A fraction (from Latin fractus, “broken”) represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size are, for example, one-half, eight-fifths, or three-quarters. A common, vulgar, or simple fraction (also called a proper fraction) consists of an integer numerator displayed above a line (or before a slash) and a non-zero integer denominator displayed below (or after) that line. Numerators and denominators are also used in fractions that are not common, including compound fractions, complex fractions, and mixed numerals. The numerator represents some equal parts, and the denominator, which cannot be zero, indicates how many of those parts make up a unit or whole. For example, in the fraction three-fifths, the numerator (three) tells us that the fraction represents three equal parts, and the denominator (five) tells us that five parts make up a whole.
To form a common fraction, one writes down a numerator above a line (or before a slash) and then writes a corresponding denominator below the line (or after the slash).
1/2 3/4 10/11
Common fractions can also be represented using decimals.
0.5 0.75 0.9090909…
When a fraction is expressed as a decimal, the number of zeroes after the decimal point corresponds to the number of equal parts indicated by the denominator. In other words, a fraction with a denominator of 10 (such as 1/10 or 0.1) has one zero after the decimal point because it represents ten equal parts; fractions with a denominator of 100 (such as 1/100 or 0.01) have two zeroes after the decimal point, because it represents 100 equal parts, and so on.
It is also possible to express fractions as percentages.
50% 75% 91.09%
To convert a fraction to a percentage, multiply the fraction by 100. For example, to convert 1/2 to a percentage, we multiply 1/2 by 100 to get 50%.
It should be noted that not all fractions can be expressed as decimals or percentages. For example, the fraction 2/3 cannot be expressed as a decimal (it would be 0.66666666… which goes on forever), and it cannot be expressed as a percentage (it would be 66.66666…%, which also goes on forever). These fractions are said to be recurring decimals or repeating decimals. Other examples of recurring decimals include 1/3 (0.3333…), 1/6 (0.16666…), and 1/7 (0.142857…).
It is called a proper fraction when a fraction is not expressed as a whole number. For example:
1/2 3/4 10/11
Proper fractions are sometimes top-heavy fractions because the numerator is always larger than the denominator. On the other hand, when a fraction is expressed as a whole number, it is called an improper fraction .
5/2 7/4 11/10
Improper fractions are sometimes referred to as bottom-heavy fractions because the numerator is always smaller than the denominator.
It is also possible to have mixed numerals, a combination of whole numbers and fractions.
2 1/2 3 3/4 10 2/11
Mixed numerals are sometimes also referred to as mixed fractions. To convert a mixed numeral to an improper fraction, multiply the whole number by the denominator and add it to the numerator. For example, to convert 2 1/2 to an improper fraction, we would multiply two by the denominator (in this case, 2), which gives us 4; we would then add that result to the numerator (1), which gives us 5; and so the mixed numeral 2 1/2 would be equivalent to the improper fraction 5/2.
3 is the whole number, and 14 is the fraction. So the mixed number would be 3 14 .
To convert a decimal to a mixed number, we first need to find the whole number. This can be done by finding the largest number in the decimal without going over it. For example, if we have the decimal 0.625, we know that six goes into 0.625 once (0.625-0.6=0.025), so the whole number part of the mixed number is 1.
Now that we have the whole number, we need to find the fractional part. We take the decimal and subtract the whole number from it to do this. So, using our example from before, we would take 0.625-1=0.025. This gives us our fractional part, which would be written as 25. Note that the fractional part will always be less than 1.