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, <math>\tfrac{1}{4}</math>, 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]
Numerators and denominators[change]
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, <math>\tfrac{1}{4}</math> is a proper fraction, and <math>\tfrac{5}{4}</math> is an improper fraction.
Examples of fractions[change]
- A room where <math>\tfrac{1}{4}</math> 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 <math>\tfrac{1}{4}</math>, and is called a "quarter". Similarly, 2 parts of the cake (2 quarters) can be written <math>\tfrac{2}{4}</math>, which is also equal to 1/2 (one-half).
Mathematical fractions[change]
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 <math>\tfrac{1}{2}</math>). When the two quantities are polynomials, this is called a rational function.
| 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 <math>\tfrac{1}{2}</math> means one divided by two, or, in decimals, 0.5.
To find <math>\tfrac{1}{2}</math> of <math>\tfrac{1}{2}</math>, the denominators are multiplied, and because denominator 2 multiplied by 2 equals 4, we have that <math>\tfrac{1}{2}</math> x <math>\tfrac{1}{2}</math> = <math>\tfrac{1}{4}</math>, or 0.5 x 0.5 = 0.25.
(In this case, “<math>\tfrac{1}{2}</math> of” means "multiplication".)
To find <math>\tfrac{1}{2}</math> divided by <math>\tfrac{1}{2}</math>, multiply <math>\tfrac{1}{2}</math> by the reciprocal of <math>\tfrac{1}{2}</math>, which is 2. That answer is 1.
Multiplying[change]
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[change]
References[change]
- ↑ "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 websites[change]
- 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 Archived 2012-07-12 at the Wayback Machine for elementary grades.
