Use LEFT and RIGHT arrow keys to navigate between flashcards;
Use UP and DOWN arrow keys to flip the card;
H to show hint;
A reads text to speech;
89 Cards in this Set
- Front
- Back
|
What are natural numbers? |
Natural numbers go from 1 on the number line and go on forever to the right. They are also whole numbers. Ex: 1,2,3,4...... |
|
|
What is a factor? |
To write an equivalent expression that is a product. A multiplier. It can be expressed as a product. EX: 3 and 5 are factors of 15. |
|
|
What are the factors of 15? |
1, 3, 5, & 15 |
|
|
What is a prime number? |
It is a natural number that has only two products or factors. That is 1 and itself. EX: 7 → 1,7 are the products of 7. |
|
|
What is a composite number? |
All non-prime natural numbers are composite numbers. Every composite number can be factored into a product of prime numbers. |
|
|
What is prime factorization? |
It is reducing a composite number into all of it's prime factors because all composite numbers can be factored into a product of prime numbers.
EX: 48 = 6 * 8 PF= 2,2,2,2,3 ↑ ↑ 2*3 2*2*2 |
|
|
What are the two types of natural numbers? |
Composite and Prime |
|
|
How do you know when you have completed the prime factorization? |
When the factors in the last factorization are all prime. |
|
|
Why is 1 not a part of the prime factorization? |
1 because it is not a prime number. |
|
|
What is the Greatest Common Factor (GCF) ? |
The common factor of a polynomial with the largest possible coefficient and the largest possible exponent(s)? |
|
|
What is one way of finding the Greatest Common Factor (GCF)? |
By making a list of factors of each number. For example if you are trying to find the GCF of 20 and 30 you would make a list of factors of both. |
|
|
What is arithmetic numbers? |
They are nonnegative rational numbers that consist of the whole numbers and the fractions. |
|
|
What is an equivalent expression? |
They have the same value for all allowable replacements. 8 = 8/1 |
|
|
What does the property of 0 and 1 help you find? |
They allow us to find equivalent expressions. |
|
|
What is the property of 0? |
This property is an additive identity. It states that for any number a, a + 0= a |
|
|
What does the LCD allow us to do? |
The Least common denominator allows us to add fractions using the smallest numbers possible. |
|
|
What is a reciprocal? |
Two numbers whose product is 1. This is also called multiplicative universes. All arithmetic numbers, except zero, have reciprocals. |
|
|
How do you divide fractions? |
You multiply by the reciprocal of the divisor. |
|
|
Decimal Notation |
It is a representation of a number containing a decimal point. |
|
|
What is the identity property of 1? |
It is a multiplicative identity that startes: for any number a, a * 1= a |
|
|
What is the Equivalent Expression for 1? |
For any number a, where does not equal 0, a/a = 1 |
|
|
What is the simplest fraction notation? |
It is the notion that has the smallest numerator and denominator. The process of finding this is called SIMPLIFYING. |
|
|
What is canceling? |
Canceling us a shortcut that you may have used to remove a factor of 1 when working with fraction notation. You may use canceling only when removing common factors in numerators and denominators. Each common factor allows us to remove a factor of 1 in a product. |
|
|
How do you multiply fractions? |
You multiply the numerators and multiply the denominators. |
|
|
How do you add fractions? |
You can only add a fraction when it has the same denominators. You also only add the numerators and keep the same denominator. |
|
|
Improper vs. Mixed |
In algebra you will find that improper fraction symbols are more useful than using a mixed fraction. |
|
|
How do you convert a mixed numeral to a fraction? |
1. You multiply the whole number by the denominator. 2. You add the results to the numerator. 3. Keep the original denominator from the mixed number. |
|
|
What is decimal notation? |
A representation of a number containing a decimal point. |
|
|
How do you add fractions? |
You add the numerators and keep the denominator the same only if they already have the same denominators. If not you have to find the LCD. |
|
|
What is the LCD? |
The Least common denominator allows us to add fractions or subtract fractions using the. Smallest numbers possible. You find the LCD by finding the LCM of the denominators. |
|
|
Place value chart |
|
|
|
Where does the decimal go in the place value chart? |
Between the ones place and the tenths place. |
|
|
How do you convert from fraction notation into decimal notation? |
1. You count the number of zeros in the denominator 2. And then you move the decimal point that number of places to the left. You leave out the denominator. |
|
|
How do you convert from a decimal notation into a fraction? |
|
|
|
How do you add with decimal notation? |
You add by lining up the decimal points. Then you being adding from the farthest place to the right and work your way to the left. |
|
|
How do you subtract with decimal notation? |
You line up the decimal points, then subtract from the furthest right while working your way to the farthest left. |
|
|
How do you multiply with decimal notation? |
1. You ignore addiction and subtraction rule of lining up the decimal points. You instead multiply the way you would multiply whole numbers. 2. You place the decimal point at the final step by adding the number of decimal places in the original factors. |
