Math Basics

Integers:

-3, -2, -1, 0, 1, 2, 3 . . .Integers are natural and whole numbers. Integers just means numbers can be positive or negative. (Natural & Whole can't be)

Whole Numbers:

0, 1, 2, 3, 4, 5 . . .Whole Numbers are natural numbers, except now you include zero 0.

Natural Numbers:

1, 2, 3, 4, 5 . . . .Natural numbers are the numbers you learned when you learned to count.

Value:

1. Money: how much something is worth. Example: the value of this coin is one dollar. 2. Mathematics: the result of a calculation. Example: 3 × 4 gives the value of 12.

Rational Numbers:

2/3, 5/6, -1/4, 2.3333333(infinite, but repeating pattern) Rational numbers include all numbers above (natural, whole, integers) but now also include fractions/decimals.

expression; variables

3x-2y is called a ______ and the letters x and y are______.

Terminating Decimal:

A decimal number that has digits that do not go on forever. Examples: 0.25 (it has two decimal digits). 3.0375 (it has four decimal digits) In contrast a Recurring Decimal has digits that go on forever. Example: 1/3 = 0.333... (the 3 repeats forever) is a Recurring Decimal, not a Terminating Decimal

Prime Factor:

A factor that is a prime number: one of the prime numbers that, when multiplied, give the original number. Example: The prime factors of 15 are 3 and 5 (3×5=15, and 3 and 5 are prime numbers).

Line Graph:

A graph that uses points connected by lines to show how something changes in value (as time goes by, or as something else happens).

Operation:

A mathematical process. The most common are add, subtract, multiply and divide (+, −, ×, ÷). But there are many more, such as squaring, square root, etc. If it isn't a number it is probably an operation. Example: In 25 + 6 = 31, the operation is add

Rational Number:

A number that can be made by dividing two integers. (Note: integers have no fractions.)

Coefficient:

A number used to multiply a variable. Example: 6z means 6 times z, and "z" is a variable, so 6 is a coefficient. Sometimes a letter stands in for the number. Example: In ax2 + bx + c, "x" is a variable, and "a" and "b" are coefficients.

Integer:

A number with no fractional part (decimal or fraction). Integers Include: • the counting numbers {1, 2, 3, ...}, • zero {0}, • and the negative of the counting numbers {-1, -2, -3, ...}

Problem:

A question that needs a solution. In mathematics some problems use words: "John was traveling at 20 km per hour for half an hour. How far did he travel?" And some use equations: "Solve x+5=22"

Equation

A statement of the form "expression=expression" is called a ______.

Variable:

A symbol for a number we don't know yet. It is usually a letter like x or y. Example: in x + 2 = 6, x is the variable.

Solution

A value for the variable that makes the equation a true statement is called a ________.

Solution:

A value we can put in place of a variable (such as x) that makes the equation true. Example: x + 2 = 7 When we put 5 in place of x we get: 5 + 2 = 7 Which is true, so x = 5 is a solution

Composite Number:

A whole number that can be divided evenly by numbers other than 1 or itself. Example: 9 can be divided evenly by 3 (as well as 1 and 9), so 9 is a composite number. But 7 cannot be divided evenly (except by 1 and 7), so is NOT a composite number (it is a prime number).

Equation:

An equation says that two things are equal. It will have an equals sign "=" like this: 7 + 2 = 10 - 1 That equation says: what is on the left (7 + 2) is equal to what is on the right (10 − 1). So an equation is like a statement "this equals that."

Linear Equation:

An equation that makes a straight line when it is graphed.

Polynomial:

An expression that can have constants, variables and exponents, that can be combined using addition, subtraction, multiplication and division, but:• no division by a variable. • a variable's exponents can only be 0,1,2,3,... etc. • it can't have an infinite number of terms.

Addend:

Any and all numbers you are adding together. 3 + 5 = 8 Three & five are the addends.

Odd Number:

Any integer (not a fraction) that cannot be divided exactly by 2. Example: −3, 1, 7 and 35 are all odd numbers.

Counting Number:

Any number you can use for counting things: 1, 2, 3, 4, 5, ... (and so on). Does not include zero, negative numbers, fractions (such as 1/2 or 3/7), or decimals (such as 0.95 or 1.3)

Even Numbers:

Even Numbers are two things: 1. Numbers that are composite numbers (have more than only 1 and itself that divide it evenly). 2. The number 2 divides it evenly Ex: 20 is an even number because: A. 1, 2, 4, 5, 10, 20 all go into 20 evenly. This makes 20 a composite number (because more than just 1 & 20 can go into 20 evenly.) B. 2 can divide 20 evenly: 20 divided by 2 equals 10. Two whole numbers (2 & 10) multiplied by each other equal 20.

