# Fraction (mathematics)

mathematical representation of a portion of a whole

A fraction is a number that shows how many equal parts there are. When we write fractions, we show one number with a line above (or a slash next to) another number.[1][2] For example, ${\displaystyle {\tfrac {1}{4}}}$, 14 and 1/4.are different ways of writing the same fraction (in this case a quarter). The top number tells us how many parts there are, and the bottom number tells us the total number of parts.[3]

## Numerators and denominators

The top part of a fraction (example: 1/4) is a numerator. Numerators can be any real numbers. The numerator can be on the top or to the left when writing fractions. The bottom part of a fraction (example: 1/4) is called a denominator. This number cannot be zero. It is on the bottom or on the right when writing fractions.

A proper fraction is a fraction with the numerator smaller than the denominator. An improper fraction is a fraction where the numerator is bigger than the denominator. For example, ${\displaystyle {\tfrac {1}{4}}}$  is a proper fraction, and ${\displaystyle {\tfrac {5}{4}}}$  is an improper fraction.

## Examples of fractions

1. A room where ${\displaystyle {\tfrac {1}{4}}}$  of the people are girls, has 1 girl for every 4 people.
2. A cake can be thought of as being made up of 4 equal parts, where each is 1 part of 4. This can be written as ${\displaystyle {\tfrac {1}{4}}}$ , and is called a "quarter". Similarly, 2 parts of the cake (2 quarters) can be written ${\displaystyle {\tfrac {2}{4}}}$ , which is also equal to 1/2 (one-half).

## Mathematical fractions

A fraction is a mathematical expression relating two quantities or numbers, where one divides the other. When the two quantities are whole numbers (or integers), this is called a rational number (such as the fraction ${\displaystyle {\tfrac {1}{2}}}$ ). When the two quantities are polynomials, this is called a rational function.

Fraction table
1/2 2/3 3/4
4/5 5/6 6/7
7/8 8/9 9/10
10/11 11/12 12/13
13/14 14/15 15/16
16/17 17/18 18/19
19/20 20/21 21/22
22/23 23/24 24/25
25/26 26/27 27/28
29/30 30/31 32/33
33/34 34/35 35/36
36/37 37/38 38/39
39/40 40/41 42/43
43/44 44/45 45/46
46/47 47/48 48/49
49/50 50/51 51/52
52/53 53/54 54/55
55/56 56/57 57/58
58/59 59/60 60/61
61/62 62/63 64/65
65/66 66/67 68/69
69/70 70/71 71/72
72/73 73/74 74/75
75/76 76/77 77/78
78/79 79/80 80/81
81/82 82/83 83/84
84/85 85/86 86/87
87/88 88/89 89/90

Mathematically, a fraction is a quotient of numbers, representing the number's value when the numerator (upper number) is divided by the denominator (lower number). Thus ${\displaystyle {\tfrac {1}{2}}}$  means one divided by two, or, in decimals, 0.5.

To find ${\displaystyle {\tfrac {1}{2}}}$  of ${\displaystyle {\tfrac {1}{2}}}$ , the denominators are multiplied, and because denominator 2 multiplied by 2 equals 4, we have that ${\displaystyle {\tfrac {1}{2}}}$  x ${\displaystyle {\tfrac {1}{2}}}$  = ${\displaystyle {\tfrac {1}{4}}}$ , or 0.5 x 0.5 = 0.25.

(In this case, “${\displaystyle {\tfrac {1}{2}}}$  of” means "multiplication".)

To find ${\displaystyle {\tfrac {1}{2}}}$  divided by ${\displaystyle {\tfrac {1}{2}}}$ , multiply ${\displaystyle {\tfrac {1}{2}}}$  by the reciprocal of ${\displaystyle {\tfrac {1}{2}}}$ , which is 2. That answer is 1.

## Multiplying

To multiply two fractions, the first numerator is multiplied by the other numerator, and the first denominator is multiplied by the other denominator. For example. 24 x 34 = 616. One can simplify this by dividing both numbers by a common factor. This would be 38 after the simplification.

## References

1. "Compendium of Mathematical Symbols". Math Vault. 2020-03-01. Retrieved 2020-08-27.
2. Weisstein, Eric W. "Fraction". mathworld.wolfram.com. Retrieved 2020-08-27.
3. "Fractions". www.mathsisfun.com. Retrieved 2020-08-27.