Answer to Question #106935 in Math for Nikita Koladiya

Question

Explain sexagesimal system used for operations on time. Give one example each of the problems involving subtraction and addition of time showing the error children make because of the sexagesimal system. How would you help children correct their error.

Answer 1

Sexagesimal (also known as base 60 or sexagenary) is a numeral system with sixty as its base.

It is used for measuring time, angles, and geographic coordinates.

One hour of time is divided into 60 minutes, and one minute is divided into 60 seconds. 

The number 60, a superior highly composite number, has twelve factors, namely 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60, of which 2, 3, and 5 are prime numbers. With so many factors, many fractions involving sexagesimal numbers are simplified. For example, one hour can be divided evenly into sections of 30 minutes, 20 minutes, 15 minutes, 12 minutes, 10 minutes, 6 minutes, 5 minutes, 4 minutes, 3 minutes, 2 minutes, and 1 minute. 60 is the smallest number that is divisible by every number from 1 to 6; that is, it is the lowest common multiple of 1, 2, 3, 4, 5, and 6.[https://en.m.wikipedia.org/wiki/Sexagesimal] 

For example, if we need to add 20 minutes to 1 hour 50 minutes, we will have 2 hours 10 minutes (NOT 1 hour 70 minutes, because we know that there's just 60 minutes in 1 hour). To simplify, we can draw 2 circles and split them into 6 equal parts for 10 minutes and use them for explanation. The same thing with subtraction, for example, given 3 hours 10 minutes and we need to substract 1 hour 30 minutes. We come back to our circles (we have 4 circles divided by 6 parts each) There are 3 whole circles and 1 part of 4th painted. Return to 1 hour 30 minutes we can say that it is 1 whole circle 3 parts. So, we need just substract 1 whole circle 3 parts(1hour 30 minutes) from our painted parts in circles (3 hours 10 minutes).