Transcript Rational Numbers

Rational Numbers
Rational numbers are numbers that can be written as the
quotient of two integers. In the form a/b , where a is
any integer and b is any integer except 0.
• All fractions and mixed numbers
• All terminating and repeating decimals
• All integers
• All rational numbers can be written in many
equivalent forms.
-x-=+
Rational Numbers
-/- =+
+x+=+
+/+=+
+x-=-
+/-=-
-x + = -
-/+=-
-2 is equivalent to: 2/-1, -4/2, -2/1, - -2/-1
3 is equivalent to: 3/1, -3/-1, -6/-2
Rational Numbers
Which is larger? -2/3 or -4/5
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Find the LCM (lowest common denominator).
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What ever you do to the bottom, you must do to the top.
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Compare the numerators.
What are the following as the quotient of two integers in
lowest terms.
a) 1 ½
3/2
b) –0.8
-4/5
c) 3
3/1
d) –2.51
-251/100
Rational Numbers
Almost all numbers are rational.
½,
7,
0,
2 ½,
0.875, 2.333, -3/10
They have equivalent forms.
0.5
7/1
0/2, 5/2, 7/8, 7/3, -0.3
Numerator
2
Denominator
4
Mixed Number 2 ½
Improper Fraction 5/2
To turn a mixed number into an improper fraction,
you keep the denominator. Then you multiply the
denominator by the whole number and add the
numerator.
Irrational Numbers
Are numbers that can not be written as a quotient.
These numbers are non-repeating & non-terminating
decimals.
There are very few of these.
• 2
= 1.4142135
• 3
= 1.7320508
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= 3.141592653
• 7/0
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Rational & Irrational Numbers
Quotient – a number resulting from a division. ½ = 0.5
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Integers – numbers in the sequence ….,-3,-2,-1,0,1,2,3
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Denominator – the number of equal parts in a whole or a group. In ½ the denominator is
the 2.
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Numerator – the number of equal parts being considered in a whole or a group. In ½
the numerator is the 1.
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Non-repeating Decimal – a decimal in which a digit or digits do not repeat.
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Non-terminating Decimal – a decimal that continues without end, such as
0.333333333….
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Mixed number – a number that is the sum of a whole number and a fraction. 2 ½.
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Improper Fraction – a fraction whose numerator is greater than its denominator.
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(LCD) Lowest Common Denominator – The lowest multiple shared by two or more
denominators. The LCD of 1/8 and 1/6 is 24.
Rational & Irrational Numbers
Name:______________________
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_____________________ – a number resulting from a division. ½ = 0.5
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____________________ – numbers in the sequence ….,-3,-2,-1,0,1,2,3
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_______________– the number of equal parts in a whole or a group. In ½ the denominator is the 2.
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______________ – the number of equal parts being considered in a whole or a group. In ½ the
numerator is the 1.
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_______________ – a decimal in which a digit or digits do not repeat.
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_______________ – a decimal that continues without end, such as 0.333333333….
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_______________ – a number that is the sum of a whole number and a fraction. 2 ½.
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_______________ – a fraction whose numerator is greater than its denominator.
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_______________ – The lowest multiple shared by two or more denominators. The LCD of 1/8 and
1/6 is 24.
Non-terminating Decimal, Denominator, Mixed number
Improper Fraction , Numerator
, Quotient, Integers, (LCD) Lowest Common Denominator, Non-repeating Decimal ,