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Greater than

Equivalent:

Having the same value. Examples: 1 Dollar is equivalent to 100 pennies. 120 seconds is equivalent to 2 minutes

Absolute Value:

How far a number is from zero. Example "6" is 6 away places from zero, but "−6" is also 6 away from zero. So the absolute value of 6 is 6, and the absolute value of −6 is also 6.

Multiple:

Is a relationship status of a number with another number, like "mom" is to "child." 15 is a multiple of 1, 3, 5, &15. Think of a multiple as being in the "mom" role. 1, 3, 5, &15 are all numbers that go into 15 evenly.

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Less than

Composite Number:

Number that have other numbers that divide them evenly. 15 is a composite number because more than just 1 & 15 can evenly divide it. 3 & 5 can also divide 15 evenly; ergo: 15 is a composite number. [This is similar to being a Multiple (say 15), but with a Multiple, we are also talking about its factors—#s that divide the Multiple evenly (1, 3, 5, &15)—and the relationship between the two. With composite #s, we're just looking at the 15.]

Coprime:

Numbers that have no common factors other than 1. Also called "relatively prime" or "mutually prime." 21 and 22 are coprime: • The factors of 21 are 1, 3, 7 and 21 • The factors of 22 are 1, 2, 11 and 22 (the only common factor is 1) But 21 and 24 are NOT coprime: • The factors of 21 are 1, 3, 7 and 21 • The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24 (the common factors are 1 AND 3)

Factors:

Numbers you can multiply to get another number. In other words: Numbers that go into other numbers evenly. Ex: 1, 3, 5, & 15 are all factors of 15 because they can be divided into 15 evenly In the same manner, 15 is a "multiple" number for 1, 3, 5, &15. Another Ex: 1, 2, 3, 4, 6, 12 are all factors of their multiple: 12 NOTE: -1, -2, -3, -4, -6, -12 are all the negative factors of 12.

Expression:

Numbers, symbols and operators (such as + and ×) grouped together that show the value of something. Example: 2×3 is an expression.

Real Numbers:

Positive or negative, large or small, whole numbers or decimal numbers are all Real Numbers.

Ordering:

Putting things into their correct place following some rule. E.g. Putting numbers in a list from highest to lowest.

evaluating the expression

Replacing a variable in an expression by a number and then finding the value of the expression is called______.

grouping; associative

Since (3+1)+20=3+(1+20), we say that changing the ___ in addition does not change the sum. This property is called the ___ property of addition.

order; commutative

Since 7+10=10+7, we say that changing the ___ in addition does not change the sum. This property is called the ____ property of addition.

Like Terms:

Terms whose variables (and their exponents such as the 2 in x2) are the same. Example: 7x and 2x are like terms because the variables are both "x." But 7x and 7x2 are NOT like terms (they are Unlike Terms)

Product:

The answer when two or more numbers are multiplied together.

Minuend:

The first number in a subtraction. The number from which another number (the Subtrahend) is to be subtracted. "minuend − subtrahend = difference" Example: in 8 − 3 = 5, 8 is the minuend.

Coordinate:

The graph of a number is the point that corresponds to the number and the number is called the coordinate of the point.

Divisor:

The number you divide by. "dividend ÷ divisor = quotient" Example: in 12 ÷ 3 = 4, 3 is the divisor3

Dividend:

The number you want to divide up into smaller chunks. "dividend ÷ divisor = quotient" Example: in 12 ÷ 3 = 4, 12 is the dividend

Whole Number:

The numbers {0, 1, 2, 3, ...} etc. There is no fractional or decimal part. And no negatives.

0

The quotient of 0 and any number (except 0) is ____.

1

The quotient of ant number (except 0) and the same number is ____.

Undefined

The quotient of any number and zero is_____.

