Converting Fractions to Decimals

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Converting Fractions to Decimals

• Lesson 5.2
• AMSTI 2006

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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?

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Problem of the Day

•  

• Complete the following within 1 minute.
• Compare 5/13 to 4/9
• Compare 0.384 to 0.4

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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.

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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.

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Video

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

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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)

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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

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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.

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Method 2 Convert by Dividing

• Example 1 to write 5/8 as a decimal, we need
  to calculate 5 8 0.625
• 8 v 5.000
• So 0.625 as a decimal.
• Try this example write 4/5 as a decimal using
  division (method 2).

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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.

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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

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If you still dont understand