Number Types And Properties: Math Terms Explained
Plain-language definitions of every number types and properties term your child meets in school, each with kid-friendly explanations, worked examples, and common mistakes to watch for.
Absolute value
Absolute value is the distance a number is from 0 on the number line, so it is always written as a nonnegative number, whether the original number was positive or negative.
Associative property
The associative property is a rule for addition and multiplication that says when you add or multiply three or more numbers, you can group the numbers in any way and the final sum or product will stay the same.
Closure property
The closure property is a rule that says if you start with numbers from a certain set and combine them using an operation (like addition or multiplication), the answer will still be a number from that same set.
Commutative property
The commutative property is a rule for addition and multiplication that says you can change the order of the numbers and still get the same answer, such as 4 + 7 = 7 + 4 or 3 × 5 = 5 × 3.
Composite number
A composite number is a whole number greater than 1 that has more than two factors, which means it can be divided evenly by 1, itself, and at least one other whole number.
Distributive property
The distributive property is a rule that says multiplying a number by a sum or difference gives the same result as multiplying that number by each part separately, then adding or subtracting the results.
Divisibility
Divisibility is a way to describe whether one whole number can be divided by another whole number with no leftovers, or remainder.
Greatest common factor
The greatest common factor is the largest whole number that divides exactly into two or more numbers, with no remainder, and is shared as a factor by all of them.
Identity property
The identity property is a rule that says there is a special number for each operation that keeps a value the same: adding 0, subtracting 0, multiplying by 1, or dividing by 1 does not change the original number.
Integer
An integer is any whole number and its opposite, including zero, such as -3, -2, -1, 0, 1, 2, 3, without any fractional or decimal part.
Irrational number
An irrational number is a real number that cannot be written as a fraction of two integers, and whose decimal form goes on forever without repeating in a pattern.
Least common multiple
A least common multiple is the smallest number that is a multiple of each number in a set, so it is the first number they all share in their multiplication tables.
Natural numbers
Natural numbers are the counting numbers used to list how many objects there are, usually 1, 2, 3, and so on, without fractions or decimals.
Negative numbers
Negative numbers are numbers that are less than 0, written with a minus sign in front (like -3 or -7.5), and they are used to show values such as debts, temperatures below zero, or movement in the opposite direction.
Odd and even numbers
Odd and even numbers are whole numbers sorted into two groups: even numbers can be divided into 2 equal whole-number parts with nothing left over, and odd numbers cannot be split into 2 equal whole-number parts because there is always 1 left over.
Opposite numbers
Opposite numbers are two numbers that are the same distance from 0 on a number line but on different sides, such as 3 and -3.
Perfect cube
A perfect cube is a number made by multiplying an integer by itself three times, such as 27 = 3 × 3 × 3, so its cube root is an integer.
Perfect square
A perfect square is a number that can be written as an integer multiplied by itself, such as 1 = 1 × 1, 9 = 3 × 3, or 144 = 12 × 12.
Positive numbers
Positive numbers are numbers greater than 0, written without a negative sign, that can be used to measure quantities like length, money, time, and many other real-world amounts.
Prime factorization
Prime factorization is writing a whole number as a product of prime numbers, usually in order from smallest to largest, and often using exponents to show repeated factors.
Prime number
A prime number is a whole number greater than 1 that has exactly two factors: 1 and itself, which means it can only be made by multiplying 1 times that number.
Properties of numbers
Properties of numbers are basic rules that numbers always follow when you add, subtract, multiply, or divide, such as how you can change the order or grouping of numbers without changing the result.
Rational number
A rational number is any number that can be written as a fraction of two integers, with a nonzero denominator, and whose decimal form either ends (terminates) or repeats.
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