Conversions Flashcards
Value of remainder
Infinite number of remainders is possible. Need the value of numerator or denominator of fraction x/y in order to determine the actual remainder
Calculating value of remainder
Can only calculate that the remainder will be a multiple of a certain number. When division produces a number with remainder (i.e. 9.48) you can only reduce the remainder to the lowest fraction (12/25), so know remainder is a multiple of 12
Convert remainder into integer
If you know the decimal remainder and the denominator, you can multiply the denominator of the improper fraction by the decimal remainder to get the remainder as an integer
9/5 = 1.8, what is the integer value of the remainder
0.8 x 5 = 4, remainder is 4
Finding remainder of the product of set of numbers
Multiply the remainders but first get rid of the excess (i.e. 2/5 x 3/5 x 2/5 = 12/5, so remainder would be 2/5)
Remainder of 12 x 13 x 17 divided by 5
- Find remainders: 2 2/5, 2 3/5, 3 2/5
- Multiply remainders: 2/5 x 3/5 x 2/5 = 12/5
- Remove excess, get a remainder of 2
How to quickly see if the product of a numerator is divisible by the denominator
If a number in the numerator is divisible by the denominator, then the product of all numbers in the numerator must be divisible by the denominator
Remainder of 500 x 600 x 700 if divided by 8
0, 600 is divisible by 8 so the product of 600 and other numbers must also be divisible by 8
Adding & subtracting remainders
Can add/subtract as long as any excess remainders have been accounted for
remainder of 12 + 13 + 17 divided by 5
2 2/5 + 2 3/5 + 3 2/5 = 7/5 remainder, clear excess so left with remainder of 2
Remainder
Must be a non-negative integer that is less than the divisor
If divisor is N, then possible remainders are any integers ranging from 0 to N-1 inclusive
Possible remainders of 5
0,1,2,3,4
