Using the Division algorithm to find q and r such that 3662 = q·16+r, where 0 ≤ r < 16. What if we take c = - 3662 instead of c = 3662? From this example we learn that q is the largest integer less than or equal to c/b.

Question

Fiesta

Mathematics

4 April, 19:30

Using the Division algorithm to find q and r such that 3662 = q·16+r, where 0 ≤ r < 16. What if we take c = - 3662 instead of c = 3662? From this example we learn that q is the largest integer less than or equal to c/b.

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Answers (1)

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Tania Andrews · Answer 1

a) If c=3662 then q=228 and r=14.

b) If c=-3662, then q=-229 and r=2

Step-by-step explanation:

a) Observe that 229*16=3664, since r must be in the interval [0,16), then 229 doesn't work, but 228*16=3648 and 3662-3648=14.

Then 3662=228*16+14.

b) Observe that - 228*16=-3648 and - 3648-14=-3662, but r = must be positive. Then - 228 doesn't work.

But observe that - 229*16=-3664 and - 3664+2=-3662. So - 3662=-229*16+2