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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

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Rational Numbers

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  1. 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.

  2. Rational Numbers • x - = + - / - = + • + 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

  3. Rational Numbers • Which is larger? -2/3 or -4/5 • Find the LCM (lowest common denominator). • What ever you do to the bottom, you must do to the top. • Compare the numerators. • What are the following as the quotient of two integers in lowest terms. • 1 ½ b) –0.8 c) 3 d) –2.51 3/2 -4/5 3/1 -251/100

  4. 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.

  5. 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 • = 3.141592653 • 7/0

  6. Rational & Irrational Numbers • Quotient – a number resulting from a division. ½ = 0.5 • Integers – numbers in the sequence ….,-3,-2,-1,0,1,2,3 • Denominator – the number of equal parts in a whole or a group. In ½ the denominator is the 2. • Numerator – the number of equal parts being considered in a whole or a group. In ½ the numerator is the 1. • Non-repeating Decimal – a decimal in which a digit or digits do not repeat. • Non-terminating Decimal – a decimal that continues without end, such as 0.333333333…. • Mixed number – a number that is the sum of a whole number and a fraction. 2 ½. • Improper Fraction – a fraction whose numerator is greater than its denominator. • (LCD) Lowest Common Denominator – The lowest multiple shared by two or more denominators. The LCD of 1/8 and 1/6 is 24.

  7. Rational & Irrational Numbers Name:______________________ • _____________________ – a number resulting from a division. ½ = 0.5 • ____________________ – numbers in the sequence ….,-3,-2,-1,0,1,2,3 • _______________– the number of equal parts in a whole or a group. In ½ the denominator is the 2. • ______________ – the number of equal parts being considered in a whole or a group. In ½ the numerator is the 1. • _______________ – a decimal in which a digit or digits do not repeat. • _______________ – a decimal that continues without end, such as 0.333333333…. • _______________ – a number that is the sum of a whole number and a fraction. 2 ½. • _______________ – a fraction whose numerator is greater than its denominator. • _______________ – 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, Quotient, Integers, (LCD) Lowest Common Denominator, Non-repeating Decimal , Improper Fraction , Numerator

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