Ch6 Notes (F09)

Ch6 Notes (F09) - Section 6-1 The Set of Rational Numbers...

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1 Section 6-1 – The Set of Rational Numbers The RATIONAL NUMBERS are numbers whose value can be expressed as the quotient or ratio of two integers a and b , represented as b a where b 0. A FRACTION is a number whose value can be expressed as the quotient or ratio of any two numbers a and b , represented as b a where b 0. a is called the ___________________ and b is called the ______________________. How Rational Numbers are Used: 1. As a division problem or a solution to a multiplication problem Example : Solve 3 x = 8 2. As a partition (or part) of a whole Example : 1 / 3 of the students were absent because they had the flu. 3. As a ratio Example : The ratio of girls to boys is 2 to 5. 4. As a probability Example : When you roll a die, the probability of rolling a 5 is 1 / 6 . To understand the meaning of a fraction b a , you must consider: 1. The whole 2. The number of b equal-sized parts into which the whole is divided 3. The number of a parts of the whole that we are selecting. Understanding the fraction concept: a) Divide each rectangle into 4 equal pieces
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2 b) Divide each shape below into 3 equal pieces Examples : 1. If represents 1, draw a rectangle that would represent 3 / 4 . 2. If the following rectangle represents 2, shade the area equivalent to ½ . 3. If represents 2 / 3 , draw a rectangle that would represent 1. 4. If the following circle has a value of 3 2 , shade the area equivalent to 1. 6. If the array of dots below has a value of 4 3 , then draw ½ .
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3 7. Locate 5 / 6 and –4 / 3 on the number line. -2 -1 0 1 2 Two fractions are equivalent fractions if they have the same value. “equi-valent = equal value” Example : Show that 2 / 3 and 4 / 6 are equivalent using an area model: Example : Show that 3 / 4 and 6 / 8 are equivalent using a number line: 0 1
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4 Example : Show that 2 / 6 and 1 / 3 are equivalent using the pattern blocks: Proper Fractions vs. Improper Fractions A fraction is called a proper fraction if the numerator is less than the denominator. A fraction is called an improper fraction if the numerator is greater than or equal to the denominator.
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Ch6 Notes (F09) - Section 6-1 The Set of Rational Numbers...

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