Chapter 1 Notes

Approximate Value

A symbol (~=) used to indicate an approximate or rounded value.

Fractions vs

Numbers less than one are often written as fractions instead of decimals.

Arithmetic

The branch of mathematics that includes four basic operations:Addition, Subtraction, Multiplication, and Division.

Addition

The process of combining two or more numbers together to get a total.

Addends and Sum

The numbers being combined are called addends, and the total is called the sum.

Adding Decimals

When adding decimals, align the decimal point and annex zeros when necessary.

Subtraction

The process of taking away one number from another number.

Inverse Operation

Subtraction is the inverse operation of addition.

Minuend, Subtrahend, Difference

The first number in subtraction is the minuend, the number to be subtracted is the subtrahend, and the answer is the difference.

Multiplication

The process of adding a number to itself as many times as indicated by another number.

Factors and Product

The numbers being multiplied are called factors, and the answer is called the product.

Partial Products

If the second factor has more than one digit, the problem will have two or more partial products that are added to get the final product.

Division

The process of finding how many times one number is contained in another number.

Inverse of Multiplication

Division is the inverse operation of multiplication.

Quotient, Dividend, Divisor

The quotient is the answer to the division problem; the dividend is divided by the divisor.

Remainder

When a number doesn’t divide evenly, the part of the dividend left is called the remainder.

Natural Numbers

The numbers used for counting.

Whole Numbers

Natural numbers including zero.

Integers

Whole numbers and their opposites, excluding fractions and decimals.

Rational Numbers

Numbers that can be expressed as either an integer or a fraction of integers.

Irrational Numbers

Numbers that cannot be expressed as an integer or fraction of integers; their decimal forms neither terminate nor repeat.

Real Numbers

The classification group that includes all rational and irrational numbers.

Positive Numbers

Integers, fractions, and decimals greater than zero.

Negative Numbers

Integers, fractions, and decimals less than zero.

Absolute Value

The distance a number is from zero, without its sign.

Law of Trichotomy

States that all comparisons can only have one sign:>,

Comparing Decimals

When comparing decimals, if the whole numbers are different, the mixed decimal with the greater whole number is greater.

Factors

All the different numbers that divide into a number evenly.

Prime Numbers

Numbers that only have two factors:1 and the number itself.

Composite Numbers

Numbers that have more than two factors.

Neither Prime nor Composite

The numbers 0 and 1 are neither prime nor composite.

Common Factor

A factor shared by two or more numbers.

Relatively Prime

Numbers that share no common factors except for 1.

Prime Factorization

The expression of a number as a product of prime factors.

Division by Primes

A method to find prime factorization by dividing by prime numbers until the final quotient is prime.

Factor Tree

A method of dividing a number into pairs of factors until only prime factors remain.

Base of Exponential Equation

The repeated factor in an expression like 5², where 5 is the base.

Exponent

Indicates how many times the base repeats in an exponential expression.

Power

The entire exponential expression, including the base and the exponent.

Reciprocal

1 divided by the number; for example, the reciprocal of 4 is ¼.

Any Number to the Power of 0

Equals 1; for example, 3^0 is 1.

Greatest Common Factor (GCF)

The largest common factor of two or more numbers.

GCF of Factors

If one number is a factor of the other, the smaller number is the GCF.

GCF of Relatively Prime Numbers

The GCF of two numbers that are relatively prime is 1.

Multiple

The product of a number and any natural number.

Least Common Multiple (LCM)

The smallest multiple shared by two or more numbers.

LCM Method

List the prime factorization, contest the powers, and multiply the circled factors.

LCM of Multiples

If one number is a multiple of the other, the larger number is the LCM.

LCM of Relatively