Transcript The Rational Numbers - StCeciliaHonorsMath

The Rational
Numbers
Honors Math – Grade 7
Problem of the Day
1
4
A small submarine descended to a depth of
mi and then
3
ascended
mi. These changes can be written as signed
2
8
(positive or negative) numbers.
Let’s recall some words for positive and negative numbers.
POSITIVE
NEGATIVE
Let’s write these signed numbers.
1
descended 2 mi
4
1
 2 mi
4
Read: negative 2 and ¼.
3
ascended mi
8
3
mi
8
Read: positive three
eighths or three eighths.
A Rational Number is a number that can be written in
a
fractional form, , where a and b are integers and b  0.
b
Here are some examples of rational numbers.
Rational
Number
Form
All integers are rational numbers.
Natural Numbers
VOCAB ALERT
N  1,2,3,4,...
Integers – the set of whole
numbers and their opposites
Whole Numbers
I  ...,3,2,1,0,1,2,3,...
W  0,1,2,3,4,...
 0.5
1.3
1

2
Set of numbers that can be -4
2
expressed as the quotient of
Rational Numbers
5
7
8
Integers
-98
two integers.
Set of whole numbers and
their opposites.
Whole Numbers
0
Set of natural numbers and 0
Natural or Counting Numbers
1, 2, 3, 4, …
Set of numbers starting with
1 and counting up by ones.
3
5
7
4
9
Identify the set(s) of numbers to which
each belongs.
7
-10
0
4
4
5
121
150
2

9
Rational Numbers can be represented in different forms.
To write a mixed number as an improper fraction…
1. Multiply the denominator by the whole number
part (integer).
2. Add the product to the numerator.
3. The denominator stays the same!
+
63
4
67
7  
9
9
x
a
Write in the form .
b
4
3
11
a
Write in the form .
b
 13
a
Write in the form .
b
2
15
3
A Rational Number in the form,
decimal.
a
,
b
can be written as a
To write a fraction as a decimal, follow one of these three methods…
Inspection
Equivalent Fractions
Division
If the fraction, has a
denominator of 10, 100,
1000, etc…, say the fraction
and write the decimal.
If the fraction can be
renamed as an equivalent
fraction with a denominator
of 10, 100 or 1000, rename
the fraction and use
inspection.
If the previous methods do
not work, divide the
numerator by the
denominator. Can be used
all the time.
7
 0.07
100
Seven hundredths
14

 0.56
25 100
3
8
Fifty-six hundredths
251

1000
17

20
8 3
5

11
Write as a decimal.
6
4
25
If the quotient has a remainder of zero, the result is a
terminating decimal.
Write as a decimal.
9
10
If the quotient has a remainder of zero, the result is a
terminating decimal.
Write as a decimal.
5

6
If the quotient has a digit or a group of digits that repeat
without end, the result is a repeating decimal.
To show that one or more digits repeat in a decimal, use an
ellipsis or an overbar.