Transcript KU122 Unit 2 Seminar

KU122 Unit 2 Seminar
Fraction Notation
• KU122-20 Introduction to Math Skills and Strategies
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Seminars: Wednesdays at 8:00 PM ET
Instructor: Tammy Mata
Email: [email protected]
Office Hours: By appointment
AIM: tammymataku
• The seminar will begin at the top of the hour.
• Audio will be available when the seminar begins.
Discussion Responses
Incomplete Discussion Responses Do Not Enhance or Contribute
to the Topic.
Example 1: Thank you so much for explain it so well of how you got your
answers to that problem. I would have never though to explain it in that ways
was very good. Can you come over to my house and help me! Lol.
This example says two things, neither which enhance the topic: Good job and
thanks. Where is some information on math that pertains to this problem’s
topic? Also, make sure that all postings contain basic good writing. An
incomplete response is not funny so LOL might be inappropriate.
Example 2: That [answer] is correct. What is the word name to the following:
55,332,346,033?
This example remarks that the assignment posting is correct and then poses
another similar problems. However, the responder puts the burden of work,
which is doing the math, all on the classmate. Make sure that you do your own
work, put forth your own effort, even in the responses, because classmates
shouldn’t have to carry someone else’s responsibility.
Discussion Responses, con’t.
Example 3: Good job! I kept thinking on ways to do this problem differently and came up with
another way. This may not be the best but could work for visual people. I can actually draw out
the problem in a rectangle with 216 holes and 12 holes in each row. You way is much quicker
but I just wanted to show another solution.
Drawing out a rectangle with holes in rows might provide a good visual, but is it really using
math? It is actually providing a diagram (which is a step when solving application problems).
Consider this: the assignment posting to which this was a response has incorrect math
work—the division is wrong. Would it be better to indicate an error within the problem and fix
it? Of course! Make sure that you check the work performed in the posting before you say
“good job!” Saying “good job” to incorrect work shows that a hard look was not given to the
problem. Always check its math.
General Advice for Responses:
• Put forth the energy to provide a thorough response that is on the topic.
• Suggestions: Show an alternate method for doing the same problem. Identify an error in
the problem and show how to correct it. Work through a similar problem. Answer or ask a
valid and specific question about the problem that illustrates critical thinking (“Will this help
me?” is not a valid and specific question that relates to the math).
• Do the math work. Talk about and show math in the responses.
• Check the math work in the posting to which you are responding.
• READ the chapter/section in the textbook assigned for the posting so you will know what the
math is suppose to be—always read the chapter/section for the assigned problem to your
last name and to the last names to whom you are responding.
FRACTION NOTATION
• 5/7 = top number, numerator; bottom number denominator
• Fraction notations indicate equal parts of whole numbers
2.1 – What part is shaded? See page 103, examples 2 and 3.
2.1 – The number 1 in fraction notation is n/n. Examples: 12/12 = 1 or
36/36 = 1
2.1 – The number 0 in fraction notation is 0/n. Examples: 0/12 = 0 or
0/36 = 0
2.1 – Any whole number in fraction notation is n/1 = n. Examples: 12/1
= 12 or 36/1 = 36. If you see a whole number in a problem that uses
fraction notation, convert the whole number to a fraction by placing it
as the numerator and 1 as the denominator.
2.1 – Simplifying fraction notation. The smallest numerator and
denominator for which a fraction can be reduced: 5/10 is simplified
to ½. See pages 108 to 110.
Fraction Notation
2.2 – Multiplying and Simplifying. We multiply fractions straight across:
numerator are multiplied with numerators; denominators are multiplied with
denominators. See pages 114 to 115 for factoring to simplify before solving.
2.2 – Reciprocals. The reciprocal of a fraction is its inverse fraction: ¾ and
4/3. See page 115.
2.2 – Division. We divide fractions by changing the division to multiplication.
Multiply the dividend by the reciprocal of the divisor. See page 116—pay
close attention to blue box at bottom of page. See pages 117 to 118 for
examples.
2.3 – Adding and subtracting fractions. If denominators are the same, add or
subtract only the numerators; if denominators are different, the Least
Common Multiple (LCM from 1.9) for the denominators must be found. The
least common multiple for denominators is labeled the “Least Common
Denominator.” The dividend and/or the divisor must be revised to be
equivalents with the LCD. See pages 122 through 126.
Fraction Notation
2.4 – Mixed numerals. This is a whole number with a fraction, such as 2 3/8 or
12 1/3. When adding or subtracting with mixed numbers, the mixed
numbers may or may not need to be converted to fraction notation. See
examples on pages 133 to 134. When multiplying or dividing with mixed
numbers, the mixed number must be converted to fraction notation. See
pages 134 to 136. REMEMBER to convert the answers to a mixed
numeral, if appropriate.
2.5 – Applications and problem solving (fraction notation in word problems).
Five steps for problem solving:
1. Familiarize yourself with the problem.
a. Carefully read to understand what you are being asked to find.
b. Draw a diagram or identify a formula that applies to the situation.
c. Assignment a letter or variable to the unknown.
2. Translate the problem to an equation using a variable (such as x).
3. Solve the equation.
4. Check the answer.
5. State the answer to the problem using the appropriate words and units.
Fraction Notation
2.5 – The 12 examples in this section provide a wealth of information on how to
read application problems, translate them into equations, and then solve
them. Please review all of these problems carefully.
Pay close attention to Example 3 on page 142 because there is a similar
problem on this unit’s MML Quiz.
Fraction Notation
Quiz Tips
• Do NOT include the math work within the answer.
• Write only the answer in numbers within the provided box for each
item—measurements are already provided.
• Simplify all fractions.
• Use the slash symbol / to indicate the division between the numerator
and denominator (the quiz will then translate this automatically to
fraction notation).
• If the problem uses mixed numerals, remember to write the answer
as a mixed numeral, such as 2 3/4 .
• If the problem requests an answer as an “integer” or “fraction,” an
integer is the same as a whole number, such as 3 or 16 or 39.
Fraction Notation
Practice Problems for Seminar:
2.1, Page 103, See Example 2, Practice Margin 6 and 12
2.1, Page 107, See Example D, Practice Margin 33
2.1, Page 109, See Examples, Practice Margin 43 and 49
2.2, Page 115, See Examples, Practice Margin 1, 3, 5, and 7
2.2, Page 117, See Examples, Practice Margin 9 and 11
2.3, Page 122, See Examples 4 and 5, Practice Margin 6 and 7
2.3, Page 125, See Examples 12 and 13, Practice Margin 14
2.4, Page 132, See Example 10, Practice Margin 15
2.5, Page 142, See Example 3, Practice Margin 3