Math Terminology: Fractions, Decimals and Operations

A parent's guide to common math terms

A father helps his son with homework.
A father helps his son with homework. Chris Ryan/Getty Images

If you're having trouble helping your child with his math homework because you don't understand the vocabulary, here's a quick review of the math terminology related to fractions, decimals and other operations.

Fraction Terms

Denominator: The denominator is the number in a fraction that is below the line or on the bottom. A good trick is to remember “d” is for denominator and “d” is for down.

Fraction: A fraction is a part of a whole.

Numerically, a fraction is represented as the part over the whole or part/whole.

Improper fraction: An improper fraction is a fraction in which the numerator is larger than the denominator. This means that the number represented by the fraction is actually more than 1 and can be reduced. Example: 5/4 = 1 ¼

Numerator: The numerator is the number in a fraction that is above the line, or the top number.

Decimal Terms

Absolute Value: Absolute value is the number of spaces a numeral is from zero. Whether the number is positive or negative doesn’t matter. The absolute value of 4 and -4 are both 4, since they are the same distance from 0 on a number line.

Decimal: A decimal is the expression of a fraction in the base of 10, using a decimal point to separate whole numbers from the fractional value. In order to be expressed as a decimal, a fraction’s denominator must be 10 or a power of 10. Each power is one place farther to the right of the decimal. Example: 1/10 =.1, 1/100 = .01, 1/1000 = .001

Place Value: Place value refers to where a particular numeral is located in a larger number. Elementary school math commonly works with tens, hundreds and thousands. Example: In the number 2567, 7 is in the ones place, 6 is in the tens place (and stands for 60), 5 is in the hundreds place (and stands for 500) and 2 is in the thousands place (and stands for 2000).

Multiplication, Division and Operation Terms

Multiple: The multiple is a number obtained by multiplying one number by another. Every number has a series of multiples. These multiples can be divided by the original number and result in a whole number. You can think of each times table as a list of multiples. For example: 2, 4, 6, 8, 10 and 12 are all multiples of 2.

Dividend: In a division problem, the dividend is the number you are dividing. Example: In the equation 20÷ 5, 20 is the dividend.

Divisor: In a division problem, the divisor is the number by which you are dividing. Example: In the equation 20÷5, 5 is the divisor.

Equation: An equation is a mathematical sentence showing that what is to the right of the ‘equals’ sign is the same value as what is to the left of it. Examples: 2+3 =5; 20 ÷ 4= 5; 4-1=3

Expression: An expression is the part of a mathematical sentence that has numerals and operation signs. An expression does not include the ‘equals’ sign. Examples: 2 x 3; 25 ÷5; 3 - 1

Fact Family: A fact family is a group of numbers that are related to each other in that those numbers can be combined to create a number of equations. Example: 2, 3 and 6 are a fact family with which you can create the equations: 2 x 3 =6; 3 x 2 = 6, 6 ÷ 2 = 3 and 6 ÷ 3 = 2.

Factor: A factor is a number that can divide evenly into another number. Numbers can have many factors. Example: 10, 3, 5, and 6 are all factors of the number 30.

Inverse: Operations and numbers are said to be inverse if they are opposites of each other. Multiplication and division are inverse operations and the number 4 is the inverse of ¼.

Operation: An operation is the mathematical act performed on two or more numbers. Addition, subtraction, multiplication and division are all operations.

Product: A product is the answer to a multiplication problem. Example: In the problem, 2 x 4 = 8, the product is 8.

Quotient: A quotient is the answer to a division problem, but without the remainder. Example: In the problem, 8 ÷ 4 = 2, the quotient is 2.

Remainder: A remainder is the amount left over when a long division problem doesn’t have an even answer. Example: In the problem, 71 ÷ 5, the answer is 14 with a remainder of 1. It is written as 71 ÷ 5 = 14 r1.

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