# 5.1 Notes Rational Number ```5.1 Notes
Rational Number:
A number that can be written as
a quotient (fraction) of two
integers.
Natural Numbers
Whole Numbers
only difference from Natural
Numbers
Integers Positive and negative whole
numbers
Rationals
Bigger than the three sets
above. In fact the rationals
contain all the sets above,
plus any fraction you can
think of.
Terminating
Decimal
It &quot;ends&quot;
If you divide it out
&quot;the long way&quot; you
eventually get a
remainder of zero.
vs
Repeating
Decimal
a &quot;digit&quot; or a
&quot;block&quot; of digits
repeat themselves
forever.
If you divide it out
&quot;the long way&quot; you
never get a
remainder of zero.
Examples:
1. Show that the number is rational by writing
the number as a &quot;quotient.&quot;
a. 7
b. -10
c. 5 3/4
d. -3 1/2
2. Write as a decimal:
a. 3/8
b. 5/11
c. 1 9/20
d. 29/80
3. Compare (use &lt; , &gt; , &lt; , &gt; , = and use
decimals)
a. 20/50 ____ 24/54
b. 25/26 ____ 49/51
c. Put in order from least to greatest:
-5/4 , -.2 , 4.31 , -3 , 5/2 , -13/3 , 16/3 , -.2
4. Write the decimal as a fraction or mixed
number. (Make sure you simplify.)
a. .7
b. .3
c. .93
d. .93
e. -3.05
5.2 Notes:
&quot;Like Fractions&quot;
Two fractions where their
denominators (the bottoms) are
the same.
FIRST: Make sure fractions are
&quot;like fractions&quot;
Numerators (Top Numbers),
Leave the Denominators (Bottom
Numbers) the same.
Algebraically adding fractions looks like this:
a
b
+
c
c
= a+b
c
(Note: c = 0)
Examples: Evaluate the following without a
1. 77 + 9
100
100
2. 3 + 2
8
8
3. -1 + 5
6
6
4. 2 - 7
15 15
()
5. 1 - -7
12 12
Examples: Evaluate the following without a
6. 2 3/4 + 1 3/4
7. -6 2/3 + 3 1/3
8. 4 1/5 - 2 3/5
9. -3 2/7 - 6 3/7
.
Examples: Evaluate the following without a
10.
11.
3a + 5a
20 20
-8
3b
-
()
-2
3b
.
5.1: p. 222-223: 20-43 , 49-60
5.2: p. 228-229: 10-25 , 27-43 ,
46-51
Use the 5.2 Activity if needed.
```