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Welcome to Math 6 Todays subject is Decimals and Fractions Mr. Whalen

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Lets start todays lesson with a question: Can you see the number in this picture?

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People with normal color vision can see the number 27 in the picture. Most people with color deficiency (often called color blindness) have trouble distinguishing shades of red and green. About 0.05 of men in the world have color deficiency. What fraction of men have color deficiency?

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Tough question? Dont worry! You will answer by the end of this lesson.

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First a Quick Review

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A fraction usually represents a number which is less than one but greater than zero. Any number between two whole numbers can be represented by a mixed number. For example: 1 . A mixed number is what we call an amount that is part whole number and part fraction. + =1 Quick review

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Quick review: a)Integers are whole numbers and their opposites. The opposite of 1 is -1. The opposite of 25 is -25. The opposite of -3 is 3.

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Integers are not decimals. They have no digits to the right of the decimal point. In the number 628, 8 stands for 8 ones 2 stands for 2 tens 6 stands for 6 hundreds So 628 represents the sum of 6 hundreds, 2 tens, and 8 ones, or 600 + 20 + 8. Quick review

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Base 10 is what we call our number system. In the Base 10 number system, all numbers are expressed using the digits 0-9. Quick review

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In base 10: The first number to the left of the decimal point represents the number of 1's. The second number represents the number of 10's. The third number represents the number of 100's. The fourth number represents the number of 1000's, and so on. We refer to this pattern as place value.

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Here are the place values: As we move to the right, divide by 10. As we move to the left, multiply by 10. We need to understand this to work with decimals.

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This is such an important concept, I want to explain it again very carefully. As we move to the right, divide by 10. As we move to the left, multiply by 10. 55 The value of this 5 is ten times greater than the value of this 5.

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___, ___ ___ ___. ___ ___ ___ Ones Thousands Hundreds Tens

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Decimals To find the value of a decimal place, we divide the value of the decimal place to the left of it by 10. The sequence of numbers 1000, 100, 10, 1, continues to the left of the decimal point: 0.1 = 1/10 0.01 = 1/100 0.001 = 1/1000 Quick review

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___, ___ ___ _3_. _3_ ___ ___ OnesThousandsHundredsTensTenthsHundredthsThousandth s Divide the 3 in the Ones place by 10, and you have the value of the 3 in the Tenths place. This pattern continues.

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Fraction- A number in the form a/b where b 0. (Fractions represent division.) Mixed Number- A number that contains both a whole number and a fraction, such as 1 . Key Vocabulary for this lesson

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A Terminating decimal, such as 0.75 has a finite number of decimal places. A Repeating decimal, such as 0.666 has a block of one ore more digits that repeat continuously. Key Vocabulary for this lesson

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Base-10 system Is what we call our number system in which all numbers are expressed using the digits 0-9. Place value refers to the value of a digit depending on its place in a number. Examples: In 675 the value of 7 is 70. In 723 the value of 7 is 700.

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Integer- The set of whole numbers and their opposites Key Vocabulary for this lesson

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Common Fractions and Equivalent Decimals 1/5 1/32/5 3/52/3 4/5 0.2 0.25 0.30.40.50.6 0.75 0.8 A solid line above the digit (or digits) indicates that the digit (or digits) repeat (s) forever.

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You must be able to read any decimal. When you read a decimal, you say the number, then identify its value by its smallest place (farthest to the right). Examples: 0.23 is read as 23 hundredths. (the 3 is in the hundredths place) 0.346 is read as 346 thousandths (the 6 is in the thousandths place)

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To write the decimal as a fraction The place name- 10 th s, 100 th s, 1000 th s will be the denominator. In math level 6, we will be dealing with decimals in the tenths, hundredths and thousandths place. Examples: 0.76 is written as 0.165 is written as

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ALWAYS! Write all fractions in simplest form. Divide the numerator and denominator by their Greatest Common Factor (GCF). I told you GCF would come in handy!

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When you divide the numerator by the denominator, you will usually end up with either a terminating decimal or a repeating decimal.

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Guided Practice: Write the decimal as a fraction or a mixed number: 1. 2.6 2. 0.35 3. 0.80 4. 3.96

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Guided Practice Answers: Write the decimal as a fraction or a mixed number: 1. 2.6= 2 3/5 2. 0.35 = 7/20 3. 0.80 = 4/5 4. 3.96 = 3 24/25

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To convert a fraction to a decimal, divide the numerator by the denominator. See examples: 34= 0.75 25= 0.4 These two are examples of terminating decimals.

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Convert the fraction to a decimal. Divide the numerator by the denominator. (A fraction represents division.)

