EC-6 (391): Mathematics (Number Concepts and Operations)

Associative Property

An operation is associative if regrouping the terms does not change the outcome ((a+b) + c = a + (b+c))

Commutative Property

An operation is commutative if changing the order of terms does not change the outcome (a + b = b + a)

Fraction Decomposition

Breaking down a fraction into smaller fractions that total to the original

Reciprocal fraction

The inverse or "flip" of a fraction where the top and bottom number switch places (1/2 -> 2/1 3/5 -> 5/3)

Natural Numbers

The set of counting numbers starting at 1 and increasing by 1s up to infinity. Sometimes called "counting numbers" (1, 2, 3, ...)

Adding fractions to come up with a larger one

The size of a number (7 has a greater magnitude than 2)

Factors

Values that are multiplied to get another number. (Some factors of 12 are 3 and 4 because 3×4=12)

Fundamental Counting Principle

a mathematical rule to calculate the finite number of outcomes in a probability problem. The number of outcomes for each event is multiplied to find the total number of outcomes for the overall problem. (Number of outfits = number of hats \times× number of shirts \times× number of pants)

Rounding

a number is simplified to its closest multiple of 10, 100, 1,000, etc. (26 rounds to 30)

Multiplicative Identity Property

a number that, when multiplied by x, yields x. (6×1=6)

Prime Factor

a prime number or term that can be multiplied by another to get a number.

Number Line

a straight line where each number is equal distance from the next one

Benchmark Fraction

an easily remembered fraction that can be used to make problems simpler (1/10, 1/4, 1/2, etc.)

Expanded Form / Expanded Notation

break apart each digit in the number and show the digits true value

Expanded Form / Expanded Notation

break apart each digit in the number and show the digits true value (4,358 → 4000 + 300 + 50 + 8)

Reducing Fractions

dividing the numerator and denominator by any common factors to put the fraction in lowest terms

Rectangular Arrays

dots or objects that show the end product of 2 numbers; the objects are arranged so there are an equal number of items in each row and column (These rectangular array show 4 × 3)

Decimal Fractions

fractions with a denominator of 10

Prime Numbers

natural numbers greater than 1 that have no numbers that will divide into them without a remainder (2, 3, 5, 7....)

Real Numbers

numbers that have a specific value (-2, 3, 1/2, 3.2, √2)

Irrational Numbers

real numbers that CANNOT be represented exactly. They can not be shown as a ratio of two integers nor placed on a number line. (pi (π))

Counting On

starting on one number and counting until reaching the second number; a typical technique is saying the counting numbers out loud while using fingers to keep track of how many numbers have been used (30 plus 5: 30, 31, 32, 33, 34, 35 (at 30, zero fingers would be held out and at 35, 5 fingers))

Denominator

the bottom term of a fraction

Greatest Common Factor (GCF) / Greatest Common Divisor (GCD)

the greatest factor that is common to two or more numbers; the largest number that will divide evenly into two or more numbers (For 12 and 15, GCF = 3 Factors of 12: 1, 2, 3, 4, 6, 12 Factors of 15: 1, 3, 5, 15)

Prime Factorization

the process of writing a number in terms of its prime factors (12=2×2×3)

Least Common Multiple (LCM)

the smallest number that is a multiple of two or more numbers; the smallest number two or more numbers will divide into evenly (For 12 and 15, LCM = 60 Multiples of 12: 12, 24, 36, 48, 60 Multiples of 15: 15, 30, 45, 60)

Numerator

the top term of a fraction

Relatively Prime

two numbers are relatively prime if they share no common factors (34 and 15)

Fractions

usually represent partial numbers

Common Denominator

when 2 fractions share the same total parts of whatever item or items are being represented (1/3 and 2/3)

Ratio

A comparison that shows the relative size of two or more values. (The ratio of boys to girls is: 4 to 5; 4:5; 4/5; 0.8.)

Unit Fraction

A fraction composed of 1 over any rational number. The inverse of a whole number.

Improper Fraction

A fraction where the numerator is larger than the denominator

Factor Tree

A visual process to find the factors of a number

Percentages

A way to represent part-to-whole relationships, where the percent is the part out of 100.

Mixed Number

A whole number with a fraction

Fraction Composition

Adding fractions to come up with a larger one

Distributive Property

An number in front of a group of terms will multiply all terms in the grouping individually (a(b+c) = ab + ac)

Scientific Notation

Numbers expressed as the product of a base-10 number and a number between 1 and 10 (2.56 x 10 = 25.6 4.32 x 10-4 = 0.000432)

Decimal

Numbers less than 1 displayed using place values and the powers of ten (0.024)

Base 10 Number system

Our number system. Each place location for a number has a value that is a power of (10 10, 100, 1000, 10000)

Order of Operations

PEMDAS: the set order in which multi-step equations must be solved: Parenthesis, Exponents, Multiplication and Division (L to R), Addition and Subtraction (L to R)

Absolute Value

The distance a number is from zero; always a positive number

Whole Numbers

The infinite set of natural numbers and zero (0,1,2,3, ...)

Integers

The infinite set of positive and negative counting numbers and zero (... , -2,-1,0,1,2, ...)

Place Value

The value of each digit in a number based on its location, or place (In 135, the 3 is in the tens place and has a value of 3 x 10 or 30.)

Area Models

Using the expanded form of a number, each number is multiplied together and the products are added to find the final answer (This area model shows 42 × 37)

Composite numbers

natural numbers that have numbers that divide into them (4,6,8,9 ...)