Here we will explain what 106 mod 1 means and show how to calculate it. 106 mod 1 is short for 106 modulo 1 and it can also be called 106 modulus 1.
Modulo is the operation of finding the Remainder when you divide two numbers. Therefore, when you ask "What is 106 mod 1?" you are asking "What is the Remainder when you divide 106 by 1?".
We will show you two methods of finding 106 mod 1 (106 modulo 1). To differentiate our methods, we will call them the "Modulo Method" and the "Modulus Method".
Before we continue, we remind you of what the different parts of a division problem are called so you can follow along: Dividend / Divisor = Quotient and in this case 106 is the Dividend, 1 is the Divisor, and the answer is called the Quotient.
Furthermore, the Quotient x.y has two parts: x to the left of the decimal point is the Whole part, and y to the right of the decimal point is the Fractional part.
Modulo Method
To find 106 mod 1 using the Modulo Method, we first divide the Dividend (106) by the Divisor (1).
Second, we multiply the Whole part of the Quotient in the previous step by the Divisor (1).
Then finally, we subtract the answer in the second step from the Dividend (106) to get the answer. Here is the math to illustrate how to get 106 mod 1 using our Modulo Method:
106 ÷ 1 = 106
106 × 1 = 106
106 - 106 = 0
Thus, the answer to "What is 106 mod 1?" is 0.
Modulus Method
To find 106 mod 1 using the Modulus Method, we first find the highest multiple of the Divisor (1) that is equal to or less than the Dividend (106).
Then, we subtract the highest Divisor multiple from the Dividend to get the answer to 106 modulus 1 (106 mod 1):
Multiples of 1 are 0, 1, 2, 3, etc. and the highest multiple of 1 equal to or less than 106 is 106. Therefore, to get the answer:
106 - 106 = 0
Thus, once again, the answer to "What is 106 mod 1?" is 0.
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