Question

Which of the following number sentences are true? a. 20 × 410 = (20 x 400) + (20x10) b. 20 x 308 = (20 x 340)-(20 x32) c. -20 ×-800 = (-20 x-1,000)(-20x200)

Answer 1

The true number sentences are: a. 20 × 410 = (20 x 400) + (20x10); b. 20 x 308 = (20 x 340)-(20 x32). The false number sentence is: c. -20 ×-800 = (-20 x-1,000)(-20x200)

Step-by-step explanation:

In order to determine which number sentences are true, we need to evaluate each equation. Let's go through them one by one:

a. 20 × 410 = (20 x 400) + (20x10)

20 × 410 = 8200

(20 x 400) + (20x10) = 8000 + 200 = 8200

Since both sides of the equation are equal to 8200, this number sentence is true.

b. 20 x 308 = (20 x 340)-(20 x32)

20 x 308 = 6160

(20 x 340)-(20 x32) = 6800 - 640 = 6160

Since both sides of the equation are equal to 6160, this number sentence is true.

c. -20 ×-800 = (-20 x-1,000)(-20x200)

-20 ×-800 = 16000

(-20 x-1,000)(-20x200) = 20000 x 200 = 4000000

Since the left side of the equation is -16000 and the right side is 4000000, this number sentence is false.