Mathematics Grade 7 File Name: Unit 3.2 Lesson Unit 3.2: Fractions ...

Mathematics Grade 7

File Name: Unit 3.2 Lesson

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, 2 1 , is 3

called a mixed fraction because it has a _____________________ and a __________________________.

Other examples are:

Improper Fractions:

A basic fraction in its simplest form looks like 4 . 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 _____________.

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Mathematics Grade 7

Label the following fractions as basic, mixed, or improper: 6 - ________________________ 7 5 - ________________________ 6 1 3 - _______________________ 4

File Name: Unit 3.2 Lesson

So lets look at all at these at once:

Look at the following fractions and decimals.

Mixed Fraction 11 4

Improper Fraction 5

4

For each fraction, convert it into a decimal.

1 1 = 1 and 1

4

4

5 = 5 ? 4 = 1.25 4

1 = 1? 4 = 0.25 4 so this is 1.25

Decimal 1.25

1.25

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.

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Mathematics Grade 7

Mixed to Improper Fraction Conversion: Convert 1 1 to improper form.

4 Lets look at 1 1 again, only this time lets draw it in boxes.

4

File Name: Unit 3.2 Lesson

How many quarters ( 1 's), does this give you? 4

4

1

4 `quarters' + 1 `quarter' is equal to 5 `quarters' or 5 . 4

So 1 1 as an improper fraction is 5 .

4

4

Example Two: Convert 2 1 into improper form.

3 Diagram:

___

___

___

=

3

3

How many thirds does this give you?

So 2 1 in improper form is __. 3

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Mathematics Grade 7

File Name: Unit 3.2 Lesson

What about big numbers?

If we convert 5 4 we can draw 5 diagrams, but what if the fraction was huge like 7

2344 3 ?????? This is too many to draw. 4

Lets look at example 2 closely. The fraction was 2 1 , how many full boxes of 3 did we 3

draw? (2), how many thirds did that give us?

(3)

(3)

(1)

____________ 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 4 to improper form.

7

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:

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Mathematics Grade 7

Example: 64 =

5 Example: 76 =

11

File Name: Unit 3.2 Lesson

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 4

Draw a diagram of quarters in such a way that you have 5 quarters:

(4)

(1)

4 quarters makes a whole box or 1

4 =1

1

4

4

Together they make 1 1 . 4

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