Fraction (mathematics)

A cake with one quarter removed. The remaining ³⁄₄ of the cake has been divided into two pieces.

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, ${\tfrac {1}{4}}$, 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.

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, ${\tfrac {1}{4}}$ is a proper fraction, and ${\tfrac {5}{4}}$ is an improper fraction.

Fraction dice.

Examples of fractions

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

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.

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. 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 simplification.

Related pages

• Algebraic fraction
• Egyptian fraction
• Mixed number
• Ratio

Other websites

• Curricula for Creating Fractions
• Interactive and dynamic worksheets to visualize fractions
• Worksheets: Identifying Fractions
• Worksheets: Improper Fractions to Mixed Numbers
• Curricula for Teaching about Equivalent Fractions Archived 2020-10-01 at the Wayback Machine
• Free online quizzes about Fractions
• Printable fraction worksheets for elementary grades.