Carl Friedrich Gauss and the Number Theory Moreover, modular arithmetic was used to solve astronomical and seasonal calculations which were problems associated with natural and man-made cycles. An example is the Chinese book Master Sun’s Mathematical Manual, which dates back from 300 AD. To help you visualize, the number line below shows the difference in value.Īccording to Britannica, the concept of modular arithmetic has been used by ancient civilizations such as the Indians and Chinese. 340/60 = 5.6, when we take the decimal part, it becomes the integer -6 Take note: When we input a/b in a calculator, we take the decimal part of the generated value, and round it up to the next integer.
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Here’s how to solve mod with a negative number:
The resulting remainder is also smaller compared to when both numbers are positive. Why does this happen? explains, with a positive number like 340, the multiple subtracted is less than the absolute value, which results in 40.īut with -340, we subtract a number with a greater absolute value, so the mod function generates a positive value. This is actually not the case.įor instance, if you have 340 mod 60, the remainder is 40.īut if you have -340 mod 60, the remainder is 20. One might presume the mod function generates the same values as positive numbers when one number is negative. Here’s how to calculate it manually:ħ – 4 = 3 Calculating Mod with a Negative Number For this example, 15 / 4 = remainder 3, which is also 15 = (4 * 3) + 3. Instead of its decimal form (0.75), when you use the mod function in a calculator, the remainder is a whole number. When you divide 15 by 4, there’s a remainder. Where a is the value that is divided by n.įor example, you’re calculating 15 mod 4. In mathematics, the modulo is the remainder or the number that’s left after a number is divided by another value. An example of this is theĢ4-hour digital clock, which resets itself to 0 at midnight. Number greater than 1, which is the mod, is reached.
Modular arithmetic, sometimes called clock arithmetic, is aĬalculation that involves a number that resets itself to zero each time a whole In this section, you’ll learn about modulo, its basic operation, and its uses in real life. People use modular arithmetic all the time, especially with anything involving remainders, time and calendar schedules. However, if you’ve ever estimated lunch for 10 people, and found that there’s a lot of food leftover, you’re actually dealing with a mod problem. Most people haven’t heard of modular arithmetic or mod outside of math class. Modulo: Definition, How it Works, and Real-Life Uses You may see modulo operations on numbers expressed as either of the following
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