Download 4.1 introduction to fractions and mixed numbers

4.1 INTRODUCTION TO FRACTIONS AND MIXED
NUMBERS
First a REVIEW. We are already familiar with positively
and negatively signed numbers (integers) and know how to
find them on the real number line. Find 1, 2 and –1 on the
number line:
-2
-1
0
1
2
Of course there are number BETWEEN these as well. In
this section we will learn about “RATIONAL
NUMBERS”, better known as “FRACTIONS”.
A RATIONAL NUMBER (FRACTION) is a number of
the form a where both a and b are INTEGERS, and b
b
is not _______. We call the number in the “top” part the
NUMERATOR and the number in the “bottom” part the
DENOMINATOR. Ex: 4/7 is a fraction. The
NUMERATOR is_____ and the DENOMINATOR is ____.
We use “fractions” every day. Can you think of some
examples?
MATERIALS!!(Do cup measurements w/ 1 cup, 1/3 cup & rice.)
We can use PICTURES to represent fractions:
Write a fraction to express each shaded area.
Write a fraction to express each non-shaded area.
We notice that the DENOMINATOR tells us how many
equivalent “parts” there are and the NUMERATOR tells
how many parts are being considered.
We can use fractions to talk about groups of people. For
example:
In the front row, what fraction is female?
What fraction is male?
What fraction is a student?
Can a “fraction” ever be more than one (1)?
(See cup measurements, how many thirds could we use to
make more than one whole cup?)
How would you write such a fraction? What do you notice
about the relationship between the numerator and the
denominator?
An IMPROPER FRACTION is one where the
NUMERATOR is GREATER THAN OR EQUAL TO the
DENOMINATOR.
Ex:
A PROPER FRACTION is one where the NUMERATOR
is LESS THAN the DENOMINATOR.
Ex:
Classify as “proper” or “improper”, then graph:
Fraction
Proper Improper
Fraction Fraction
9
5
9
11
9
9
0
9
MIXED NUMBERS
Lets start by reviewing. Illustrate 1/2. How can we write
5/2 using a drawing? How many “wholes” do we have?
How many halves do we have?
So we can write 5/2 as:
When an improper fraction is written as a whole number
plus a proper fraction, we call this a MIXED NUMBER.
For 5/2 this would be 2 + ½ and we simply write 2 ½ .
For –5/2 this would be –2 – ½ and we simply write –2 ½.
We must be able to write a MIXED NUMBER as an
IMPROPER FRACTION, and an IMPROPER
FRACTION as a MIXED NUMBER. Each will always
have the SAME SIGN!
Ex: Say we have 2 1/3. How many thirds is that?
For the 2 wholes, there must be 3 thirds in each.
2 x 3 = 6 plus one more third = 7/3
What did we do?
Writing a MIXED NUMBER as an IMPROPER
FRACTION:
1) MULTIPLY the DENOMINATOR x WHOLE
NUMBER
2) ADD the NUMERATOR to that product
3) This sum is the NUMERATOR of the improper
fraction, the DENOMINATOR remains the same
Ex:
3
Write 9 as an improper fraction
5
So if to write a mixed number as an improper fraction we
MULTiply, to write an improper fraction as a mixed
number, we will DIVide!
Ex: Say we have 17 How many WHOLES is that? How
5
many fractional parts are left?
For every 5/5 we will have a whole. All we need to do is
divide 17 by 5 = 3 whole times with 2 remaining.
Or
Writing an IMPROPER FRACTION as a MIXED
NUMBER:
1) DIVIDE the NUMERATOR by the DENOMINATOR
2) Write the WHOLE number part
3) Write the remainder over the same DENOMINATOR
for the proper fraction part
** Note: if you begin with a PROPER fraction, it cannot
have a whole number part!
**Also: your fractional part of a MIXED number should
ALWAYS be a PROPER fraction
Ex: Write
Ex:
18
 as a mixed number
7
24
Round
to the nearest whole number.
7
We treat the ABSOLUTE VALUE of a fraction just as we
did for an integer. Remember that when we find the
absolute value (or distance from zero) of a number it will
ALWAYS be _______________ or zero.
Ex:
 -5 =
-5/3  =
7  =
7/9  =
 0 =
 -1/4 =