Arithmetic Flashcards
Irrational numbers
Square root of any number that is not a perfect square
Pic is irrational, decimals go forever and constantly changing
Rational number
A number that can be represented by the quotient of two integers
Examples
5 = 5/1
.325 = 325/1000
1/3
An even plus and even equals an
Even
An odd plus an odd equals an
Even
An odd plus an even equals an
Odd
An even minus and even equals an
Even
An odd minus an odd equals an
Even
An odd minus an even equals an
Odd
An even minus and odd equals an
Odd
An even times an even equals an
Even
An odd times an odd equals an
Odd
An odd times an even equals an
Even
Order of operations
Parentheses Exponents Multiplication Division Addition Subtraction
Prime numbers
Have only two divisors, themselves and one
2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109
Divisor
The number you divide by
Dividend / Divisor = Quotient
Greatest common divisor
The greatest common divisor (gcd) of two or more integers, when at least one of them is not zero, is the largest positive integer that divides the numbers without a remainder. For example, the GCD of 8 and 12 is 4.
Multiple
A multiple is the product of any quantity and an integer. In other words, for the quantities a and b, we say that b is a multiple of a if b = na for some integer n, which is called the multiplier or coefficient. If a is not zero, this is equivalent to saying that b/a is an integer with no remainder.
If b is a multiple of a then b/a equals an integer with no remainder
Greatest common factor
To find either the Least Common Multiple (LCM) or Greatest Common Factor (GCF) of two numbers, you always start out the same way: you find the prime factorizations of the two numbers. Then you put the factors into a nice neat grid of rows and columns, and compare and contrast and take what you need.
Least common multiple
It is the smallest number that is a factor of both numbers
The least common multiple has to be divisible by both numbers with a resulting integer
http://www.purplemath.com/modules/lcm_gcf.htm
A number is evenly divisible by 2 if
It’s units digit is divisible by 2
A number is divisible by 3 if
The sum of its digits is divisible by 3
A number is evenly divisible by 4 if
The number made by the tens and units digit is divisible by 4
A number is evenly divisible by 5 if
It’s units digit is a 0 or a 5
A number is evenly divisible by 6 if
It’s divisible by both 2 and 3
A number is evenly divisible by 9 if
The sum of its digits is divisible by 9
A number is evenly divisible by 10 if
It’s unit digit is a 0
Consecutive integers
Integers that follow consecutively
Comparing two positive fractions by
Cross multiplying the denominators into the opposite numerator and comparing. The aide with the larger number is greater
If the numerators are the same, the smaller denominator is a larger number
Decimal Places
Each place in a decimal is worth ten times more than the place to its immediate right
Adding and subtracting decimals
Align the decimals and add
Multiplying decimals
Multiply as normal and then place decimal the number of digits equivalent to what is to the right of the decimal
Dividing decimals
Make divisor a whole number by moving the decimal to the right, then move the decimal of the dividend the same amount
Part =
Percent + Whole
Percent =
Part / Whole
Whole
Part / Percent
% increase =
New amount - old amount / old amount x 100
% decrease =
Original - new amount / original amount x 100
Original price =
New price / 100% - % markdown
Original price =
New price / 100% + % markup
Inverse proportions
Flip one of the ratios and solve for the missing variable
Averaging consecutive integers
The average of a group of consecutive or spaced integers is always at the exact middle number
If the number of integers in the group is odd the average is the middle integer
If the number of integers in the group is even the middle number is the average of the inner most integers
