38 terms

Abundant Number

A number for which the sum of all its proper factors is greater than the number itself. For example 24 is an abundant number because it's proper factors 1+2+3+4+6+8+12=36.

Common Factor

A factor that 2 or more numbers share. For example, 7 is a common factor of 14 and 35 because 7 is a factor of 14 and 7 is a factor of 35.

Common Multiple

A multiple that 2 or more numbers share. For example, the first few multiples of 5 are 5,10,15,20,25,30,35,40. The first few multiples of 7 are 7,14,21,28,35. From these lists we can see that the common multiple of 5 & 7 is 35.

Composite Number

A whole number with factors other than itself and one (that is, a whole number that is not prime). Some composite numbers are 6, 15, 20.

Conjecture

A claim about a pattern or relationship based on observations. Models, drawings, and other kinds of evidence can be used to support a conjecture.

Consecutive Numbers

Whole numbers in a sequence that follow each other, such as 31, 32, 33.

Counterexample

An example that disproves a claim. If someone claims that a pattern is true for all cases, you only need to find 1 counterexample to disprove that claim.

Deficient Number

A number for which the sum of all its proper factors is less than the number itself. For example, 14 is a deficient number because its proper factors, 1+2+7=10. All prime numbers are added together is less than 14, so 14 is a deficient number

Determine

To use the given information and any related facts to find the value or make a decision. Related terms: decide, find, calculate, and conclude.

Distributive Property

A mathematical property used to rewrite expressions involving addition and multiplication. The Distributive Property states that for any three numbers: a,b,and c, a(b+c)=ab+ac. If an expression is written as a factor multiplied by a sum, you can use the Distributive Property to multiply the factor by each term in the sum.

Divisor

A number that divides a given number leaving a 0 remainder. Fore example, 5 is a divisor of 20 since 20/5=4, has a remainder of 0. A divisor of a given number is also known as a factor of that number.

Equivalent Expressions

Expressions that have the same value. Expressions that represent the same quantity. For example, 2+5 and 3+4 and 7 are equivalent expressions.

Even Number

A whole number ending with 0, 2, 4, 6, or 8 in the ones place. A multiple of 2. When you divide a even number by 2, the remainder is 0.

Expanded Form

A way to write numbers by showing the value of each digit. The form of an expression made up of sums or differences of terms rather than the products of factors.

Explain

To give facts and details that make an idea easier to understand. For example, a written summary supported by a diagram, chart, table or a combination of these.

Exponent

A mathematical notation indicating the number of times a quantity is multiplied by itself. The small raised number that tells you how many times a factor is used.

Exponential Form

A form of writing numbers that uses exponents.

A quantity expressed as a number raised to a power.

A compact way or writing an expression involving repeated multiplication of the same number.

Ex. 2^3 = 2x2x2= 8

A quantity expressed as a number raised to a power.

A compact way or writing an expression involving repeated multiplication of the same number.

Ex. 2^3 = 2x2x2= 8

Factor

One of two or more whole numbers that multiplied to get a product. For example 13 & 4 are both factors of 52 because 13 x 4 = 52.

Factor Pair

Two whole numbers other than zero that are multiplied together to get a product.

A couple of numbers that are multiplied together to form a product; 1x10 & 2x5 are factor pairs of 10.

A couple of numbers that are multiplied together to form a product; 1x10 & 2x5 are factor pairs of 10.

Factored Form

An expression written as the product of its factors. The factored form of an expression made up of products rather than sums of terms. The factored form of 20 is 2x10.

Factorization

To make a factorization of a given number means to write it as a product of two or more whole numbers. The factorization of 60 = 2x2x15 or 3x20.

Fundamental Theorem of Arithmetic

Every composite natural number can be written as a product of primes in exactly one way. For example, 60 = 2x2x3x5

Greatest Common Factor (GCF)

The largest factor that two or more numbers have in common. GCF of 12 & 30 is 6.

Justify

To support your answer with reasons or examples.

Least Common Multiple (LCM)

The smallest multiple (other than zero) that two or more numbers have in common. LCM of 6 & 8 is 24.

Multiple

The product of a given whole number and another whole number. For example, some multiples of 3 are 3, 6, 9, and 12.

Near-Perfect Number

A number for which the sum of all its proper factors is one less than the number itself. All powers of 2 are near-perfect numbers. For example, 32 is a near perfect number because its proper factors 1+2+4+8+16=31.

Numerical Expression

A mathematical expression that has a combination of numbers and at least one operation. For example, 12=10+2.

Odd Number

A whole number that is not evenly divisible by 2.

A whole number ending with 1, 3, 5, 7, or 9 in the ones place.

A whole number ending with 1, 3, 5, 7, or 9 in the ones place.

Order of Operations

A set of rules that tells the order in which to compute.

When there is more than one operation and parentheses are used, first do what is inside the parentheses, then the exponents. Next, multiply or divide from left to right. Then add of subtract from left to right (PEMDAS of Please Excuse My Dear Aunt Sally).

When there is more than one operation and parentheses are used, first do what is inside the parentheses, then the exponents. Next, multiply or divide from left to right. Then add of subtract from left to right (PEMDAS of Please Excuse My Dear Aunt Sally).

Perfect Number

A number with proper factors that add up to exactly the number. For example, 6 is a perfect number 1+2+3=6.

Prime Factorization

Expressing a whole number as a product of prime numbers.

A way of expressing a composite number as a product of its prime factors.

A whole number expressed as a product of factors that are all prime numbers.

It is finding the factors of a number that are prime. EX. Factor Tree.

Prime factorization of a number is unique except for the order of the factors. For example prime factorizations of 42 is 2x3x7 or 7x2x3. Order can change the numbers do not.

A way of expressing a composite number as a product of its prime factors.

A whole number expressed as a product of factors that are all prime numbers.

It is finding the factors of a number that are prime. EX. Factor Tree.

Prime factorization of a number is unique except for the order of the factors. For example prime factorizations of 42 is 2x3x7 or 7x2x3. Order can change the numbers do not.

Prime Number

A whole number that has exactly two factors, 1 and itself. Fore example, 3, 7, 13 ......

Proper Factor

Any of the factors of a number, except the number itself. Proper Factors of 16 are 1, 2, 4, and 8.

Relatively Prime Numbers

Two numbers that have 1 as the only common divisor/factor.

2 numbers that are relatively prime when the GCF of a set of numbers is 1. For example, 20 & 33 are relatively prime because they only have 1 as a common factor

2 numbers that are relatively prime when the GCF of a set of numbers is 1. For example, 20 & 33 are relatively prime because they only have 1 as a common factor

Represent

To stand for or take the place of something else. Symbols, equations, charts, and tables are often used to represent particular situations.

Square Numbers

When you Multiply a whole number by itself, you get a square number.

The product of a number multiplied by itself.

Result of multiplying a number by itself. ex: 2x2=4; square number is 4

The product of a number multiplied by itself.

Result of multiplying a number by itself. ex: 2x2=4; square number is 4

Venn Diagram

A diagram that uses circles to display elements of different sets. Overlapping circles show common elements.

A method of comparing and contrasting two (or more) things. Each circle represents one thing, and the characteristics of that thing go inside the circle. The overlapped parts of the circles represents overlapped characteristics.

A method of comparing and contrasting two (or more) things. Each circle represents one thing, and the characteristics of that thing go inside the circle. The overlapped parts of the circles represents overlapped characteristics.