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LECTURE 4 IMA 101: Basic Math 6/17/2010 1 IMA101: Basic Mathematics.

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Presentation on theme: "LECTURE 4 IMA 101: Basic Math 6/17/2010 1 IMA101: Basic Mathematics."— Presentation transcript:

1 LECTURE 4 IMA 101: Basic Math 6/17/2010 1 IMA101: Basic Mathematics

2 Lecture Outline 6/17/2010 IMA101: Basic Mathematics 2 HW/Journal overview Wrapping up mixed numbers Decimals Square roots

3 Mixed Numbers: Addition 6/17/2010 IMA101: Basic Mathematics 3

4 Mixed Numbers: Subtraction 6/17/2010 IMA101: Basic Mathematics 4 Remember to distribute the subtraction sign to the whole part and the fraction of the subtracted mixed number

5 Complex Fractions 6/17/2010 IMA101: Basic Mathematics 5 Recall: A fraction is just a number (numerator) divided by another number (denominator) Simplify the following:

6 Order of Operations 6/17/2010 IMA101: Basic Mathematics 6

7 Decimals 6/17/2010 7 IMA101: Basic Mathematics

8 Introduction to Decimals Decimals as fractions  -1.5  8361.2759 Fractions as Decimals  5/10  3/4  1/5 6/17/2010 8 IMA101: Basic Mathematics

9 Understanding Decimals 6/17/2010 IMA101: Basic Mathematics 9 Place values Writing whole numbers as decimals  42 Comparing two decimals  1.992.99  1.9991.99  -0.58-0.57

10 Rounding decimals Similar to rounding whole numbers  >,=5  1  <5  0 3.14159265  Round to the nearest…  Tenth  Hundredth  Thousandth  Ten-thousandth  … 6/17/2010 10 IMA101: Basic Mathematics

11 Addition and Subtraction with Decimals Same as with whole numbers Line up the decimal points, and pull it down to the result Examples  382.5 – 227.1 =  2.56 – (-4.4) = 6/17/2010 11 IMA101: Basic Mathematics

12 Dividing to get a decimal 6/17/2010 IMA101: Basic Mathematics 12 5/8  use long division

13 Multiplication with decimals 6/17/2010 IMA101: Basic Mathematics 13 IGNORE the decimal point First multiply by the numbers, just like you would a whole number Then count the number of places (in BOTH numbers) Move the decimal of the result over that number of places Examples:  5.9 * 0.21.4 * 0.006

14 Multiplication with decimals 6/17/2010 IMA101: Basic Mathematics 14 Student Practice:  67.164 * 31  46.28 *.0098  6981 *.097

15 Decimals: Multiplication by 10 6/17/2010 IMA101: Basic Mathematics 15 Decimals represent fractions of 10, 100, 1000… So multiplying a decimal by 10 means we just divide the denominator of each fraction by 10 8361.2759 Notice: we just move the decimal point to the right by 1

16 Decimals: Multiplication by powers of 10 6/17/2010 IMA101: Basic Mathematics 16 Count the number of zeros and move the decimal point to the right that many spaces 3.14159265 * 10 = 3.14159265 * 100 = 3.14159265 * 1000 = 3.14159265 * 10000 =

17 Dividing a Decimal by a whole number 6/17/2010 IMA101: Basic Mathematics 17 Long division: move decimal point in the same spot 71.68/ 28

18 Dividing a Decimal by a Decimal 6/17/2010 IMA101: Basic Mathematics 18 Move decimal point over (for BOTH numbers) until you are dividing by a whole number. 0.2592/ 0.36

19 Dividing by a Decimals 6/17/2010 IMA101: Basic Mathematics 19 Student Practice: -5.714/ 2.40.02201/ 0.08 12.243 / 0.900.003164/0.04

20 Dividing a Decimal by 10 6/17/2010 IMA101: Basic Mathematics 20 Same idea as multiplication, except this time we move the decimal point to the _____. Example  9.0 / 10 =  4592.13 / 10 =

21 Fractions and Decimals: Revisited 6/17/2010 IMA101: Basic Mathematics 21 Writing fraction as the equivalent decimal Use long division with decimals 5/8

22 Repeating decimals 6/17/2010 IMA101: Basic Mathematics 22 Numbers that are never factors of a power of 10 (i.e. whose factors are not 2 or 5) do not form FINITE decimals Use a bar to indicate repeated digits Example: 1/3

23 Repeating Decimals 6/17/2010 IMA101: Basic Mathematics 23 Student examples 1/114/7 2/94/13 [Rounding repeating decimals]

24 Fractions and Decimals 6/17/2010 IMA101: Basic Mathematics 24 Decide if it’s easiest to work in terms of decimals or in terms of fractions Are the decimals easily divided by the denominator? (3/4) * 0.88 + (1/3) * 6.60

25 IMA101: Basic Mathematics 6/17/2010 25 Square roots

26 6/17/2010 IMA101: Basic Mathematics 26 Recall:  9 2 = 81 81 is a perfect square 9 is the Square ROOT of 81 √81 = 9 Recall:  -9 * -9 = 81 so -9 is also a square root of 81  We denote this as - √81 = -9  -9 * 9 = -81, but since -9≠ 9, -81 is NOT a square  We can NEVER take the square root of a negative number. Why?

27 Perfect Squares 6/17/2010 IMA101: Basic Mathematics 27 3 2 = 99 2 =81

28 Perfect squares: memorize these 6/17/2010 IMA101: Basic Mathematics 28 123456789101112 1123456789101112 224681012141618202224 3369121518212427303336 44812162024283236404448 551015202530354045505560 661218243036424854606672 771421283542495663707784 881624324048566472808896 9918273645546372819099108 10 2030405060708090100110120 11 2233445566778899110121132 12 24364860728496108120132144

29 Properties of Square Root 6/17/2010 IMA101: Basic Mathematics 29 Note that we cannot “distribute” the square root when we add or subtract two terms  √ 15 = √ (4+9) ≠ √4 + √9 = 2 + 3 = 5 However, when we multiply or divide the square root  6 = 2*3 = (√4) * (√ 9) =√ (4*9) = √ (36) = 6

30 How to find the square root of a number 6/17/2010 IMA101: Basic Mathematics 30 Using prime factorization √400 √2304 = √3136=

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