unit 1b: rational numbers mathematics 9 miss wilkinson october 2, 2013
TRANSCRIPT
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Unit 1B: Rational Numbers
Mathematics 9Miss Wilkinson
October 2, 2013
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IntroductionRational Numbers are numbers that can be expressed in the form where a & b are integers and b ≠ 0.
Rational numbers are parts of a whole, expressed as a fraction (1/4), decimal (0.25), or percent (25%).
Examples:
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Fun Fact: Who Was Correct?
• The ancient greek mathematician Pythagoras believed that all numbers were rational (could be written as a fraction).
• One of his students Hippasus proved (using geometry, it is thought) that you could not represent the square root of 2 as a fraction, and so it was irrational.
• The discovery of irrational numbers is said to have been shocking to the Pythagoreans, and Hippasus is supposed to have drowned at sea, apparently as a punishment from the gods.
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Part 1: Comparing and Ordering Rational
NumbersOBJECTIVES
• In part 1, we will learn to reduce, compare and order rational numbers,
• Be able to express rational numbers in fractional form with a common denominator or decimal form.
• Learn to compare rational numbers using a number line and identify rational numbers between two given rational numbers.
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Reducing Fractions• We reduce a fraction to lowest terms by finding
an equivalent fraction in which the numerator and denominator are as small as possible.
• To reduce fractions, find the greatest common factor for the numerator and denominator.
Examples:1. 2. 3.
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Compare & Order Fractions
• We can compare rational numbers by expressing them all as fractions with a common denominator or by expressing them as decimals.
A) To compare fractions, express each pair of fractions with the common denominator. • To find a common denominator, determine the
lowest common multiple (LCM) of the given denominators.
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Ex: Which is greater → or ?
• Step 1: The LCM of 6 and 9 is 18.
• Step 2: We know that 6 divides into 18 three times so we will multiply the numerator of the first term by three, and 9 divides into 18 two times, so we will multiply the numerator of the second term by two.
• Step 2: Re-write and as: and
• Step 3: Compare the numerators.
therefore, < <
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PracticeCompare the fractions by circling the correct symbol. Remember: The fractions must have the same denominator to be able to compare!
1. 2. 3.
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B) We can also compare fractions by converting them to decimals.• To convert fractions to decimals, divide the
denominator by the numerator.• Note: A fraction is essentially a division
operation.
Example: means 3 ÷ 4 = 0.75
1. = 2. =
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C) We can compare decimals by converting decimals to fractions. To do this, write the number as you would read it.Example: 0.05 is read as 5 hundredths. Therefore, put 5 over 100 and reduce to lowest term.
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Practice Convert the following decimals into fractions. Remember to reduce to lowest terms!
1. 0.3 = 2. - 0.48= 3. 0.024 =
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Rational Numbers on a Number Line
OBJECTIVE• FOCUS: learn to compare rational
numbers using a number line and identify rational numbers between two given rational numbers.
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Example 1
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Example 2
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Checkpoint 1
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