Least Common Multiple:

The smallest positive number that is a multiple of two or more numbers. Example: the Least Common Multiple of 3 and 5 is 15, because 15 is a multiple of 3 and also a multiple of 5. Other common multiples include 30 and 45, etc, but they are not the smallest (least). (Also called Lowest Common Multiple)

Zero:

The whole number between −1 and 1, with the symbol 0. Shows that there is no amount. Example: 6 − 6 = 0 (the difference between six and six is zero). Zero is not positive and is also not negative. Zero is also useful as a "place-holder" so that you can write a numeral properly. Example: 502 (five hundred and two) could be mistaken for 52 (fifty two) without the zero in the tens place.

Natural Number:

The whole numbers from 1 upwards: 1, 2, 3, and so on ... Or from 0 upwards in some fields of mathematics: 0, 1, 2, 3 and so on .No negative numbers and no fractions.

Prime Numbers:

These are numbers that can only be divided evenly by 1 and itself. Ex: 13 is prime because only 1 and 13 can divide 13 evenly. (Using any other number would give you partial—not whole—numbers. Ex: 13 divided by 2 gives you an answer with some partial numbers: 6.5 . . . That ".5" is not a whole number—it's part of a whole number. In fact .5 is half of a whole number: 1.) * 1 is NOT considered a prime number. Again: 1 IS NOT A PRIME NUMBER. It's a "unit." * 2 is the only even prime number * 2 is prime because only 1 and itself (2) go into 2 evenly

Classify:

To arrange in groups, by some property. Shapes can be classified by the number of sides they all have.

Evaluate:

To calculate the value of. Example: Evaluate the cost of each pie when 3 pies cost $6. Answer: $2 each

Calculate:

To work out an answer, usually by adding, multiplying etc.

Relatively Prime:

Two numbers are "relatively prime" when they have no common factors other than 1. In other words you cannot evenly divide both by some common value.

Distributive

We know 9(10+8) = 9x10 + 9x8 by the ____ property.

Interval:

What is between two points or values. Examples: • A line with definite end points (called a "Line Segment"). • A definite length of time marked by a start and finish. • The numbers between two specific values.

Greatest Common Factor (GCF):

When we find all the factors (number that go into other numbers evenly) of two or more numbers, and some factors are the same ("common"), then the largest of those common factors is the Greatest Common Factor. Also called "Highest Common Factor." Example: the GCF of 12 and 16 is 4, because 1, 2 and 4 are common factors of both 12 and 16, and 4 is the greatest (largest).

Operator:

a symbol (such as +, −, ×, etc) that shows an operation (i.e. you want to do something with the values).

Mixed fraction:

a whole number and a fraction combined into one "mixed" number. Example: 1½ (one and a half) is a mixed fraction. (Also called a Mixed Number)

Number line:

also called an axis

Regroup:

borrow (when subtracting)

Prime Number:

can be divided evenly only by 1, or itself. And it must be a whole number greater than 1. Example: 5 can only be divided evenly by 1 or 5, so it is a prime number. But 6 can be divided evenly by 1, 2, 3 and 6 so it is NOT a prime number (it is a composite number).

Real Numbers

everything, all of it, any kind of number.

Prime factors:

numbers that are all the prime numbers that, when multiplied together, equal the original number.

Common Factors:

numbers you multiply together to get another number.

Distance:

same as what you get when you subtract numbers from each other: What's the distance between 5 and 25? 20. What's the difference between 5 and -15? Also 20.

Mean:

the average of the numbers: a calculated "central" value of a set of numbers. To calculate: Just add up all the numbers, then divide by how many numbers there are.

[ ] brackets:

used as/called outer pair of parentheses. It just means you do what's inside this bracket after you do what's in the inner parenthesis.

{ } braces:

used as/called outer pair of parentheses. It just means you do what's inside this bracket after you do what's in the inner parenthesis.

Quotient:

what number you get when you divide one number by another number: dividend ÷ divisor = quotient

Sum:

what you get when you add numbers together. 3 + 5 = 8 Three & five are the addends, & 8 is the sum.

Product:

what you get when you multiply numbers together

Difference:

what you get when you subtract numbers from each other. Example: 8 - 3 = 5 The difference between 8 and 3 is 5.

Irrational Numbers:

∏ (pi), and √2 (the square root of 2) Irrational numbers are not part of any group of numbers. They are not natural, whole, integers, or rational. There are two types of Irrational numbers: 1. There is an infinite number of digits with no repeating pattern. e.g. 3.48640567098031890. . . . 2. There is an infinite number of digits and a pattern of sorts, but the pattern is nonrepeating. e.g. 4.4118411241170 . . .