Kit Library / Mathematics / Class 9 Ganita Manjari
⚡ Topic Learning KitShared by a Veda learner · Generated with Veda AI
Veda Bites are swipeable micro-lessons — each one teaches exactly one idea. Here's a taste from this kit; the app has the full deck.
Division breaks closure for rationals.
Rational numbers are closed under addition, subtraction, and multiplication, meaning the result is always a rational number. However, they are not closed under division because division by zero is undefined, which is not a rational number.
↳ Rational numbers are closed under +, -, × but not ÷ (due to zero).
Zero has no multiplicative inverse.
The multiplicative inverse of a number $x$ is $\frac{1}{x}$, such that $x \times \frac{1}{x} = 1$. Every non-zero rational number has a multiplicative inverse.
↳ Zero is the only rational number without a multiplicative inverse.
Subtraction and division are not associative.
An operation is associative if $(a \circ b) \circ c = a \circ (b \circ c)$. Addition and multiplication of rationals are associative, but subtraction and division are not.
↳ For rationals, + and × are associative; − and ÷ are not.
This mock test covers key Class 9 Maths topics including rational numbers (closure, identities, inverses), arithmetic and geometric progressions, coordinate geometry, polynomials, and circle properties. It tests both con...
~8 min · full explanation, examples & memory tricks in the app
18 questions laddered from warm-up to topper-level, each with an explanation. A taste:
In the standard form of a rational number, the common factor of numerator and denominator is always:
Beginner1
A rational number is in standard form when its denominator is positive and the numerator and denominator have no common factor other than 1.
Which of the following is not true for rational numbers?
BeginnerRational numbers are closed under division.
Rational numbers are not closed under division because division by zero is not defined.
Which of the following numbers does not have a multiplicative inverse?
Beginner0
0 does not have a multiplicative inverse because there is no rational number which when multiplied by 0 gives 1.
Which of the following operations is not associative for rational numbers?
BeginnerBoth (B) and (C)
Both subtraction and division are not associative for rational numbers. For example, (a - b) - c ≠ a - (b - c).
18 flashcards in this kit — the app reviews them with spaced repetition so the right card returns on the right day.
Every game is built from this kit's own content — scores feed your mastery, so playing counts as studying.
The full Veda Bites deck, complete notes, spaced-repetition flashcards, leveled MCQs, tests and games for this kit — plus Daily Facts and the Arena, every day.
