Chapter 1, 2, & 3: Whole Numbers, Fractions, & Decimals
Whole Numbers
The set { 0, 1, 2, 3, ...}
Counting Numbers
The set { 1, 2, 3, ...}
Least Common Denominator (LCD)
The smallest denominator possible for two or more fractions which we want to write in equivalent forms, all with the same denominator.
Average
The sum of the quantities divided by the number of quantities.
Multiplication
This is a short method of adding a number to itself a given number of times.
Subtraction
This is the process of finding the difference between two numbers.
Addition
This is the process of finding the sum of two or more numbers.
Lowest Terms
When a fraction is written with the smallest possible numbers for both its numerator and denominator.
Distributive Law of Multiplication
a x (b + c) = a x b + a x c
Associative Law of Multiplication
a x (b x c) = (a x b) x c
Commutative Law of Multiplication
a x b = b x a
Order of Operations (def.)
The rules for priority must be followed when we simplify expressions which involve more than one operation.
List of the Order of Operations
1) Perform operations inside parentheses 2) Evaluate powers and roots from left to right 3) Multiplication and division from left to right 4) Addition and subtraction from left to right
Simple Fraction
A fraction where both the numerator and the denominator are whole numbers.
Complex Fraction
A fraction where either the numerator or the denominator, or both, are fractions or mixed numbers.
Improper Fraction
A fraction with a value greater than 1.
Proper Fraction
A fraction with a value less than 1.
Decimal Fraction
A fraction written as a multiple of 10, using a decimal point.
Prime Number
A natural number bigger than 1 whose only divisors are 1 and itself.
Composite Number
A natural number greater than 1 that is not prime.
Prime Factorization
A number written as a product of prime factors.
Estimation
A way of approximating the answer to a question quickly.
Mixed Number
A whole number and a fraction written together with the understanding that they are to be added together.
Multiplicand
In multiplication, a quantity that is to be multiplied by another.
Minuend
In subtraction, a quantity or number from which another is to be subtracted.
Subtrahend
In subtraction, a quantity or number to be subtracted from another.
Commutative Law of Addition
Numbers may be added in any order and the sum will be exactly the same. a + b = b + a
Factors
Numbers or expressions that are multiplied together to form a product.
Relatively Prime Numbers
Numbers such that there is no whole number other than 1 that divides the numbers without leaving a remainder.
Associative Law of Addition
Tells us that the way numbers are grouped does not affect the sum. (a + b) + c = a + (b + c)
Remainder
The amount left over after a division when the divisor does not divide into a dividend exactly.
Numerator
The dividend in a fraction.
Denominator
The divisor in a fraction.
Greatest Common Divisor (GCD)
The largest number that exactly divides two or more other numbers.
Recipricol
The multiplicative inverse of a fraction or whole number.
Multiplier
The number of times the multiplicand is to be multiplied.
Divisor
The number that divided the dividend.
Dividend
The number that is divided by the divisor.
Addends
The numbers that are added together.
Decimal Point
The period before the digits in a decimal.
Division
The process of finding out how many times the divisor goes into the dividend.
Power
The product obtained by multiplying a number by itself a given number of times.
Fraction
The quotient of two whole numbers.
Quotient
The result of the division of the dividend by the divisor.
Product
The result of the multiplication of the multiplicand and the multiplier.
Arithmetic
The science of numbers.