Arithmetic Flashcards
What is an integer?
A whole number that can be positive, negative or zero.
Ex: 0 , 1 , -1 NOT 1.24, -1.24
What is a divisor?
A number by which another number is to be divided.
Ex: If x and y are integers and x is not equal to zero x is a divisor (factor) of y provided that y = xn for some integer n.
What is a dividend?
A number to be divided by another number (divisor).
Ex: If x / y then x is a dividend to which y is the divisor.
What is a multiple?
A multiple is the resulting number of two integers being multiplied.
Ex: If z is a multiple of xn for some integer n and some integer x then x and n are both factors of z and z is divisible by or or n.
What are quotients and remainders?
Quotient is the result obtained after a dividend interacts with a divisor. The remainder is what is left over.
Ex: y = xq + r ; r is greater than or equal to zero and less than x. Where x is the divisor.
Ex: 28 / 8 ; q = 3 and remainder is equal to 4
What are odd and even integers?
Any integer that is divisible by 2 is an even integer ( can be negative or positive ), zero is even!
Any integer that is not divisible by 2 is an odd integer ( can be negative or positive ).
What are the rules of odd and even integers?
- If at least one factor of a product of integers is even then the product is even.
- If all factors of a product of integers is odd then the product is odd.
- If two integers are both even or both odd, their sum and their difference are even. Otherwise, their sum and their difference are odd.
Ex: -8 is even and 29 is odd
What are prime numbers?
A prime number is a positive integer that has exactly two different positive divisors, 1 and itself. The number 1 is not a prime number! Every integer greater than 1 is either prime or can be uniquely expressed as a product of prime factors.
What are the prime numbers from 1 to 100?
There are25prime numbers between 1 and 100. They are2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89, and97.
2 is the only number that is even and prime.
What are the formulas for consecutive integers, consecutive even integers, and consecutive odd integers?
n + 1, n + 2, n + 3, …,
2n, 2n + 2, 2n +4, …,
2n + 1, 2n + 3, 2n + 5,…,
Name two formulas to express 1
n / n = 1
n * 1 / n = 1
Where n is not equal to zero
Define numerator and denominator.
n/d such that d can never be zero.
What constitutes two fractions being equivalent?
Two fractions are equivalent if they represent the same number.
Ex: 8/36 and 14/63 both represent the number 2/9.
What is the GCD?
A fraction can be reduced to its lowest terms by dividing by the greatest common divisor ( or factor ) of the numerator and denominator.
How do you add and subtract fractions?
If they have the same denominator then perform the desired function on the numerator.
If they do not have the same denominator then try and locate the least common multiple to convert them to similar fractions.
How do you multiply fractions?
To multiply two fractions, simply multiply the two numerators and the two denominators.
How do you divide fractions?
To divide by a fraction invert the divisor and multiply.
How do you convert a mixed number to a fraction?
A mixed number is a number that consists of a whole number and a fraction. To convert simply multiply the whole number by the denominator and add the result to the numerator.
Converting fractions to decimals.
321 / 1,000 = .321
321 / 10,000 = .0321
156 / 100 = 1.56
Recap scientific notation.
x 10 ^ 2 move the decimal to the right.
x 10 ^ -2 move the decimal to the left.
Adding and subtracting decimals.
Simply remember to match the decimal points up. Add zeros if necessary.
Multiplication of decimals.
Simply multiply the numbers as normal and move decimals over in the product equal to number of digits to the right of decimals in integers.
Dividing by decimals.
To divide a number (the dividend) by a decimal (the divisor), move the decimal point of the divisor to the right until the divisor is a whole number. Then move the decimal point of the dividend the same number of places to the right.
