Unit 3.2: Fractions, Decimals and Percent Lesson: Comparing and Ordering Fractions and Decimals

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Charles Fisher
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1 Unit 3.2: Fractions, Decimals and Percent Lesson: Comparing and Ordering Fractions and Decimals Objectives: Students will use benchmarks, place value and equivalent fractions to compare and order fractions and decimals. A number line will be used to verify the order of fractions and decimals. Procedure: At the end of this lesson you should be able to place decimals and fractions in order. We need to discuss the difference in how fractions are presented. Before we begin, lets look at what an improper fraction and a mixed fraction are: Mixed Fractions: This is the combination of a whole number and a fraction. For example, called a mixed fraction because it has a and a. 2 3, is Other examples are: Improper Fractions: A basic fraction in its simplest form looks like. Note that the is 7 less than the. An improper fraction has a, which is larger than the. For example: 8 is called an improper 3 fraction, because the is larger than the.

2 Label the following fractions as basic, mixed, or improper: So lets look at all at these at once: Look at the following fractions and decimals. Mixed Fraction Improper Fraction Decimal 5.25 For each fraction, convert it into a decimal. = and = = = = so this is.25 What do you notice about each of these numbers? In each case. Because they are, we will have to be able to convert between each form. 2

3 Mixed to Improper Fraction Conversion: Convert to improper form. Lets look at again, only this time lets draw it in boxes. How many quarters ( s), does this give you? quarters + quarter is equal to 5 quarters or 5. So as an improper fraction is 5. Example Two: Convert 2 3 into improper form. Diagram: How many thirds does this give you? = 3 3 So 2 3 in improper form is. 3

4 What about big numbers? If we convert 5 7 we can draw 5 diagrams, but what if the fraction was huge like 3 23?????? This is too many to draw. Lets look at example 2 closely. The fraction was draw? (2), how many thirds did that give us? 2 3, how many full boxes of 3 did we (3) (3) () gives us thirds or. Lets try one more example to see if this short cut will allow us not to draw the boxes. Convert 3 7 to improper form. How many 7ths are there in total? ( ) ( ) ( ) ( ) sevenths or. This works, so the process to use to convert quickly without drawing boxes is: In your own words describe how to convert a mixed fraction to a improper fraction:

5 6 5 = 6 7 = Converting Improper Fractions to Mixed form Now that we know how to go from mixed to improper, we need to reverse this process and go from improper to mixed form. Lets look at our first example: 5 Draw a diagram of quarters in such a way that you have 5 quarters: () () quarters makes a whole box or = Together they make. 5

6 Answer this question: How many times does go into 5, and what is left over. goes into one time, with left over. 5 note the division of 5 = and remainder, or also. goes into 5 one time there is left over we are working in fourths Convert 7 3 into a mixed fraction. Draw boxes of thirds, and shade them until you have a total of 7 shaded thirds. ( ) ( ) ( ) Answer this question how many times does 3 go into 7? What is left over? there is left over 3 goes into 7 times we are working in If you have to divide it out, do so to find the remainder. 6

7 Lets do some without drawing the boxes. Convert 7 into a mixed fraction = with remainder Convert into mixed form. How many times does go into, and what is left over? (Divide if you have to) Ok, now lets move onto the next part of ordering the fractions. 7

8 Ordering Fractions Place the following in order from least to greatest. 2 3, 0.7, 3, 3 To complete this question, it is easiest to change all the fractions into decimal form, so that you can compare all the numbers in one form. 2 3, 0.7, 3, 3 Placing in order you get: Answer: Place the following numbers in order from greatest to least. 0.7, 7, 0.77, 7, 0.57, 8 Convert each to decimal first. 0.7, 7, 0.77, 7, 0.57, 8 Now order: Answer: 8

9 Using Benchmarks to Order Fractions: Sometimes we can look at a fraction and compare it to a known amount called a benchmark to place it in order. For example: Place the following on the number line using the bench marks 0, 2 and : 3 9,, To place 3 20 Think, =, and 3 20 on the number line compare it to 0, 0.5 and. Which number is it closest to? is close to, so place it there. Now look at 20, = and 20 is just above, so place it there. 20 Finally look at This is close to =. So place just before. 9

$(from text) Have students order the given fractions onto a number line$

10 (from text) Have students order the given fractions onto a number line using benchmarks. Complete page 9#3,,5,6,7,8,9,0,abd Homework book pages

Section 3.1 Fractions to Decimals

Section 3.1 Fractions to Decimals A fraction is a part of a whole. For example, it means 1 out of 5 possible pieces. is a fraction; Fractions also illustrate division. For example, also means 1 5 which