|
|
How do you divided when the divisor is a whole number? |
1. You place the decimal point in the quotient directly above the decimal point in the dividend.
2. You divide as whole numbers.
|
|
|
How do you divide when the divisor is not a whole number? |
1. You move the decimal point in the divisor as many places to the right as it takes to make it a whole number. You also move the decimal point in the dividend the same number of places to the right and place the decimal point in the quotient. 2. Divide as whole numbers. |
|
|
How do you convert from a fraction notation to a decimal notation when there is not 10, 100, 100..... in the denominator? |
You divide the numerator by the denominator. |
|
|
What is rounding? |
Approximating the value of a number. |
|
|
what does the symbol % mean? |
It means "per hundred". EX: 30% is defined to mean 30 x 0.01, 30 x 1/100, or 30/100 |
|
|
How do you go from percent notation to decimal notation? |
You move the decimal point two places to the left and drop the percent symbol. |
|
|
How do you go from decimal notation to percent notation? |
You move the decimal two places to the right and write the percent symbol. |
|
|
How do you convert from a fraction notation to a percent notation? |
By first converting the fraction into a decimal notation, and then moving the decimal two places to the right, as well as adding the percent symbol. |
|
|
What is a power? |
It is an abbreviation for a product in which the factors are the same. An expression for a power is called exponential notation. |
|
|
What is exponential notation? |
A representation of a number using a base raised to a power. 10^3 = 10 x 10x 10 10 is the base and 3 is the exponent. The base of 10 is used as a factor 3 times. |
|
|
What is the order of operations? |
P- Parenthesis ( ), Brackets [ ], Braces { } E - Exponents M - Multiplication D - Division Do all multiplications and divisions in order from left to right A - Addition S - Subtraction Do all addition and subtraction in order from left to right. This means whatever comes first from left to right will be done first. EX: 10 -6 +3 = 7 You would subtract 6 from 10 first and then add 3. You would work left to right unless there is grouping symbols 10 - (6+3) = 9 ORDER OF OPERATIONS (10-6) + 3 = 7 IS IMPORTANT |
|
|
What is a variable |
It is what you sometimes call a letter. |
|
|
When is a letter a variable? |
A letter is a variable when it can represent various (VARIABLE) numbers. EX: let x = your age. x is a variable since it changes (Varies) from year to year. |
|
|
What is a constant? |
Like a variable, it is what you sometimes call a letter. |
|
|
When is a letter a constant? |
A letter is a constant when it can stand for just one number. That means the nubmer stays the same. EX: Let y = your date of birth Since your original birth date never changes y is a constant. |
|
|
What is an algebraic expression? |
It is an expression that consists of variables, constants, numerals, operation signs, and/or grouping signs. |
|
|
What is substituting? |
It is when we replace a variable with a number, so we are then substituting for the variable with a number. ex: Evaluate X+Y , when x=3 and y= 4 we substitute x with 3 and y with 4 3+4 |
|
|
What is evaluating the expression? |
We evaluate the expression when we replace all variables in an given expression with numbers and carry out the operations in the expression. |
|
|
What is the value? |
The numerical result after a number has been substituted into an expression EX: Solve X+Y when X=3, Y=4 X + Y <- substitute (plug in) the numbers 3 + 4 now solve 3+4 = 7 <- 7 is the value of the expression |
|
|
What is the area of a rectangle? |
Area= Length x Width A= lw |
|
|
What are the key words, phrases and concepts for addition? |
add, added to, sum, total, plus, more than, increased by |
|
|
What are the key words, phrases and concepts for subtraction?
