Unit: Rational Number Lesson 3.1: What is a Rational Number? Objectives: Students will compare and order rational numbers.

Transcription

1 Unit: Rational Number Lesson 3.: What is a Rational Number? Objectives: Students will compare and order rational numbers. (9N3) Procedure: This unit will introduce the concept of rational numbers. This is not really a new thing, as it is a defining of a number class so for future learning. Lets review number classes quickly: Natural Numbers Whole Numbers Integers Rational Numbers are numbers which Fractions as Rational Numbers Look at the following Fractions, which ones are equal?,,, It may help to change each on into its decimal form. = = = = = = = =

2 List the fractions which are equal: How can they be the same? If you think of multiplying by, when is in the form of, it makes sense. = = You can use the same way to convert to. How is and the rest of them different? and are called. In decimal form they are called. So 0.25 and 0.25 are called List 3 opposite pairs of fractions: List 3 opposite pairs of decimals: 2

3 Mixed numbers as Rational Numbers. Are mixed numbers Rational numbers? What was the definition of a rational number that related to fractions? Rational Numbers are So any number that is a mixed number can be written as a, for example: 3 2 = = Are all mixed fractions rational numbers? Why? Lets look at mixed decimals What is.2 in fraction form?.2 = = = = Is this a rational number? Do you think all mixed decimals can be written as fractions? 3

4 Which of the following are rational numbers? 5, ,,, 7, Number Lines: Number lines are an excellent way to show rational numbers, on both sides of the zero. On the number line below place the following numbers..,.,.3, 0., 0.5, Why is. less than 0.5? A classmate tells you that. is greater than 0. because. is larger than 0., how would you correct your classmate s thinking?

5 Name three rational numbers between: a) 0 and b) 0 and 0.5 c). and.3 d) - and. Lets try the same exercise with fractions. Place the following fractions on the number line below: ,,,,,,

6 Name three rational numbers in fraction form between: a) 3 3 and b) 3 and 2 c) 2 and 2 d) 3 and 2 Ordering Rational Numbers in Decimal or Fraction Form Decimals: Place the following in order: 0.25, 0.2, 0.25,.7,.6 It may be easier to use equivalent decimals to write them all in thousandths. Now place them in order. 6

7 Try these. 0.69, 2.3, 2.2, 2.27, 2.33 Again make them all have the same amount of decimals. Now order them: Now lets try some fractions: In grade 7 we did this by converting all the fractions to decimals and then ordering the decimals, then using the decimals to rewrite the original fractions down. For example: Order the following fractions in order from least to greatest ,,,,, First change the fractions into decimal form: Now place these in order: You may need to rewrite with same number of decimals places. Now rewrite them in their fraction forms: 7

8 Example: Order the following fractions from least to greatest. Another way of doing this is to convert all the fractions to having the same denominator; this is a lot of work ,,,,, The lowest common denominator is 2, so convert each fraction to having a denominator of 2: Now they can be ordered using their equivalent fractions. Now change them back into their original fractions. 8

9 The last part is to order fractions and decimals when they are together. Here is an example from the textbook. Order the following and place them on a number line ,, 3., 2.7,, First convert the fractions to decimal form. Now place them in order. Since it is easier to find locations of decimals on a number line, find the locations first, then place the original number down

10 Example: What rational number does the letter on the number line below represent? A B C -3-2 A - B C - How did you decide what the decimal portion of the number was going to be? Example: What rational number does the letter on the number line below represent? B C A A - B - C - How did you decide what the decimal portion of the number was going to be? 0

11 Example: What rational number does the letter on the number line below represent? C B A -2-0 A - B - C - How did you decide what the fractions portion of the number was going to be? Complete the following Page 00-03#-3, # without number line, #5-2, #23,2,25 order them showing how you did it; do not draw the number line.