Math Is Fun Forum

1. Partnership : When two or more than two persons run a business jointly, they are called partners and the deal is known  as partnership

2. Ratio of Division of Gains:

(i)When investments of all the partners are for the same time, the gain or loss is distributed among the partners in the ratio of their investments.
Suppose A and B invest Rs. x and Rs. y respectively for a year in a business, then at end of the year
(A's share of profit) : (B's share of profit) = x:y
(ii) When investments are for different time periods, then equivalent capitals are calculated for a unit of time by taking (capital x number of units of time).Now, gain or loss is divided in the ratio of these capitals.
Suppose A invests Rs. x for p months and B invests Rs. y for q months, then 
(A's share of profit) : (B's share of profit) = px : qy

3. Working and Sleeping Partners:

A partner who manages the business is known as a working partner and the one who simply invests the money is a sleeping partner.

I hope these concepts will be helpful for you to solve some of your math problems.

What is a prime number

A number is greater than 1 is called a prime number, if it has only two factors, namely 1 and the number itself.

Prime numbers up to 100 are:2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

Procedure to find out the prime number

Suppose A is given number.

Step 1: Find a whole number nearly greater than the square root of A. K > square root(A)
Step 2: Test whether A is divisible by any prime number less than  K. If yes A is not a prime number. If not, A is prime  number.

Example:

Find out whether 337 is a prime number or not?

Step 1: 19 > square root (337)
Prime numbers less than 19 are 2, 3, 5, 7, 11, 13, 17
Step 2: 337 is not divisible by any of them

Therefore 337 is a prime number

These are simple and easy tricks which are helpful to solve your math homework problems  .

With this simple short cuts you can find out a number is divisible by a given number
Divisible by 2: A number is divisible by 2, if its unit’s digit is any of 0, 2, 4, 6, 8.
Example: 6798512

Divisible by 3: A number is divisible by 3, if sum of its digits divisible by 3.
Example : 123456
1+2+3+4+5+6 = 21
21 is divisible by 3 so 123456 is also divisible by 3

Divisible by 4: if the last two digits of a given are divisible 4, so the number can be divisible by 4.
Example : 749232
Last two digits are 32 which are divisible by 4 so the given number is also divisible by 4

Divisible by 5: If unit’s digit of a number is either ‘0’ or ‘5’ it is divisible 5.
Example : 749230

Divisible by 6: If a given number is divisible by 2 and 3 (which are factors of 6), then the number is divisible by 6.
Example : 35256
Unit’s digit is 6 so divisible by 2
3+5+2+5+6 = 21 so divisible by 3
So 35256 divisible by 6

Divisible by 8: if last 3 digits of a given number is divisible 8, then the given number is divisible 8.
Example: 953360
360 is divisible by 8, so 953360 is divisible by 8

Divisible by 9: A number is divisible by 9, if sum of its digits divisible by 9.
Example : 50832
5+0+8+3+2 = 18 divisible by 9 so 50832 divisible by 9

Divisible by 10: A number is divisible 10, if it ends with 0.
Example : 508320

Divisible by 11: A number is divisible by 11,if the difference of sum of its digits at odd places and sum of its digits at even places , is either 0 or a number divisible by 11.
Example : 4832718
(sum of digits at odd places ) – (sum of digits at even places)
=(8+7+3+4)-(1+2+8) = 11 which is divisible by 11.
So 4832718 is divisible by 11.

I hope this simple tricks, will be very helpful to solve math’s homework problems easily.

To calculate the day of the week for a given date, first of all we need to find out the number of odd days.

Today I thought of sharing a beautiful problem I learned in my school, though it is easy, it is tricky too.
Odd Days are number of days more than the complete number of weeks in given period.
Leap Year is  the year which is divisible by 4.
A normal year has 365 days
A leap year has 366 days
One  normal year = 365 days = 52weeks + 1day
One  normal year has one odd day

One  leap year = 366 days = 52weeks + 2days
One  leap year has two odd days

100 years = 76 ordinary years + 24 leap years = 5200 weeks + 124 days = 5217 weeks + 5 days
100 years have 5 odd days

400 years have (20+1) 0 odd days

The number of odd days and the corresponding day of the week is given below

0-Sunday
1-Monday
2-Tuesday
3-Wednesday
4-Thursday
5-Friday
6-Saturday

So by finding out the number of odd days you can find out the day of the week. I hope this procedure Will be helpful in solving math problems in exams.

Thanks.