d > 2 .

, which has the same value (0.5) as

4 {\displaystyle {\tfrac {50}{100}}} is in lowest terms—the only positive integer that goes into both 3 and 8 evenly is 1. The fraction bar may be horizontal (as in 1/3), oblique (as in 2/5), or diagonal (as in 4⁄9). Thus two thirds times three quarters is six twelfths.

{\displaystyle 4} , the algebraic fraction is called a rational fraction (or rational expression). {\displaystyle {\tfrac {8}{-5}}} 2 In the case of fractions of integers, the fractions a/b with a and b coprime and b > 0 are often taken as uniquely determined representatives for their equivalent fractions, which are considered to be the same rational number. Examples include {\displaystyle {\tfrac {1}{3}}+{\tfrac {1}{4}}+{\tfrac {1}{6}}+{\tfrac {1}{68}}} Since 5×17 (= 85) is greater than 4×18 (= 72), the result of comparing is 1 can be decomposed as the sum of two fractions: .

7 For example, There are total of 5 children. 3 . 18 1150). {\displaystyle {\tfrac {3}{8}}} b

× 1 Each fraction from one equivalence class may be considered as a representative for the whole class, and each whole class may be considered as one abstract fraction. The numerator represents a number of equal parts, and the denominator indicates how many of those parts make up a unit or a whole. {\displaystyle {\tfrac {3}{3}}}

3

b 1 Scientific publishing distinguishes four ways to set fractions, together with guidelines on use:[23]. / 9 . In a complex fraction, either the numerator, or the denominator, or both, is a fraction or a mixed number,[19][20] corresponding to division of fractions. − 10 It is easy to work out the chosen type of fraction to convert to; simply multiply together the two denominators (bottom number) of each fraction.

{\displaystyle {\tfrac {17}{3}}}

How long will the footprints on the moon last?

0.3333 This is also a good place to introduce the notion of congruence (same size and same shape). {\displaystyle 2+{\tfrac {3}{4}}.} When multiplication is intended, + If (For example, 3/1 may also be expressed as "three over one".) × , When the numerator is one, it may be omitted (as in "a tenth" or "each quarter"). 12.3456 is not in lowest terms because both 3 and 9 can be exactly divided by 3. For instance.

Students need to understand fractions naming conventions where the number of shaded equal parts is represented by the numerator, while the total number of equal parts is the denominator.

(For example, 1/2 may be read "one-half", "one half", or "one over two".) For example,

An algebraic fraction whose numerator or denominator, or both, contain a fraction, such as

[13][14] It is said to be an improper fraction, or sometimes top-heavy fraction,[15] if the absolute value of the fraction is greater than or equal to 1.

Several states in the United States have adopted learning trajectories from the Common Core State Standards Initiative's guidelines for mathematics education. In primary schools, fractions have been demonstrated through Cuisenaire rods, Fraction Bars, fraction strips, fraction circles, paper (for folding or cutting), pattern blocks, pie-shaped pieces, plastic rectangles, grid paper, dot paper, geoboards, counters and computer software.

{\displaystyle 4} In computer displays and typography, simple fractions are sometimes printed as a single character, e.g.

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