Chapter 5: Fractions 59Because a whole number like 7 is a rational number, even though you wouldn’t usually think of
it as a fraction, it can be written as the quotient of two integers. You could write
7
1 , which you
would think of as a fraction. You could actually write many different quotients that equal 7, like
42
6 or
700
100. Those look like the other quotients you think of as fractions, like5
8 ,17
3 , and4
51.In those examples, there were two proper fractions, or fractions whose value is less than 1. Those
were
5
8 and
4
51. You can spot a proper fraction because the numerator is less than the denominator.
On the other hand,
17
3 and
7
1 (and all the fractions equal to7
1 ) are improper fractions. They’re worth
more than 1, because their numerators are larger than their denominators.
DEFINITION
A proper fraction is one whose value is less than one. An improper fraction is one
whose value is more than one.Fractions use their denominator to tell you how many parts the whole was broken into and their
numerator to tell you how many of those parts you have.
5
8 says the whole was broken into 8 parts
(called eighths), and you have 5 of them. That’s less than the whole, so it’s a proper fraction.
To interpret^173 , you have to imagine that many wholes were each divided into 3 parts, called
thirds, and you have a total of 17 of those parts. You could piece your parts back together and
make 5 full wholes, with 2 of the pieces left over. You can write that as^173 = 523 , which is called a
mixed number. Mixed numbers are a combination of a whole number and a fraction, a condensed
way of saying 5 +^23.
DEFINITION
A mixed number is made up of a whole number and a fraction, written side by side. It
tells you that you have a number of wholes plus part of another.CHECK POINT- Change^185 to a mixed number.
- Change^374 to a mixed number.
- Change 713 to an improper fraction.
4. Change 1243 to an improper
fraction.
5. Change 1178 to an improper fraction.