Multiplication quiz

More questions about Multiplication

These visible examples show the question style. LearnClash turns the full topic into ranked duels and spaced repetition.

1. 1 Easy

   Which property allows changing how factors group?

   Answer: Associative property

   Why: Associativity means regrouping numbers in a long multiplication chain will never alter the final answer.

2. 2 Medium

   Multiplying a complex number by its conjugate yields what?

   Answer: A real number

   Why: The imaginary cross terms cancel each other out completely, leaving only the real sum $a^2 + b^2$.

3. 3 Hard

   What is the largest dimension of a real normed division algebra?

   Answer: 8

   Why: Hurwitz proved in 1898 that real normed division algebras exist only in dimensions 1, 2, 4, and 8, which correspond to the octonions.

4. 4 Easy

   Which keyboard symbol represents multiplication in code?

   Answer: Asterisk

   Why: Early computer keyboards lacked a dedicated multiplication cross, so language designers chose the asterisk instead.

5. 5 Medium

   What is the product of $x^3$ and $x^4$?

   Answer: $x^7$

   Why: Because exponents count repeated factors, multiplying 3 factors of $x$ by 4 factors of $x$ gives a total of 7.

6. 6 Hard

   What is the fewest multiplications needed to multiply two 2x2 matrices?

   Answer: 7

   Why: Standard matrix multiplication uses 8 scalar multiplications, but Strassen showed 7 suffices, which was proven to be the theoretical minimum.