Q 01/05

Which property of multiplication says 3 × 4 and 4 × 3 give the same product, no matter the order?

A) Associative Property

B) Identity Property

C) Commutative Property

D) Distributive Property

Answer · why

C) Commutative Property

Commutative Property: turn 3 rows of 4 dots on their side and they become 4 rows of 3, still 12 dots in all, which is why swapping the order can never...

Q 02/05

Multiplying two negative numbers together always gives what kind of result?

A) A negative number

B) A positive number

C) An irrational number

D) Exactly zero

Answer · why

B) A positive number

A positive number: follow the pattern 2 × −3 = −6, 1 × −3 = −3, 0 × −3 = 0, and the next step down, −1 × −3, has to climb to +3.

Q 03/05

Which old trading word names a dozen dozens, or 144 of anything?

A) A score

B) A ream

C) A gross

D) A bushel

Answer · why

C) A gross

A gross is 144 items, a name taken from the Old French for 'large dozen'; a dozen gross, 1,728, is a great gross.

Q 04/05

Which property says (2 × 3) × 4 and 2 × (3 × 4) give the same result, whatever the grouping?

A) Associative

B) Commutative

C) Identity

D) Distributive

Answer · why

A) Associative

Associative: because the grouping never matters, 7 × 25 × 4 can be done as 7 × 100, the regrouping trick behind many mental-arithmetic shortcuts.

Q 05/05

Which property of multiplication lets a(b + c) be expanded to ab + ac?

A) Commutative Property

B) Associative Property

C) Distributive Property

D) Identity Property

Answer · why

C) Distributive Property

The Distributive Property spreads a factor across every term in the brackets; it's why 7 × 12 can be done as 7 × 10 plus 7 × 2.