# 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. For example, ${\tfrac {1}{4}}$ , 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. A cake with one quarter removed. The remaining 34 of the cake has been divided into two pieces.

The top part of the fraction is called a numerator. The bottom part of the fraction is called a denominator. For example, for the fraction ${\tfrac {1}{4}}$ , the 1 is the numerator, and the 4 is the denominator.

## Examples of fraction

1. A room where ${\tfrac {1}{4}}$  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 ${\tfrac {1}{4}}$ , and is called a "quarter". Similarly, 2 parts of the cake (2 quarters) can be written ${\tfrac {2}{4}}$ , 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 ${\tfrac {1}{2}}$ ). 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 ${\tfrac {1}{2}}$  means one divided by two, or, in decimals, 0.5.

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

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

To find ${\tfrac {1}{2}}$  divided by ${\tfrac {1}{2}}$ , multiply ${\tfrac {1}{2}}$  by the reciprocal of ${\tfrac {1}{2}}$ , 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 simplication.