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# CoNverTinG FraCtioNs tO DeCiMaLs

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### Transcript

• 1. Converting Fractions to Decimals Lesson 5.2 AMSTI 2006
• 2. Discussion• Who can explain what a fraction is?• Who can explain what a decimal is?• Can you find a decimal that is equivalent to ¼?• What method did you use to find this?
• 3. Problem of the DayComplete the following within 1 minute. Compare 5/13 to 4/9 Compare 0.384 to 0.4
• 4. Egyptian Fractions The Egyptians of 3000 BC had an interesting way to represent fractions. Although they had a notation for 1/2 and 1/3 and 1/4 and so on (these are called reciprocals or unit fractions since they are 1/n for some number n), their notation did not allow them to write 2/5 or 3/4 or 4/7 as we would today. Instead, they were able to write any fraction as a sum of unit fractions where all the unit fractions were different. A fraction written as a sum of distinct unit fractions is called an Egyptian Fraction.
• 5. Why use Egyptian Fractions Today? For two very good reasons: The first reason is a practical one. 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 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 and, by carefully comparing them, perhaps by weighing them against each other, balance them so they are all the same! But is there a better way? We will see that using unit fractions makes this easier. The second reason is that it is much easier to compare fractions using Egyptian fractions than it is by using our present-day notation for fractions! For instance: Which is bigger: 5/8 or 4/7? but remember - you are not allowed to use your calculator to answer this! Again unit fractions can make this much simpler. On this page we see how both of these work in Egyptian fractions.
• 6. VideoLets watch a video to preview how to convert fractions to decimals, the Egyptian way!
• 7. Converting Fractions to Decimals To convert a Fraction to a Decimal manually, follow these steps: Step 1: Find a number you can multiply by the bottom of the fraction to make it 10, or 100, or 1000, or any 1 followed by 0s. Step 2: Multiply both top and bottom by that number. Step 3. Then write down just the top number, putting the decimal place in the correct spot (one space from the right for every zero in the bottom number)
• 8. Method #1: Converting with Proportions Example # 1: Express 3/4 as a Decimal Step 1: We can multiply 4 by 25 to become 100 Step 2: Multiply top and bottom by 25 3 = 75 4 100
• 9. Example # 1 continued…. Step 3: Write down 75 with the decimal place 2 spaces from the right (because 100 has 2 zeros); Answer = 0.75 Can you explain what we just did? Try to express ¼ as a decimal using method # 1.
• 10. Method #2: Convert by Dividing Example #1: to write 5/8 as a decimal, we need to calculate 5 ÷ 8: 0.625 8 √ 5.000 So = 0.625 as a decimal. Try this example: write 4/5 as a decimal using division (method #2).
• 11. Skittles Activity• Sort your skittles into groups by color. • Find the fraction of each color.• Convert your fractions into a decimals. • Record your data on chart paper. • Compare and discuss with the class.
• 12. Lets Practice!! We are going to use this website to fish out some fractions and decimals. Lets see how well you understand this lesson. Go to www.iknowthat.com Select “Math” in the left margin Select “Fishy Fractions” Select “Fractions and Decimal Match”
• 13. If you still don’t understand…