In this lesson, well look at some rules and properties of addition, subtraction, and multiplication in modular arithmetic. Math circle thursday january 22, 2015 what is modular arithmetic. Modulo a prime number we have seen that modular arithmetic can both be easier than normal arithmetic in how powers behave, and more di. Arithmetic properties commutative, associative, distributive. Well explore various ways to represent whole numbers, place value, order of operations, rounding and various other properties of arithmetic. A when one number is less than zero and the other two are greater than zero b when all numbers are positive c when one number is greater than zero and the other two are less than zero d when at least one number equals. Now that you know fermat s little theorem, solve problem 3 in a mildly simpler way than before. The least common multiple of two numbers is the smallest positive integer with both numbers as a factor.
Modular arithmetic is something we use everyday when we look at a clock. In no specific order, they are the commutative, associative, distributive, identity and inverse properties. Use the links above to go to a page that deals only with that arithmetic property. Now, let us look at the properties of arithmetic mean. In modular arithmetic, we select an integer, n, to be our \modulus. Head from properties of arithmetic to the basic algebra section, or explore everything else printable math worksheets has to. We know that a a 0, and one of the elementary results seen previously is that n j0 for any integer n. If all the observations assumed by a variable are constants, say k, then arithmetic mean is also k. Modular arithmetic definition of modular arithmetic by. Under what circumstances will the product of three numbers always be negative. Modular arithmetic and elementary algebra 1 euclids algorithm. Though it seems that arithmetic on z n is the same as on z, do not be deceived. Compute 414 463 mod 4 1 50 50 note cancelation property.
Math challenge washington middle school march 4, 2010 warmup activity pretend that its 3. Arithmetic mean is one of the measures of central tendency which can be defined as the sum of all observations to be divided by the number of observations. Modular arithmetic definition is arithmetic that deals with whole numbers where the numbers are replaced by their remainders after division by a fixed number. But when n is a prime number, then modular arithmetic keeps many of the nice properties we are used to with whole numbers. The product of two nonzero elements of z n can sometimes be 0. Properties of arithmetic printable math worksheets.
Arithmetic properties prealgebra math khan academy. Answer the following questions, but dont worry about ampm. First, there is the fact that congruence modulo n satis es 3 popular properties of relations. The lcm of 4 and 6 is 12 it is the smallest number that has both 4 and 6 in its divisors. Euclids algorithm or the euclidean algorithm is a very ecient and ancient algorithm to nd the greatest common divisor gcda. There are several useful properties of modular arithmetic. Introduction integer congruences department of mathematics. With this interactive quiz and worksheet, you will have a chance to test yourself on modular arithmetic and how to solve relevant practice. Multiplication and addition have specific arithmetic properties which characterize those operations. Properties of multiplication in modular arithmetic. This kind of \reduced algebra is essential background for the mathematics of computer science, coding theory, primality testing, and much more. An operation is commutative if changing the order of the operands does not change the result. Read about properties of exponents algebra reference in our free electronics textbook.
1549 1648 589 834 479 972 305 784 1601 1075 1665 1346 929 999 371 419 524 1346 1549 150 1521 115 1692 1550 1461 1374 709 720 270 48 179 1378 1477 919 1497 401 23 1086 1083 306 537 1346 1278 1156 611 296