the rational numbers honors math – grade 7. problem of the day a small submarine descended to a...
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The Rational Numbers
Honors Math – Grade 7
Problem of the DayA small submarine descended to a depth of mi and then
ascended mi. These changes can be written as signed
(positive or negative) numbers.
4
12
8
3
Let’s recall some words for positive and negative numbers.
POSITIVE NEGATIVE Let’s write these signed numbers.
midescended4
12
miascended8
3
mi4
12
mi8
3
Read: negative 2 and ¼.
Read: positive three eighths or three eighths.
A Rational Number is a number that can be written in
fractional form, , where a and b are integers and .0bb
a
Here are some examples of rational numbers.
Rational Number
Form
All integers are rational numbers.
Integers – the set of whole numbers and their opposites
VOCAB ALERT
Natural Numbers
,...4,3,2,1NWhole Numbers
,...4,3,2,1,0W ,...3,2,1,0,1,2,3..., I
Rational Numbers
Integers
-98-4
Whole Numbers
0
Natural or Counting Numbers
1, 2, 3, 4, …
8
75
5
33.1
5.0
2
12
9
47
Set of numbers starting with 1 and counting up by ones.
Set of natural numbers and 0
Set of whole numbers and their opposites.
Set of numbers that can be expressed as the quotient of two integers.
Identify the set(s) of numbers to which each belongs.
7 -10 0
5
44
150
121
9
2
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!
99
47
x
63
+
If the mixed number is
negative, the improper
fraction will be negative! 67
Write in the form .b
a
11
43
13
Write in the form .b
a
3
215
Write in the form .b
a
A Rational Number in the form, , can be written as a decimal.
b
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.
100
7
Seven hundredths
07.0
1000
251
25
14
100 56.0
Fifty-six hundredths
20
17
8
3
38
11
5
Write as a decimal.
25
64
If the quotient has a remainder of zero, the result is a terminating decimal.
Write as a decimal.
10
9
If the quotient has a remainder of zero, the result is a terminating decimal.
Write as a decimal.
6
5
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.