Converting Fractions Converting Fractions to Decimalsto Decimals

Lesson 5.2Lesson 5.2

AMSTI 2006AMSTI 2006

DiscussionDiscussion

• Who can explain Who can explain what a fraction is?what a fraction is?

• Who can explain Who can explain what a decimal is?what a decimal is?

• Can you find a Can you find a decimal that is decimal that is equivalent to ¼?equivalent to ¼?

• What method did What method did you use to find you use to find this?this?

Problem of the DayProblem of the Day

  

Complete the following within 1 minute.Complete the following within 1 minute.

Compare 5/13 to 4/9Compare 5/13 to 4/9

Compare 0.384 to 0.4Compare 0.384 to 0.4

Egyptian FractionsEgyptian Fractions

The Egyptians of 3000 BC had an interesting way The Egyptians of 3000 BC had an interesting way to represent fractions.to represent fractions.Although they had a notation for 1/2 and 1/3 and Although they had a notation for 1/2 and 1/3 and 1/4 and so on (these are called 1/4 and so on (these are called reciprocalsreciprocals or or unit fractionsunit fractions since they are 1/n for some since they are 1/n for some number n), their notation did not allow them to number n), their notation did not allow them to write 2/5 or 3/4 or 4/7 as we would today. write 2/5 or 3/4 or 4/7 as we would today. Instead, they were able to write Instead, they were able to write anyany fraction as fraction as a a sum of unit fractionssum of unit fractions where where all the unit all the unit fractions were differentfractions were different. .

A fraction written as a sum of distinct unit A fraction written as a sum of distinct unit fractionsfractions is called an is called an Egyptian FractionEgyptian Fraction. .

Why use Egyptian Fractions Why use Egyptian Fractions Today?Today?

For two very good reasons: For two very good reasons: The first reason is a practical one. The first reason is a practical one.

Suppose you have 5 sacks of grain to share between 8 people, so Suppose you have 5 sacks of grain to share between 8 people, so each would receive 5/8 of a sack of grain in terms of present-day each would receive 5/8 of a sack of grain in terms of present-day fractions. How are you going to do it simply, without using a fractions. How are you going to do it simply, without using a calculator? You could try pouring the 5 sacks of grain into 8 heaps calculator? You could try pouring the 5 sacks of grain into 8 heaps and, by carefully comparing them, perhaps by weighing them and, by carefully comparing them, perhaps by weighing them against each other, balance them so they are all the same! But is against each other, balance them so they are all the same! But is there a better way? We will see that there a better way? We will see that using unit fractionsusing unit fractions makes makes this easier. this easier.

The second reason is that it is much easier to The second reason is that it is much easier to compare fractionscompare fractions using Egyptian fractions than it is by using our present-day using Egyptian fractions than it is by using our present-day notation for fractions! For instance: Which is bigger: 5/8 or 4/7? notation for fractions! For instance: Which is bigger: 5/8 or 4/7?

but remember - you are but remember - you are notnot allowed to use your calculator to allowed to use your calculator to answer this! Again unit fractions can make this much simpler. answer this! Again unit fractions can make this much simpler.

On this page we see how both of these work in Egyptian fractions. On this page we see how both of these work in Egyptian fractions.

VideoVideo

Lets watch a video to preview Lets watch a video to preview how to convert fractions to how to convert fractions to decimals, the Egyptian way!decimals, the Egyptian way!

Converting Fractions to Converting Fractions to DecimalsDecimals

To convert a Fraction to a Decimal manually, To convert a Fraction to a Decimal manually, follow these steps:follow these steps:

Step 1: Find a number you can multiply by Step 1: Find a number you can multiply by the the bottom of the fractionbottom of the fraction to make it 10, or 100, or to make it 10, or 100, or 1000, or any 1 followed by 0s.1000, or any 1 followed by 0s.

Step 2: Multiply both top and bottom by that number.Step 2: Multiply both top and bottom by that number.

Step 3. Then write down just the top number, Step 3. Then write down just the top number, putting the decimal place in the correct spot (one putting the decimal place in the correct spot (one space from the right for every zero in the bottom space from the right for every zero in the bottom number) number)

Method #1: Converting Method #1: Converting with Proportionswith Proportions

Example # 1:Example # 1: Express 3/4 as a Express 3/4 as a DecimalDecimal

Step 1: We can multiply 4 by Step 1: We can multiply 4 by 2525 to to become 100become 100

Step 2: Multiply top and bottom by 25Step 2: Multiply top and bottom by 25

3 = 753 = 75 4 1004 100

Example # 1 continued….Example # 1 continued….

Step 3: Write down 75 with the Step 3: Write down 75 with the decimal place 2 spaces from the right decimal place 2 spaces from the right (because 100 has 2 zeros);(because 100 has 2 zeros);

Answer = 0.75Answer = 0.75

Can you explain what we just did?Can you explain what we just did? Try to express ¼ as a decimal Try to express ¼ as a decimal

using method # 1.using method # 1.

Method #2: Convert by Method #2: Convert by DividingDividing

Example #1:Example #1: to write 5/8 as a to write 5/8 as a decimal, we need to calculate 5 ÷ 8:decimal, we need to calculate 5 ÷ 8: 0.625 0.625

8 √ 5.000 8 √ 5.000

So = 0.625 as a decimal. So = 0.625 as a decimal.

Try this example: write 4/5 as a Try this example: write 4/5 as a decimal using division (method #2).decimal using division (method #2).

Skittles Activity

1.Sort your skittles into groups by color.

2.Find the fraction of each color.

3.Convert your fractions into a decimals.

4.Record your data on chart paper.

5.Compare and discuss with the class.

                                                                                                                                                                                                                                                                                                                          

Lets Practice!!Lets Practice!!

We are going to use this website to We are going to use this website to fish out some fractions and decimals. fish out some fractions and decimals.

Lets see how well you understand Lets see how well you understand this lesson.this lesson.

Go to Go to www.iknowthat.comwww.iknowthat.com Select “Math” in the left marginSelect “Math” in the left margin Select “Fishy Fractions” Select “Fishy Fractions” Select “Fractions and Decimal Select “Fractions and Decimal

Match”Match”

If you still don’t If you still don’t understand…understand…