A glossary lets you look up a word and leave with its definition and an example you can check. The terms are in alphabetical order, each with a concrete fraction: 12/20 reduces to 3/5 with the GCF, which is 4, and 4/6 is a build-up of 2/3. If you are looking for “common fraction,” it is another word for a fraction and is under C.
| Term | Definition | Example | More information |
|---|---|---|---|
| Apparent fraction | A fraction whose numerator is a multiple of its denominator, so it equals a whole number. Some textbooks use this name; many US courses just call it an improper fraction. | 12/4 = 3 | Types of fractions |
| Approximation (≈) | A nearby value used in place of the precise one. It is only useful if you say how far off it is. | 1/3 ≈ 0.333, off by 1/3000 | Round to a fraction |
| Building up | Multiplying numerator and denominator by the same nonzero number. The value does not change. | 2/3 × 2/2 = 4/6 | Equivalent fractions |
| Common denominator | A denominator shared by several fractions. Any common multiple works; the least one is the LCM. | 1/4 and 1/6 fit over 12 or over 24 | Least common denominator |
| Common fraction | Another word for a fraction, used in some books to set it apart from a decimal. It is handled the same way. | “A common fraction” and “a fraction” name the same thing | What are fractions |
| Complex fraction | A fraction with another fraction in the numerator, the denominator or both. | (1/2)/(3/4) = 2/3 | Complex fractions |
| Decimal comma and decimal point | Two ways to write the same number. US English uses the point; many other countries, including Spain, use the comma. | 0.75 and 0,75 are the same number | Fraction to decimal |
| Decimal fraction | A fraction whose denominator is 10, 100, 1000… It reads directly as a decimal. | 7/100 = 0.07 | Decimal fractions |
| Denominator | The bottom number; it tells how many equal parts the whole is split into. It is never 0. | In 5/8, the denominator is 8 | Numerator and denominator |
| Divisibility rule | A rule that tells you whether one integer is divisible by another without dividing. | 2340 is divisible by 3 because 2 + 3 + 4 + 0 = 9 | Divisibility rules |
| Equivalent fractions | Different ways of writing the same number. | 1/2 = 3/6 = 5/10 | Equivalent fractions |
| Factor (or divisor) | An integer that divides another integer exactly. | 3 and 4 are factors of 12 | GCF vs. LCM |
| Fraction | The quotient a/b of two integers with b not equal to 0. The bar also means division. | 3/4 = 3 ÷ 4 = 0.75 | What are fractions |
| Greatest common factor (GCF) | The largest positive common factor, also called the greatest common divisor (GCD). Use it to reduce a fraction. | GCF(12, 20) = 4 | GCF calculator |
| Improper fraction | A positive fraction whose numerator is greater than or equal to its denominator; it equals 1 or more. Here 4/4 counts as improper. | 11/4 = 2 3/4 | Improper fraction to mixed number |
| Irrational number | A number that cannot be written as a quotient of integers; its decimal neither terminates nor repeats. | √2 ≈ 1.41421, off by less than 0.00001 | Rational numbers |
| Least common multiple (LCM) | The smallest positive common multiple. Use it to match denominators. | LCM(4, 6) = 12 | LCM calculator |
| Like and unlike fractions | Like fractions have the same denominator and add directly. Unlike fractions have different denominators. | 1/5 + 3/5 = 4/5; 1/5 and 1/3 are unlike | Add fractions |
| Lowest terms | A fraction whose numerator and denominator share no factor greater than 1. Also called simplest form. | 3/5, because the GCF of 3 and 5 is 1 | Simplify fractions |
| Mixed number | The sum of a whole number and a proper fraction. | 2 1/3 = 7/3 | Mixed number to fraction |
| Numerator | The top number; it counts how many of those parts are taken. | In 5/8, the numerator is 5 | Numerator and denominator |
| Opposite | The number with the same size and the opposite sign. Added to the original, it gives 0. | The opposite of 5/9 is −5/9 | Negative fractions |
