Answer:3|4 Devided by 1|8 =1|2
Step-by-step explanation:
3 1
4 devided by 8 =1|2
how did i get that?
this is how to get the quotient:
The answer after we divide one number by another. dividend ÷ divisor = quotient. ExaWhen we want to prove some properties about modular arithmetic we often make use of the quotient remainder theorem.
It is a simple idea that comes directly from long division.
The quotient remainder theorem says:
Given any integer A, and a positive integer B, there exist unique integers Q and R such that
A= B * Q + R where 0 ≤ R < B
We can see that this comes directly from long division. When we divide A by B in long division, Q is the quotient and R is the remainder.
If we can write a number in this form then A mod B = Rmple: in 12 ÷ 3 = 4, 4 is the quotient.
Examples
A = 7, B = 2
7 = 2 * 3 + 1
7 mod 2 = 1
A = 8, B = 4
8 = 4 * 2 + 0
8 mod 4 = 0
A = 13, B = 5
13 = 5 * 2 + 3
13 mod 5 = 3
A = -16, B = 26
-16 = 26 * -1 + 10
-16 mod 26 = 10
We have
n mod 3 = 2
n mod 5 = 1
3 and 5 are coprime so we can use the Chinese Remainder Theorem
By the Chinese Remainder Theorem:
Given
n mod x = a
n mod y = b
where x and y are coprime, we have:
n = (y * (y^-1 mod x) * a + x * (x^-1 mod y) * b ) mod (x * y)
n = (5 * (5^-1 mod 3) * 2 + 3 * (3^-1 mod 5) * 1 ) mod (3 * 5)
n = 5 * 2 * 2 + 3 * 2 * 1 mod 15
n = 26 mod 15
n = 11
Remember that in long division if we divide A by B the remainder must be >= 0 and < B.
So, if we look at -16/26:
If we say that the quotient is 0 we get:
_0_R-16
26 / -16
-0 (Since 0 * 26 = 0)
--------
-16
We got a remainder of -16.
But the remainder can't be negative!
The remainder must be >= 0 and < 26.
Instead, if we try -1 as the quotient we get:
__-1_R_10
26 / -16
-(-26) (Since -1 * 26 = -26)
--------
10
