Numbers and symbols

Improper Fraction

A fraction which has a larger numerator than denominator. For example, 12/7 is an improper fraction.

Number Line

A line representing the set of all real numbers. The number line is typically marked showing integer values

Mixed Number

A number written as the sum of an integer and a proper fraction. For example, 5¾ is a mixed number. 5¾ is the sum 5 + ¾.

Composite Number

A positive integer that has factors other than just 1 and the number itself. For example, 4, 6, 8, 9, 10, 12, etc. are all composite numbers. The number 1 is not composite.

Fraction

A ratio of numbers or variables. Fractions may not have denominator 0.

Negative Number

A real number less than zero. Zero itself is neither negative nor positive.

Rational Numbers

All positive and negative fractions, including integers and so-called improper fractions. Formally, rational numbers are the set of all real numbers that can be written as a ratio of integers with nonzero denominator. Rational numbers are indicated by the symbol Q.

Integers

All positive and negative whole numbers (including zero). That is, the set {... , -3, -2, -1, 0, 1, 2, 3, ...}. Integers are indicated by either Z or J.

Even Number

An integer that is a multiple of 2. The even numbers are { . . . , -4, -2, 0, 2, 4, 6, . . . }.

Odd Number

An integer that is not a multiple of 2. The odd numbers are { . . . , -3, -1, 1, 3, 5, . . . }.

Factor of an Integer

Any integer which divides evenly into a given integer. For example, 8 is a factor of 24.

Digit

Any of the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 used to write numbers. For example, the digits in the number 361 are 3, 6, and 1.

Inequality

Any of the symbols <, >, ≤, or ≥.

Constant

As a noun, a term or expression with no variables. Also, a term or expression for which any variables cancel out. For example, -42 is a constant. So is 3x + 5 - 3x, which simplifies to just 5. As an adjective, constant means the same as fixed. That is, not changing or moving.

Irrational Numbers

Real numbers that are not rational. Irrational numbers include numbers such as π, e, etc.

Denominator

The bottom part of a fraction. For 3/5 , the denominator is 5.

Greatest Common Factor

The largest integer that divides evenly into each of a given set of numbers. Often abbreviated GCF or gcf. For example, 6 is the gcf of 30 and 18. Sometimes GCF is written using parentheses: (30, 18) = 6.

Median of a Set of Numbers

The median of a set of numbers is the value for which half the numbers are larger and half are smaller. If there are two middle numbers, the median is the arithmetic mean of the two middle numbers.

Arithmetic Mean

The most commonly used type of average. To find the arithmetic mean of a set of n numbers, add the numbers in the set and divide the sum by n.

Whole Numbers

The numbers 0, 1, 2, 3, 4, 5, etc.

Cardinal Numbers

The numbers 1, 2, 3, . . . as well as some types of infinity. Cardinal numbers are used to describe the number of elements in either finite or infinite sets.

Multiplicative Inverse of a Number

The reciprocal of x is . In other words, a reciprocal is a fraction flipped upside down. Multiplicative inverse means the same thing as reciprocal.

Difference

The result of subtracting two numbers or expressions. For example, the difference between 7 and 12 is 12 - 7, which equals 5.

Least Common Multiple

The smallest positive integer into which two or more integers divide evenly. For example, 24 is the LCM of 8 and 12. Sometimes the LCM is written using brackets: [8, 12] = 24.

Least Common Denominator

The smallest whole number that can be used as a denominator for two or more fractions. The least common denominator is the least common multiple of the original denominators.

Set Braces

The symbols { and } which are used to indicate sets.

Numerator

The top part of a fraction 12/47. For , the numerator is 12

Exponentiation

The use of exponents.

Average

This almost always refers to the arithmetic mean. In general, however, the average could be any single number that represents the center of a set of values.

Prime Factorization

Writing an integer as a product of powers of prime numbers 30 = 2*3*5

Exponent

x in the expression a^x. For example, 3 is the exponent in 2^3.