|
subtract, subtracted from, difference, minus, less than, decreased by, take away |
|
|
What are the key words, phrases and concepts for multiplication?
|
Multiply, multiplied by, product, times, of |
|
|
What are the key words, phrases and concepts for division?
|
divide, divided by, quotient |
|
|
What is the area of a Triangle? |
Area = (1/2)(base)(height) A= 1/2bh |
|
|
What is the area of a parallelogram? |
Area = Base x Height A=bh |
|
|
what is a set? |
A collection of objects, but most often we will be considering sets of numbers. So a set in math is a collection of numbers. One way we can use a set is by roster notation. |
|
|
What is a roster notation? |
A way of naming sets by listing all the elements in the set. EX: 0,3,7 would be written as {0,3,7} |
|
|
What are subsets? |
Sets that are part of other sets. |
|
|
What are the two important sets of real numbers? |
The Natural Numbers and the Whole Numbers. |
|
|
What is the subset of Natural Numbers? |
{1,2,3...} This subset is commonly used for counting. |
|
|
What is the subset of Whole Numbers? |
{0,1,2,3...} This is the set of natural numbers and 0. |
|
|
What are integers? |
The whole numbers and their opposites. It is a set that states for every natural number we have, we obtain a new number to the left of zero on the number line. For the number 3, there will be an opposite -3 For number 4, there will be an opposite -4 and so on. |
|
|
What is the set of integers? |
{...-3,-2,-1,0,1,2,3...} |
|
|
What do we call integers to the left of zero? |
Negative integers |
|
|
What are the natural numbers also called when regarding integers? |
positive integers |
|
|
regarding integers, what would zero be? |
zero is neither a positive nor a negative integer. |
|
|
What are opposites? |
They are numbers that are the same distance from zero on either side. EX : -3 and 3 are opposites of each other.
0 is its own opposite. |
|
|
What are rational numbers? |
This is a set that is made to create a larger number system. This includes quotients of integers with nonzero divisors. ex: 1/4, -1/4, 7/1, 3, -3, 0, 2.5, -0.5, 10 1/2 |
|
|
What a rule of rational numbers? |
The set of rational numbers = the set of numbers a/d, where a and b are integer's and b is NOT equal to 0. |
|
|
What does it mean to graph a number? |
To find and mark its point on the number line. |
|
|
What is a terminating decimal? |
A decimal that can be written using a finite number of decimal places. |
|
|
What is a repeating decimal notation and how do we abbreviate it? |
A decimal in which the pattern repeats indefinitely. You abbreviate this by writing a bar over the repeating part. |
|
|
What are irrational numbers? |
Points on the line for which there is no rational number or in other words a real number that cannot be named as a ratio of two integers. |
|
|
Decimal notation for rational numbers... |
either terminates or repeats. |
|
|
Decimal notation for irrational numbers.... |
neither terminates nor repeats. |
|
|
What makes up the real number system? |
The rational and irrational numbers together corresponds to all the points on the number line and this makes up the real number system. |
|
|
How are real numbers named? |
They are named left to right and it increases as we move to the right. Also for any two number on the line, the one on the left is less than the one on the right. ex: -2 < -1 , -1 < 0 , 0 < 1 , 6 < 7 |
|
|
What are inequalities? |
A mathematical sentence using less than (<), greater than (>), less than or equal to, greater than or equal to signs, and not equal to. |
|
|
what is a rule concerning the order of Inequalities ? |
a < b also means b > a |
|
|
Distance is always a...... |
nonnegative number |
|
|
What is absolute value? |
Absolute value is the distance that a number is from zero on the number line. We use the symbol lxl to represent the absolute value of x. EX: the absolute value of -4 would be l-4l = 4 because the distance from 0 to -4 is 4, and distance is always a nonnegative number. ALL negative numbers absolute values will be positive, and positive number remain the same. SO all absolute values are positive. |
