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Key Concepts — Quick Reference
This chapter
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) |