State whether the statements are True or False.

Multiplication fact (–8) × (–10) = 80 is same as division fact 80 ÷ (– 8) = (–10)

Let us solve it simultaneously starting from multiplication fact.

Given multiplication fact, (-8) × (-10) = 80

We shall first simplify left hand side (LHS) of this multiplication fact.

LHS = (-8) × (-10)

⇒ LHS = -8 × -10

⇒ LHS = -1 × -1 × 8 × 10

⇒ LHS = (-1 × -1) × (8 × 10)

⇒ LHS = 1 × 80 [∵ -1 × -1 = 1 & 8 × 10 = 80]

⇒ LHS = 80

And RHS = 80 [∵ right hand side, RHS of multiplication fact = 80]

⇒ Multiplication fact is true.

Now, given division fact, 80 ÷ (-8) = (-10)

We shall first simplify left hand side (LHS) of this division fact.

LHS = 80 ÷ (-8)

⇒ LHS = -(80 ÷ 8)

⇒

⇒ LHS = -10

And RHS = -10 [∵ right hand side, RHS of division fact = -10]

⇒ Division fact is also true.

So, Multiplication fact is same as division fact.

Thus, this is a true statement.