| Percent (%) | A fraction with denominator 100. The sign is written right after the number, with no space. | 35% = 35/100 = 7/20 | Percent to fraction |
| Proper fraction | A positive fraction whose numerator is less than its denominator; it lies between 0 and 1. | 7/9 | Types of fractions |
| Rational number | A number that can be written as a quotient of two integers with a nonzero denominator. Its decimal terminates or repeats. | −2 = −2/1; 0.125 = 1/8 | Rational numbers |
| Reciprocal | The fraction with numerator and denominator swapped. Multiplied by the original, it gives 1. Zero has no reciprocal. | The reciprocal of 4/9 is 9/4 | Reciprocal of a fraction |
| Repeating decimal | A decimal with a block of digits that repeats forever. In print the block gets an overline; here it goes in parentheses. | 0.(3) = 0.333… = 1/3 | Terminating and repeating decimals |
| Simplify (or reduce) | Divide numerator and denominator by a common factor. Dividing by the GCF leaves lowest terms. | 18/24 = 3/4 (GCF 6) | Simplify fractions |
| Terminating decimal | A decimal with a limited number of digits. A fraction in lowest terms gives one when its denominator has only the prime factors 2 and 5. | 1/8 = 0.125 = 125/1000 | Terminating and repeating decimals |
| Unit fraction | A fraction with numerator 1. The larger the denominator, the smaller the value. | 1/9 is less than 1/7 | Unit fractions |
The entries that get mixed up most, such as improper and apparent, are compared further down.
One calculation that uses half a dozen terms
Adding 9/10 and 7/15 brings in several glossary terms: the fractions are unlike, you need a common denominator, and the result changes name halfway through.
Worked example: 9/10 + 7/15
The two fractions have different denominators, so they cannot be added as they stand.
- Find the LCM. The multiples of 10 and 15 first meet at 30.
- Build up. 9/10 = 27/30 (times 3) and 7/15 = 14/30 (times 2).
- Add the numerators. Now they are like fractions: 27/30 + 14/30 = 41/30.
- Classify. 41/30 is improper, because 41 is greater than 30, and as a mixed number it is 1 11/30.
- Check whether it reduces. 41 is prime and does not divide 30, so 41/30 is already in lowest terms.
Result: 41/30, which is 1 11/30.
Check: 41/30 = 1.3666…; 0.9 + 0.4667 = 1.3667, with 0.4667 rounded to 4 decimal places (error less than 0.00004).
Pairs of terms that get confused
Four pairs are often mixed up. In each, the two terms answer different questions, which is why one number can carry both names.
| Pair | Difference | Example |
|---|---|---|
| Improper and apparent | One asks whether the value reaches 1; the other, whether it is a whole number | 15/6 is improper but not apparent; 18/6 is both |
| Decimal fraction and terminating decimal | The first is a way of writing; the second is a property of the value | 3/8 is not a decimal fraction, but 3/8 = 375/1000 = 0.375 is terminating |
| GCF and LCM | The GCF is a factor and reduces; the LCM is a multiple and matches denominators | For 6 and 8, the GCF is 2 and the LCM is 24 |
| Reciprocal and opposite | The reciprocal gives product 1; the opposite gives sum 0 | For 2/7: reciprocal 7/2, opposite −2/7 |
With 6 and 8, the GCF is used to reduce fractions such as 6/8 and the LCM to add fractions with those denominators; one is never used in place of the other. To see when each one applies, the guide on GCF vs. LCM compares them with problems.
To use these words in real calculations, the fraction calculator shows the result reduced and as a mixed number, and how to type fractions in Word explains how to write them in a document.
Sources
The classification of improper fractions, equivalent fractions and the mixed number agrees with the English Wikipedia article Fraction (accessed October 17, 2026). It defines an improper fraction as one with absolute value of at least 1, so 7/7 counts; a mixed number as the sum of a nonzero integer and a proper fraction; and equivalent fractions by multiplying numerator and denominator by the same nonzero number. That article does not use the term “apparent fraction”; it is listed here because some textbooks use it.