Fraction (mathematics)

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, ${\tfrac {1}{4}}$ , ¹⁄₄ 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]

A cake with one quarter removed. The remaining ³⁄₄ 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.

Fraction dice.

Examples of fractionEdit

Scaled fraction used in step by step.
A room where ${\tfrac {1}{4}}$ of the people are girls, has 1 girl for every 4 people.
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 fractionsEdit

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

Fraction numbers used in addition in lines

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.

MultiplyingEdit

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. ²⁄₄ x ³⁄₄ = ⁶⁄₁₆. One can simplify this by dividing both numbers by a common factor. This would be ³⁄₈ after the simplication.

Related pagesEdit

ReferencesEdit

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

Other websitesEdit

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[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.

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