Converting Fractions to Decimals

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# Converting Fractions to Decimals - PowerPoint PPT Presentation

Converting Fractions to Decimals. Lesson 5.2 AMSTI 2006. 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?. Complete the following within 1 minute. Compare 5/13 to 4/9

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## Converting Fractions to Decimals

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### Converting Fractions to Decimals

Lesson 5.2

AMSTI 2006

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?
Complete the following within 1 minute.

Compare 5/13 to 4/9

Compare 0.384 to 0.4

Problem of the Day
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.
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 notallowed 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.
Video

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

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)
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

Example # 1 continued….
• Step 3: Write down 75 with the decimal place 2 spaces from the right (because 100 has 2 zeros);
• Can you explain what we just did?
• Try to express ¼ as a decimal using method # 1.
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).

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.
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”