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In repeating decimals, one or more digits will repeat infinitely. When you recognize it, draw a line over only the repeating digits. Writing Fractions as Decimals

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Guided Practice: Write the decimal as a fraction or a mixed number: 5. 0.15 6. 1.25 7. 0.43 8. 2.6

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Guided Practice Answers: Write the decimal as a fraction or a mixed number: 5. 0.1515/100= 3/20 6. 1.251 1/4 7. 0.4343/100 8. 2.62 6/10=2 3/5

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Order the fractions and decimals from least to greatest: 0.5,, 0.37 Instructions: Step 1: Rewrite all fractions as decimals. = 0.2, Then it is easy! 0.2, 0.37, 0.5

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Guided Practice: Order the fractions and decimals from least to greatest. 9. 2/3, 0.42, 0.78 10. 5/16, 0.67, 1/6 11. 0.52, 1/9, 0.3

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Order the fractions and decimals from least to greatest. 9. 2/3, 0.42, 0.78 0.42, 0.6, 0.78 10. 5/16, 0.67, 1/6 0.16, 0.3125, 0.67 9. 0.52, 1/9, 0.3 0.1, 0.3, 0.52 2/3 = 0.6 Guided Practice Answers: 5/16 = 0.3125 1/6=0.16 1/9=0.1

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Independent Practice: Write each decimal as a fraction or a mixed number. 1. 0.31 2. 5.71 3. 0.13 4. 3.23 5. 0.5 6. 2.4 7. 0.19 8. 6.5 9. 2.08 10. 2.019

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Independent Practice: Write each fraction or mixed number as a decimal. 11. 1/9 12. 1 3/5 13. 8/9 14. 3 11/40 15. 2 5/6 16. 3/8 17. 7/8 18. 4 4/5 19. 5/8 20. 6 1/8

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Independent Practice: Order from least to greatest. 21. 0.49, 0.82, 22. 0.11,, 0.13 23. 0.125, 0.29, 24., 0.42, 25. 0.94,, 0.6 26., 0.76, 0.31 27. 0.09, 0.1, 28., 0.4, 0.004 29. 0.018,, 3/10 30. 0.45, 0.050,

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Independent Practice Answers Write each or a mixed number. 1. 0.31 = 2. 5.71 = 3. 0.13 = 4. 3.23 = 5. 0.5 = 6. 2.4 = 7. 0.19 = 8. 6.5 = 9. 2.08 = 10. 2.019 =

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Independent Practice Answers: Write each fraction or mixed number as a decimal. 11. 1/9= 0.1 12. 1 3/5= 1.6 13. 8/9= 0.8 14. 3 11/40= 3.275 15. 2 5/6= 2.83 16. 3/8= 0.375 17. 7/8= 0.875 18. 4 4/5= 4.8 19. 5/8= 0.625 20. 6 1/8= 6.125

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Independent Practice Answers Order from least to greatest. 21. 0.49, 0.82, 22. 0.11,, 0.13 23. 0.125, 0.29, 24., 0.42, 25. 0.94,, 0.6 0.49, 0.5, 0.82 0.11, 0.13, 0.3 0.1, 0.125, 0.29 0.4, 0.42, 0.6 0.6, 0.8, 0.94

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Independent Practice Answers Order from least to greatest. 26., 0.76, 0.31 27. 0.09, 0.1, 28., 0.4, 0.004 29. 0.018,, 3/10 30. 0.45, 0.05, 0.31, 0.375, 0.76 0.02, 0.09, 0.1 0.004, 0.045, 0.4 0.018, 0.17, 0.3 0.05, 0.45, 0.84

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Conclusion: The key to success is achieving mastery over the numbers and the basic operations. Fractions and decimals are two ways to represent amounts less than one whole but greater than zero. Practice converting from one form to another. And comparing and ordering them.

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Assignments- 1.Whats the error? Write a COMPLETE explanation. A student found the decimal equivalent of to be 0.38. Explain the error. What is the correct answer?

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Assignments- 2.Write 5/6 and 5/9 as decimals. Show your work. Explain how you know whether a decimal repeats. Write a COMPLETE explanation.

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Assignments- 3.Complete the supplementary practice exercise, entitled: Skillswise: Comparing Fractions and Decimals

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Most people with color deficiency (color blindness) have trouble distinguishing shades of red and green. About 0.05 of men in the world have color deficiency. What fraction of men have color deficiency? EASY! 0.05 is five hundredths or That is in simplest form.

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Thats all for now! Be sure to complete all of the assignments. See you next time.