Question

Which expressions correctly show "the sum of the product of 3 and 8 and the product of 12 and 2"? Select two that are correct. *

3 + 8 + 12 + 2
(12 × 2) + (3 × 8)
3 × 8 × 12 × 2
(3 + 8) × (12 + 2)
(3 × 8) + (12 × 2)

Answer 1

The two correct expressions are:

• (12 × 2) + (3 × 8)

• (3 × 8) + (12 × 2)

Explanation:

Let 'a' and 'b' be the two numbers.

When we say the product of 'a' and 'b', it

• algebraically means: a × b

Let 'c' and 'd' be the two numbers.

When we say the product of 'c' and 'd', it

• algebraically means: c × d

And when we say the sum of the product of 'a' and 'b' and the product of 'c' and 'd', it algebraically means:

(a × b) + (c × d)

or

(c × d) + (a × b)

as

(a × b) + (c × d) = (c × d) + (a × b)

So when we say "the sum of the product of 3 and 8 and the product of 12 and 2".

It algebraically means:

(12 × 2) + (3 × 8)

or

(3 × 8) + (12 × 2)

as

(12 × 2) + (3 × 8) = 24 + 24 ∵ 12 × 2 = 24, 3 × 8 = 24

= 48

(3 × 8) + (12 × 2) = 24 + 24 ∵ 3 × 8 = 24, 12 × 2 = 24,

= 48

Therefore, the two correct expressions are:

• (12 × 2) + (3 × 8)

• (3 × 8) + (12 × 2)