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'fraction'
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| Title of object: |
fraction |
| Canonical Name: |
Fraction |
| Type: |
Definition |
| Created on: |
2002-04-06 12:06:10 |
| Modified on: |
2004-10-11 02:23:18 |
| Classification: |
msc:11-01 |
| Defines: |
solidus, proper fraction, numerator, denominator, improper fraction, lowest terms |
Revision comment (for changes between this and next version):
| Changes for correction #2632 ('An addition'). |
Preamble:
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\usepackage{amssymb}
\usepackage{amsmath}
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Content:
A \emph{fraction} is a rational number expressed in the form $\frac{n}{d}$ or $n/d$, where $n$ is designated the \emph{numerator} and $d$ the \emph{denominator}. The slash between them is known as a \emph{solidus} when the fraction is expressed as $n/d$.
The fraction $n/d$ has value $n \div d$. For instance, $3/2 = 3 \div 2 = 1.5$.
If $n$ and $d$ are positive, and $n/d < 1$, then $n/d$ is known as a \emph{proper fraction}. Otherwise, it is an \emph{improper fraction}. If $n$ and $d$ are relatively prime, then $n/d$ is said to be in \emph{lowest terms}. To get a fraction in lowest terms, simply divide the numerator and the denominator by their greatest common divisor:
$$\frac{60}{84} = \frac{60 \div 12}{84 \div 12} = \frac{5}{7}.$$
The rules for manipulating fractions are
\begin{eqnarray*}
\frac{a}{b} & \qquad = \qquad & \frac{ka}{kb}\\
\frac{a}{b} + \frac{c}{d} & \qquad = & \frac{ad + bc}{bd}\\
\frac{a}{b} - \frac{c}{d} & \qquad = & \frac{ad - bc}{bd}\\
\frac{a}{b} \times \frac{c}{d} & \qquad = & \frac{ac}{bd}\\
\frac{a}{b} \div \frac{c}{d} & \qquad = & \frac{ad}{bc}.
\end{eqnarray*} |
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