When y is divided by 6, the remainder is 4. What will be the remainder if y-6 is divided by 3 ?
a. 0
b. 1
c. 2
d. 3
e. 4
my answer is b. 1 , but teacher give me the answer is d. 3 , I don't understand, anyone can explain
I agree with you.
Dividing by 3 can never give a remainder of 4.
Y is divided by 6, the remainder is 4, so I think 6x6+4=40 , so y=40
40-6/3
=34/3
remainder=1
y can be any number 6x+4
so, y = 3(2x)+3+1
= 3(2x+1) + 1
so, when divided by 3 it leaves a remainder of 1.
so, the teacher give me the wrong answer?
my answer is right
To find the remainder when y-6 is divided by 3, we need to first understand some properties of remainders and division.
Given that when y is divided by 6, the remainder is 4, we can write it as:
y = 6n + 4, where n is an integer (quotient)
Now, let's consider y-6:
y - 6 = 6n + 4 - 6
= 6n - 2
To determine the remainder when y-6 is divided by 3, we divide it by 3 and observe the remainder.
(6n - 2) ÷ 3
To simplify the expression, we can divide each term separately:
6n ÷ 3 = 2n
-2 ÷ 3 can be written as -1 remainder 1 (or -1 + 1/3)
Therefore, the remainder when y-6 is divided by 3 is 1.
Your answer of b. 1 is correct.
It is possible that your teacher made an error. I would recommend discussing with your teacher and explaining the steps you used to arrive at your answer.